# Multicriteria interpretability driven Deep Learning

Marco Repetto<EMAIL_ADDRESS>Siemens Italy, Digital Indutries,
Milan, Italy  University of Milano-Bicocca, Department of Economics,
Management and Statistics, Milan, Italy

###### Abstract

Deep Learning methods are renowned for their performances, yet their lack of
interpretability prevents them from high-stakes contexts. Recent model
agnostic methods address this problem by providing post-hoc interpretability
methods by reverse-engineering the model’s inner workings. However, in many
regulated fields, interpretability should be kept in mind from the start,
which means that post-hoc methods are valid only as a sanity check after model
training. Interpretability from the start, in an abstract setting, means
posing a set of soft constraints on the model’s behavior by injecting
knowledge and annihilating possible biases. We propose a Multicriteria
technique that allows to control the feature effects on the model’s outcome by
injecting knowledge in the objective function. We then extend the technique by
including a non-linear knowledge function to account for more complex effects
and local lack of knowledge. The result is a Deep Learning model that embodies
interpretability from the start and aligns with the recent regulations. A
practical empirical example based on credit risk, suggests that our approach
creates performant yet robust models capable of overcoming biases derived from
data scarcity.

###### keywords:

Artificial Intelligence , Machine Learning , Deep Learning , Multiple
Objective Programming , Multicriteria optimization

##  1 Introduction

Deep Learning (DL) models are used extensively nowadays in many fields ranging
from self-driving cars (Rao and Frtunikj,, 2018) to brain-computer interfaces
(Zhang et al.,, 2019) to gaming (Vinyals et al.,, 2019). Recent software and
hardware democratized DL methods allowing scholars and practitioners to apply
them in their fields. On the software side, recent frameworks as Tensorflow
(Abadi et al.,, 2015) and PyTorch (Paszke et al.,, 2019) allowed to create
complex DL models avoiding the need to write ad-hoc compilers as did by LeCun
et al., (1990). On the hardware side, the decrease in the cost of the
necessary hardware to train such models, allowed many people to build and
deploy sophisticated Neural Networks with minimal costs (Zhang et al.,, 2018).
The democratization of such powerful technologies allowed many fields to
benefit from it aside from computer science. Some of those that benefitted the
most are Economics (Nosratabadi et al.,, 2020), and Finance (Ozbayoglu et
al.,, 2020). DL applications have piqued the interest of governments, who are
concerned about possible social implications. It is well known that these
models necessitate extra vigilance when it comes to training data in order to
minimize biases of any kind, especially in high-stakes judgments (Rudin,,
2019). To counter these side effects, the governments enacted several
regulatory standards, and the jurisprudence started to elaborate on the right
to explanation concept (Dexe et al.,, 2020). In this effort to build
interpretable but DL grounded models, scholars have started developing post-
hoc interpretation methods. These approaches, however, are at odds with what
is prescribed by recent guidelines, requiring interpretability from the start
(European Commission,, 2019). Another issue is that such approaches focus only
on the interpretation after a model’s training and cannot be used to insert
prior information or remove biases.

This work focuses on ensuring the interpretability of DL models from the
beginning through knowledge injection and investigating their potential in
empirical settings as in credit risk prediction. In this regard, we make three
contributions to the literature. First, we allow the Decision Maker (DM) to
inject previous knowledge and alleviate dataset biases in the model training
process by controlling the features’ effect. Physics-guided Neural Networks
(PGNN) are based on similar methodologies that are widely employed in physics-
related applications (Daw et al.,, 2021). Knowledge injection, whether physics
related or not, generally involves some sort of constraints in terms of
features relationship with the outcome that can be implemented as posed by von
Rueden et al., (2021) in four different ways: (i) on the training data; (ii)
on the hypothesis set; (iii) on the learning algorithm; (iv) on the final
hypothesis. Our methodology infuses knowledge on the learning algorithm level
as this procedure relates to some post-hoc interpretability methods. According
to our understanding, these architectures were never proposed outside of the
physics and engineering fields. And even in such areas, effects constraints
were conditional on the context as in Muralidhar et al., (2018) or applied to
non-DL techniques (Kotłowski and Słowiński,, 2009; Lauer and Bloch,, 2008; von
Kurnatowski et al.,, 2021). Our approach applies to any DL architecture and is
not conditional on features’ context. We test the validity of our technique in
credit risk as the concept of Sustainable AI will considerably impact this
field. The recent frameworks, as the one proposed by Bücker et al., (2021) do
not allow for interpretability from the start as posed by European Commission,
(2019). These techniques can spot biases but cannot counter them, as their
scope is only explainability and not knowledge injection. Our methodology can
handle both these aspects by leaving a model that is compliant with the new
guidelines on Sustainable AI. Second, we allow for non-linear effects and
local lack of knowledge by defining ad-hoc knowledge functions on models
parameters. This additional specification is necessary for two reasons. To
begin, the empirical literature in credit risk agrees that the performances of
DL models are due primarily to the fact that they capture non-linear patterns
(Ciampi and Gordini,, 2013). The second reason for including this non-linear
pattern is that knowledge may be lacking in some regions of the feature space.
Third, we explore the relationship between post-hoc interpretability methods
that are model agnostic, as for the case of Accumulated Local Effects (Apley
and Zhu,, 2020). These methods play two critical roles in our strategy.
Initially, they provide the DM with graphical visualizations that allow him to
communicate with non-experts. Second, they serve as sanity checks for our
methodology and hyperparameter optimization based on explainability.

The rest of this paper is structured as follows. The knowledge injection in
the model and the multicriteria problem development are all covered in Section
2. The data sample utilized to test our technique, software packages, and
hardware is briefly discussed in Section 3. Section 4 summarizes the findings
and examines the most important ones. Section 5 comes to a close.

##  2 Methodology

###  2.1 Deep Learning

DL is an AI subfield and type of Machine Learning technique aimed at
developing systems that can operate in complex environments (Goodfellow et
al.,, 2016). Deep architectures underpin DL systems (Bottou et al.,, 2007)
which can be defined as:

$\mathcal{F}=\\{f(\cdot,w),w\in\mathcal{W}\\}$ (1)

where $f(\cdot,w)$ is a shallow architecture as for example the Perceptron
proposed by Rosenblatt, (1958). Prior to Rosenblatt, McCulloch and Pitts,
(1943) proposed a system in which binary neurons arranged together could
perform simple logic operations. Nowadays, neither the Perceptron nor the
system proposed by McCulloch and Pitts, (1943) is used in current Artificial
Neural Networks (ANNs) configurations. Modern architectures rely on gradient-
based optimization techniques and particularly on Stochastic Gradient Descent
(SGD) (Saad,, 1998). One of these first architectures trained through
gradient-based methods was the Multilayer Perceptron (MLP) (Rumelhart et al.,,
1986) followed by the Convolutional Neural Network proposed by LeCun et al.,
(1990).

This paper tests our approach on two DL architectures: the MLP and the ResNet
(RN). The choice of using the MLP is because it is somehow the off the shelve
solution in many use-cases and especially in credit risk (Ciampi et al.,,
2021) and in several works on retail credit risk (Lessmann et al.,, 2015). MLP
consists of a direct acyclic network of nodes organized in densely connected
layers. After being weighted and shifted by a bias term, inputs are fed into
the node’s activation function and influence each subsequent layer until the
final output layer.

In a binary classification task, the output of an MLP can be described as in
Arifovic and Gencay, (2001) by:

$f(x)=\phi\left(\beta_{0}+\sum_{j=1}^{d}\beta_{j}G\left(\gamma_{j0}+\sum_{i=1}^{p}\gamma_{ji}x_{i}\right)\right)$
(2)

RN differs from the canonical MLP architecture since it has ”shortcut
connections” that mitigate the problem of degradation in the case of multiple
layers (He et al.,, 2015). Although the usage of shortcut connections is not
new in the literature (Venables and Ripley,, 1999), the key proposal of He et
al., (2015) was to use identity mapping instead of any other nonlinear
transformation. Figure 1 shows the smallest building block of the ResNet
architecture in which both the first and the second layers are shortcutted,
and the inputs $x$ are added to the output of the second layer.

---
Figure 1: Residual Network skip connection block.

###  2.2 Multicriteria optimization

Multiple Criteria Decision-Making (MCDM) is a branch of Operations Research
and Management Science. MCDM represents the set of methods and processes
through which the concern for several conflicting criteria can be explicitly
incorporated into the analytical process Ehrgott et al., (2002). Several
strategies, spanning from a priori to interactive ones, have been developed to
address this issue (Miettinen,, 2012). Historically MCDM’s first roots are the
ones laid by Pareto at the end of the 19th century. However, the modern MCDM
has its origins more recently in the work of Koopmans, (1951) who modified the
canonical single objective linear programming model by reframing it as a
vector optimization problem. An MCDM problem takes the following form:

$\displaystyle\min_{\boldsymbol{x}}$
$\displaystyle\\{f_{1}(\boldsymbol{x}),f_{2}(\boldsymbol{x}),\dots,f_{k}(\boldsymbol{x})\\}$
(3) subject to $\displaystyle\boldsymbol{x}\in S$ (4)

where $f_{i}:{\rm I\\!R}^{n}\rightarrow{\rm I\\!R}$ is the ith objective and
the vector $\boldsymbol{x}$ contains the decision variables that belong to the
feasible set $S$. Scalarization is a common approach for dealing with
Multicriteria optimization problems. By scalarization, a vector optimization
problem turns into a single objective optimization problem. Additional
concerns affect the DM’s preferences scheme as a result of this. In our
approach, we begin by using a weighted sum scalarization to handle our
problem:

$\displaystyle\min_{\boldsymbol{x}}$
$\displaystyle\boldsymbol{w}^{\top}\boldsymbol{f}(\boldsymbol{x})$ (5) subject
to $\displaystyle\boldsymbol{x}\in S$ (6)

where the weights are the relative preference of the DM toward a specific
goal. The incorporation of such preferences can happen in two ways, either a
priori or a posteriori. In our approach, we use an a posteriori method as this
best suits the DM’s lack of knowledge, which may be uncertain about the
relative importance of each objective.

###  2.3 Knowledge injection

Knowledge in this paper is intended as validated information about relations
between entities in specific contexts as in von Rueden et al., (2021). The key
feature of such a definition is that it allows for formalization, implying
that such knowledge can be transformed into mathematical constraints somehow.

Let’s assume we have a deep architecture such that
$\hat{y}=\mathcal{F}(\boldsymbol{x},\mathcal{W})$ and we observe the true
label $y$ then we can train a supervised model by using a differentiable loss
function as for the case of regression by using the mean squared error (MSE):

$Loss_{f}(\boldsymbol{x},\mathcal{W})=\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}$
(7)

or in our case, of a binary classification with the binary cross-entropy:

$Loss_{f}(\boldsymbol{x},\mathcal{W})=\frac{1}{n}\sum_{i=1}^{n}\left[y_{i}\log(\hat{y}_{i}+(1-y_{i})\log(1-\hat{y}_{i})\right]$
(8)

this will constitute the first objective of our Multicriteria loss function,
that is, data fitting. The knowledge injection instead will act on the
features’ effects on the model outcome, which means that our knowledge-based
objective will be:

$Loss_{k}(\boldsymbol{x},\mathcal{W})=k(\boldsymbol{x})\odot\frac{\delta\mathcal{F}(\boldsymbol{x},\mathcal{W})}{\delta\boldsymbol{x}}$
(9)

where the right-hand side of the Hadamard product is the gradient of our DL
model at the feature level $\boldsymbol{x}$ whereas $k(\boldsymbol{x})$ is a
function that penalizes/favorites specific effect of the gradient with range
$[-1,1]$. Since knowledge is hardly spread through the whole feature space, a
possible strategy is to define $k(\boldsymbol{x})$ that maps the feature space
to the knowledge we expect on that particular feature neighbor.

In its most straightforward formulation, $k(\boldsymbol{x})$ can be a scalar,
and in this formulation is easier to investigate its behavior at the model
level. Let us assume $k(\boldsymbol{x})=\boldsymbol{1}$ then what is enforced
is that all partial derivatives should be negative therefore enforcing
monotonicity and, in particular decreasing monotonicity. The opposite holds
for the case when $k(\boldsymbol{x})=\boldsymbol{-1}$. When
$k(\boldsymbol{x})=\boldsymbol{0}$ there is no constraint on the gradient
behavior, meaning that knowledge is non-existent and therefore not injected.
Following Daw et al., (2021) we can augment our Multicriteria function with a
further constraint that measures the network complexity as, for example, an
$L_{2}$ regularization on the weights. The result is the following
unconstrained minimization problem:

$\min_{\mathcal{W}}\boldsymbol{\lambda}^{\top}\begin{bmatrix}Loss_{f}(\boldsymbol{x},\mathcal{W})\\\
||\mathcal{W}||_{2}\\\ Loss_{k}(\boldsymbol{x},\mathcal{W})\end{bmatrix}$ (10)

###  2.4 Interpretability methods

Model interpretability is gaining popularity due to the increasing
applications of non-linear models (Molnar et al.,, 2020). Model-agnostic and
model-aware approaches are the two main types of interpretability approaches.
The model is never accessed in model-agnostic interpretability methods. Unlike
the model-agnostic approach, the model-aware technique has access to model
parameters such as the gradient. Model-agnostic methods apply to all models,
whereas model-aware are restricted to a specific class of models. On the other
hand, model-aware approaches are more efficient and converge faster to the
genuine interpretability metric.

####  2.4.1 Model-aware interpretability

One of the first techniques proposed by the literature was to use the product
of the model’s gradient with feature values (Baehrens et al.,, 2010). Simonyan
et al., (2014) proposed Saliency Maps based on the gradient of model output
with respect to the input features. In other words, the score of multiclass
$c$ classifier can be locally approximated by:

$S_{c}(I)\approx w_{c}^{T}I+b_{c}$ (11)

where $w_{c}^{T}$ is the gradient of the model at that particular class $c$ in
that particular feature configuration $I_{0}$:

$w=\frac{\partial S_{c}}{\partial I}\Bigr{|}_{I_{0}}$ (12)

Sundararajan et al., (2017) through an axiomatic approach, questioned the
validity of such procedure, arguing that using only the gradient may result in
misleading feature attributions with respect to a baseline observation. They
proposed the concept of Integrated Gradients, a path-dependent approach in
which the gradients are accumulated over the linear combinations between the
observation and a baseline. This implies the evaluation of the following:

$IG_{0}=(I_{0}-I^{\prime})\int^{1}_{\alpha=0}\frac{\partial
S_{c}(I^{\prime}+\alpha(I_{0}-I^{\prime})}{\partial I}d\alpha$ (13)

####  2.4.2 Model-agnostic interpretability

One of the first model-agnostic technique was the Partial Dependence (PD)
proposed by Friedman, (1991). PD plots evaluate the change in the average
predicted value, as specified features vary over their marginal distribution
Goldstein et al., (2015). However the main limitation of the PD is the
dependence within features since evaluating the PD carries the risk of
computing points outside the data envelope. Apley and Zhu, (2020) proposed the
Accumulated Local Effects (ALEs) to address this flaw. ALEs have the advantage
of avoiding the problem of evaluating variables’ effects outside the data
envelope (Apley and Zhu,, 2020). Computing the ALE implies the evaluation of
the following:

$ALE_{\hat{f},S}(x_{S})=\sum_{k=1}^{k_{S}(x)}\frac{1}{n_{S}(k)}\sum_{i:x_{S}^{(i)}\in
N_{S}(k)}\left[\hat{f}(z_{k,j},x_{\setminus
S}^{(i)})-\hat{f}(z_{k-1,j},x_{\setminus S}^{(i)})\right]-C$ (14)

where: $\hat{f}$ is the black-box model, $S$ is the subset of variables’
index, $X$ is the matrix containing all the variables, $x$ is the vector
containing the feature values per observation, $z$ identifies the boundaries
of the K partitions, such that $z_{0,S}=min(x_{S})$, $C$ is a constant term to
center the plot. To make Equation 14 model-aware we can substitute finite
differences with the gradient as $\frac{\delta\hat{f}(z_{S},X_{\setminus
S})}{\delta z_{S}}\approx\hat{f}(z_{k,j},x_{\setminus
S}^{(i)})-\hat{f}(z_{k-1,j},x_{\setminus S}^{(i)})$. Because of that, the
resulting model-aware formula is:

$ALE_{\hat{f},S}(x)=\int_{z_{0,S}}^{x}\left[\int\frac{\delta\hat{f}(z_{S},X_{\setminus
S})}{\delta z_{S}}d\mathcal{P}(X_{\setminus S}|z_{S})\right]dz_{S}-C$ (15)

As a result, knowledge injection, as proposed in the previous section, will
have an effect on the ALEs because the final model will have a different
gradient than the non-knowledge injected one.

##  3 Data, software, hardware

###  3.1 Data

To test the goodness of our approach, we provide an empirical application in
the context of credit risk. In particular on the problem of bankruptcy
prediction. We used a publicly available dataset of Polish enterprises donated
to the UCI Machine Learning Repository by Zikeba et al., (2016). The data
contains information about the financial conditions of Polish companies
belonging to the manufacturing sector. The dataset contains 64 financial
ratios ranging from liquidity to leverage measures 111For a complete
description of the financial indicators, please consider Table 4 in the
Appendix.. Moreover, the dataset distinguishes five classification cases that
depend on the forecasting period. In our empirical setting, we focus on
bankruptcy status after one year. In this subset of data, the total number of
observations is 5910, out of which only 410 represents bankrupted firms. It is
worth noting that we do not counter the class imbalance in the empirical
setting, although this is something done commonly in the literature. We
retained class imbalance to test the robustness of our approach even in
conditions of scarcity of a particular class and used robust metrics such as
the Area Under the Receiving Operating Curve (AUROC). Moreover, as our
empirical experiment focuses on testing our approach on model
interpretability, we restricted the number of features we considered to six.
This is due to the fact that ALEs are inspected as plots, and having a plot
for each feature increases complexity without providing any additional benefit
to the reader or our approach. The choice was to focus on Attr 13, Attr 16,
Attr 23, Attr 24, Attr 26, and Attr 27. The attributes were selected by using
a ROC-based feature selection (Kuhn and Johnson,, 2019).

###  3.2 Software and hardware

The overall pipeline management is built in R (R Core Team,, 2020). The
preprocessing relied on the tidymodels ecosystem (Kuhn and Wickham,, 2020) as
well as on the tidyverse (Wickham et al.,, 2019). The DL models are developed
in Julia (Bezanson et al.,, 2017) using the Flux framework (Innes et al.,,
2018; Innes,, 2018). The interoperability between the two languages is
possible via the JuliaConnectoR library (Lenz et al.,, 2021). To debug the
model and to check the validity of our approach, we employed the ALEPlot
package (Apley,, 2018). As for the hardware environment, the pipeline is
carried out on a local machine with 12 logical cores (Intel i7-9850H), 16 GB
RAM, and a Cuda enabled graphic card (NVIDIA Quadro T2000). Both Julia and R
codes are freely available for research reproducibility on GitLab, and an ad-
hoc Docker container has been created on DockerHub.

##  4 Results

To test the performance of our approach on the Polish firms’ dataset, we use a
standard practice in the field of DL. At first, we split the dataset into
training and testing. Three-quarters of the dataset is for training the model
and the rest for testing its performance. In the case of a model that contains
no hyperparameters, a setting like this will suffice. However, in DL, this is
never the case as these models require a thorough calibration of
hyperparameters. In our setup, the hyperparameters are the elements contained
in $\boldsymbol{\lambda}$. Therefore a common strategy is to use the training
set to do what is called hyperparameter optimization (Goodfellow et al.,,
2016). Therefore, the training set is further divided into training and
validation sets, and the model is fitted and validated with different
parameters. In our case, we draw from the training set ten samples using the
bootstrap technique as proposed by Efron and Tibshirani, (1997), and we
trained our model using different combinations of hyperparameters. As for the
choice on implementing such hyperparameter search, we relied on grid search,
also known as full factorial design (Montgomery,, 2017). We then trained the
model on the entire training set and classified bankruptcy state on the test
set with the optimal hyperparameters.

For a deep understanding of the results, we divided the analysis into three
parts. Firstly we performed hyperparameter optimization and subsequent hold-
out testing using both the MLP and the RN, with the former being the best
performing model. Secondly, with the MLP, we analyzed the effect on the
interpretation by using ALE plots. Thirdly we tested the robustness of our
approach by diminishing the amount of data.

###  4.1 Performance review

Table 1 presents the mean AUROC as well as its standard errors as our model
validation involved ten bootstrap samples. The first striking result is that
both the MLP and RN perform poorly without any regularization nor knowledge
injection. This result is in line with Zikeba et al., (2016), which also found
that the ANN architectures suffer in terms of generalization. What instead is
of great interest is the increase in performance when both regularisation and
knowledge injection are brought to the table. In particular, the ResNet seems
to perform better with low levels of knowledge injection and a modest level of
regularization. However, what is more, relevant is the behavior of the MLP.
The model is more sensitive to knowledge injection and performs significantly
better in model validation. This result is evident when $\lambda_{3}=0.3$, all
the MLP models are above an AUROC of $0.8$ with a modest amount of standard
error. Another significant result of the MLP is performance deterioration when
regularization starts to ramp $\lambda_{2}=0.3$ up even with injected
knowledge. What is worth noting is that the dataset suffers from significant
class imbalance, and nothing has been done to alleviate it to test the
effectiveness of our approach in such context. Indeed knowledge injection
alleviates misclassification and creates a model that is on par with other
robust classifiers.

Table 1: Performances of Multilayer Perceptron and Residual Network on the training set with various hyperparameter settings. The performance is measured as the mean and standard errors of the Area Under the Receiving Operating Curve in each bootstrap sample. Bold values indicate the best performing hyperparametrization for each model. |  |  |  | Multilayer Perceptron |  | Residual Network
---|---|---|---|---|---|---
$\lambda_{1}$ | $\lambda_{2}$ | $\lambda_{3}$ |  | Mean | Standard error |  | Mean | Standard error
1.0 | 0.0 | 0.0 |  | 0.6585 | 0.0178 |  | 0.5061 | 0.0843
0.9 | 0.1 | 0.0 |  | 0.6924 | 0.0111 |  | 0.5308 | 0.0805
0.8 | 0.2 | 0.0 |  | 0.6302 | 0.0757 |  | 0.6326 | 0.0180
0.7 | 0.3 | 0.0 |  | 0.7175 | 0.0059 |  | 0.5584 | 0.0900
0.9 | 0.0 | 0.1 |  | 0.7905 | 0.0087 |  | 0.6418 | 0.0740
0.8 | 0.1 | 0.1 |  | 0.8286 | 0.0149 |  | 0.5744 | 0.0769
0.7 | 0.2 | 0.1 |  | 0.7586 | 0.0336 |  | 0.5059 | 0.0746
0.6 | 0.3 | 0.1 |  | 0.6163 | 0.1219 |  | 0.6604 | 0.0879
0.8 | 0.0 | 0.2 |  | 0.8263 | 0.0129 |  | 0.5124 | 0.0664
0.7 | 0.1 | 0.2 |  | 0.8242 | 0.0170 |  | 0.6102 | 0.0186
0.6 | 0.2 | 0.2 |  | 0.8206 | 0.0123 |  | 0.5037 | 0.0443
0.5 | 0.3 | 0.2 |  | 0.7617 | 0.0601 |  | 0.6249 | 0.0593
0.7 | 0.0 | 0.3 |  | 0.8202 | 0.0119 |  | 0.6074 | 0.0172
0.6 | 0.1 | 0.3 |  | 0.8289 | 0.0139 |  | 0.5410 | 0.0417
0.5 | 0.2 | 0.3 |  | 0.8306 | 0.0135 |  | 0.5318 | 0.0150
0.4 | 0.3 | 0.3 |  | 0.8178 | 0.0198 |  | 0.5628 | 0.0378

The performances in Table 1 are promising. However, to precisely measure model
generalization error, the performances that need to be considered are those
taken from the test set. Table 2 presents these performances by taking into
account only the optimally parametrized models and their baseline, that is,
the model with $\lambda_{1}=1$. The clear-cut result from this table is that
the MLP generalizes way better than its counterpart, with a slight decrease in
performance in line with the expectations. This result suggests that knowledge
injection corroborated with mild regularization can enhance the generalization
performances of a DL classifier as the MLP and make it robust to class
imbalances.

Table 2: Performances of Multilayer Perceptron and Residual Network on the test set with validated and baseline hyperparameter settings. The performance is measured as the Area Under the Receiving Operating Curve in the test sample. $\lambda_{1}$ | $\lambda_{2}$ | $\lambda_{3}$ | Multilayer Perceptron | Residual Network
---|---|---|---|---
1.0 | 0.0 | 0.0 | 0.577 | 0.582
0.5 | 0.2 | 0.3 | 0.821 | -
0.4 | 0.3 | 0.1 | - | 0.518

In the following sections, we will investigate further the performance of the
MLP with and without knowledge injection in terms of interpretability and
robustness to data scarcity. We will focus only on the MLP, as it was the most
performant architecture. Moreover, analyzing the interpretations of a non-
performant classifier as the RN has no useful meaning from a practical point
of view.

###  4.2 Interpretability review

A mentioned in the previous sections, post-hoc interpretability methods are
essential tools for model debugging and to inspect any model bias. As a
result, we present figure 2(a), which demonstrates MLP ALEs with and without
knowledge injection. The ALEs of the model without knowledge injection show
several misbehaviors that may be due to class imbalance or hidden biases in
the training sample. In detail:

  * 1.

Attr 13: which is also known as the EBITDA-To-Sales ratio, is a profitability
indicator. Therefore we should expect to decrease the probability of
bankruptcy, especially in cases where the ratio is positive. The opposite
occurs instead. An increase of the ratio above zero increases the probability
of bankruptcy. This effect is at odds with the literature on the subject as,
for example, in Platt and Platt, (2002).

  * 2.

Attr 16: is the inverse and a proxy of the Debt-To-EBITDA ratio which is
leverage ratio. For the inverse of a leverage ratio we would assume negative
impact on bankruptcy as in Beaver, (1968).

  * 3.

Attr 23: is the Net profit ratio and is a productivity ratio Lee and Choi,
(2013) which tends to have a negative impact on bankruptcy.

(a) Accumulated Local Effects plot of the Multilayer Perceptron architecture,
without regularization and knowledge injection (i.e.
$\lambda_{1}=1,\lambda_{2}=0.0,\lambda_{3}=0.0$).

(b) Accumulated Local Effects plot of the Multilayer Perceptron architecture,
with regularisation and knowledge injection optimally selected from the
hyperparameter optimization procedure (i.e.
$\lambda_{1}=0.5,\lambda_{2}=0.2,\lambda_{3}=0.3$).

Figure 2: Accumulated Local Effects plot of the Multilayer Perceptron
architecture, with and without regularization and knowledge injection.

To counter this common biased effects we assumed the following logistic form
for all the features’ knowledge function:

$k(x)=\frac{1}{1+e^{-100x}}$ (16)

Such a knowledge function penalizes only positive effects above zero and
retains the correctly captured effects below it. With this setting, in the
case of moderate knowledge injection, the effects align with the literature
findings.

###  4.3 Robustness checks

A fundamental question is how model performances deteriorate with less
training data. In previous works, knowledge injection has been implemented
indeed to alleviate such problems as in von Kurnatowski et al., (2021). To
discover how our approach deals with scarce data, we systematically diminished
the training set and measured the corresponding performance on the test set.
These results are in Table 3 which depicts the different performances in the
test set as the training data proportion decreases. In concordance with the
literature on knowledge injection, our approach prevents performance
degradation even in extreme cases where only half the dataset is used for
training.

Table 3: Performances of Multilayer Perceptron on the test set under different proportions of train/test split. The performance is measured as the Area Under the Receiving Operating Curve in the test sample. Train/Test |  | With knowledge
---
($\lambda_{1}=0.5,\lambda_{2}=0.2,\lambda_{3}=0.3$)
| Without knowledge
---
($\lambda_{1}=0.1,\lambda_{2}=0.0,\lambda_{3}=0.0$)
0.85 | 0.829 | 0.615
0.80 | 0.828 | 0.543
0.75 | 0.821 | 0.577
0.7 | 0.822 | 0.605
0.65 | 0.790 | 0.613
0.6 | 0.817 | 0.646
0.55 | 0.803 | 0.505
0.5 | 0.823 | 0.641

##  5 Conclusion

In this paper, we presented a novel approach to knowledge injection at the
level of feature effects of a DL model. Model interpretability is a
particularly crucial topic, and recent legislation implies interpretability
from the start. Recent post-hoc interpretability methods fail to provide this.
Our approach solves the problem by allowing to control model interpretation
from the start. The approach consists in solving a Multicriteria minimization
problem in which knowledge adherence competes with greedy data fitting and
regularization. We accounted for partial knowledge and nonlinearity by
defining ad-hoc knowledge functions on the model’s parameters. We presented a
use case of bankruptcy prediction using a Polish firm’s dataset to test our
approach. The results suggest that knowledge injection improves performances
and keeps model interpretation in line with the literature findings, avoiding
idiosyncratic effects resulting from either class imbalance or possible biases
in the dataset. The DM can check the effects of our approach through post-hoc
interpretability methods that play a crucial role in fine-tuning the model
before production. Another critical question that we answered is model
performance degradation in case of data shortage. Our results suggest that
knowledge injection gives the modeler more freedom in terms of the necessary
data for proper model training.

This new methodology creates many new opportunities in terms of research. One
possible further research can be the investigation of more complex knowledge
functions. A second research path would be to enforce knowledge consistency
within different scenarios, as in the case of time series. These are only a
few possible new research efforts that will pave the way for knowledge-
informed DL.

## References

  * Abadi et al., (2015) Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G. S., Davis, A., Dean, J., Devin, M., Ghemawat, S., Goodfellow, I., Harp, A., Irving, G., Isard, M., Jia, Y., Jozefowicz, R., Kaiser, L., Kudlur, M., Levenberg, J., Mané, D., Monga, R., Moore, S., Murray, D., Olah, C., Schuster, M., Shlens, J., Steiner, B., Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V., Viégas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y., and Zheng, X. (2015).  TensorFlow: Large-scale machine learning on heterogeneous systems.
  * Altman, (1968) Altman, E. I. (1968).  Financial ratios, discriminant analysis and the prediction of corporate bankruptcy.  The journal of finance, 23(4):589–609.
  * Altman and Sabato, (2007) Altman, E. I. and Sabato, G. (2007).  Modelling Credit Risk for SMEs: Evidence from the U.S. Market.  Abacus, 43(3):332–357.
  * Apley, (2018) Apley, D. (2018).  ALEPlot: Accumulated Local Effects (ALE) Plots and Partial Dependence (PD) Plots.
  * Apley and Zhu, (2020) Apley, D. W. and Zhu, J. (2020).  Visualizing the effects of predictor variables in black box supervised learning models.  Journal of the Royal Statistical Society: Series B (Statistical Methodology), 82(4):1059–1086.
  * Arifovic and Gencay, (2001) Arifovic, J. and Gencay, R. (2001).  Using genetic algorithms to select architecture of a feedforward artiÿcial neural network.  Physica A, page 21.
  * Baehrens et al., (2010) Baehrens, D., Schroeter, T., Harmeling, S., Kawanabe, M., Hansen, K., and Müller, K.-R. (2010).  How to explain individual classification decisions.  The Journal of Machine Learning Research, 11:1803–1831.
  * Beaver, (1968) Beaver, W. H. (1968).  Alternative accounting measures as predictors of failure.  The accounting review, 43(1):113–122.
  * Bezanson et al., (2017) Bezanson, J., Edelman, A., Karpinski, S., and Shah, V. B. (2017).  Julia: A fresh approach to numerical computing.  SIAM review, 59(1):65–98.
  * Bottou et al., (2007) Bottou, L., Chapelle, O., DeCoste, D., and Weston, J. (2007).  Scaling Learning Algorithms toward AI.  In Large-Scale Kernel Machines, pages 321–359. MIT Press.
  * Bücker et al., (2021) Bücker, M., Szepannek, G., Gosiewska, A., and Biecek, P. (2021).  Transparency, auditability, and explainability of machine learning models in credit scoring.  Journal of the Operational Research Society, pages 1–21.
  * Ciampi et al., (2021) Ciampi, F., Giannozzi, A., Marzi, G., and Altman, E. I. (2021).  Rethinking SME default prediction: A systematic literature review and future perspectives.  Scientometrics, pages 1–48.
  * Ciampi and Gordini, (2013) Ciampi, F. and Gordini, N. (2013).  Small enterprise default prediction modeling through artificial neural networks: An empirical analysis of Italian small enterprises.  Journal of Small Business Management, 51(1):23–45.
  * Daw et al., (2021) Daw, A., Karpatne, A., Watkins, W., Read, J., and Kumar, V. (2021).  Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling.  arXiv:1710.11431 [physics, stat].
  * Dexe et al., (2020) Dexe, J., Ledendal, J., and Franke, U. (2020).  An Empirical Investigation of the Right to Explanation Under GDPR in Insurance.  In Gritzalis, S., Weippl, E. R., Kotsis, G., Tjoa, A. M., and Khalil, I., editors, Trust, Privacy and Security in Digital Business, Lecture Notes in Computer Science, pages 125–139, Cham. Springer International Publishing.
  * Efron and Tibshirani, (1997) Efron, B. and Tibshirani, R. (1997).  Improvements on Cross-Validation: The 632+ Bootstrap Method.  Journal of the American Statistical Association, 92(438):548–560.
  * Ehrgott et al., (2002) Ehrgott, M., Gandibleux, X., and Hillier, F. S., editors (2002).  Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys, volume 52 of International Series in Operations Research & Management Science.  Springer US, Boston, MA.
  * European Commission, (2019) European Commission (2019).  Ethics guidelines for trustworthy AI.  Technical report.
  * Friedman, (1991) Friedman, J. H. (1991).  Multivariate Adaptive Regression Splines.  The Annals of Statistics, 19(1):1–67.
  * Goldstein et al., (2015) Goldstein, A., Kapelner, A., Bleich, J., and Pitkin, E. (2015).  Peeking Inside the Black Box: Visualizing Statistical Learning With Plots of Individual Conditional Expectation.  Journal of Computational and Graphical Statistics, 24(1):44–65.
  * Goodfellow et al., (2016) Goodfellow, I., Bengio, Y., and Courville, A. (2016).  Deep Learning.  MIT Press.
  * He et al., (2015) He, K., Zhang, X., Ren, S., and Sun, J. (2015).  Deep Residual Learning for Image Recognition.  arXiv:1512.03385 [cs].
  * Innes, (2018) Innes, M. (2018).  Flux: Elegant machine learning with julia.  Journal of Open Source Software.
  * Innes et al., (2018) Innes, M., Saba, E., Fischer, K., Gandhi, D., Rudilosso, M. C., Joy, N. M., Karmali, T., Pal, A., and Shah, V. (2018).  Fashionable modelling with flux.  CoRR, abs/1811.01457.
  * Koopmans, (1951) Koopmans, T. (1951).  Analysisofproductionasanefficientcombinationofactivities.  Activityanalysisofproductionandallocation, TC Koopmans, editor, Wiley, New York.
  * Kotłowski and Słowiński, (2009) Kotłowski, W. and Słowiński, R. (2009).  Rule learning with monotonicity constraints.  In Proceedings of the 26th Annual International Conference on Machine Learning, ICML ’09, pages 537–544, New York, NY, USA. Association for Computing Machinery.
  * Kuhn and Johnson, (2019) Kuhn, M. and Johnson, K. (2019).  Feature Engineering and Selection: A Practical Approach for Predictive Models.  CRC Press.
  * Kuhn and Wickham, (2020) Kuhn, M. and Wickham, H. (2020).  Tidymodels: A Collection of Packages for Modeling and Machine Learning Using Tidyverse Principles.
  * Lauer and Bloch, (2008) Lauer, F. and Bloch, G. (2008).  Incorporating Prior Knowledge in Support Vector Machines for Classification: A Review.  Neurocomputing, 71(7-9):1578–1594.
  * LeCun et al., (1990) LeCun, Y., Boser, B., Denker, J., Henderson, D., Howard, R., Hubbard, W., and Jackel, L. (1990).  Handwritten Digit Recognition with a Back-Propagation Network.  In Advances in Neural Information Processing Systems, volume 2. Morgan-Kaufmann.
  * Lee and Choi, (2013) Lee, S. and Choi, W. S. (2013).  A multi-industry bankruptcy prediction model using back-propagation neural network and multivariate discriminant analysis.  Expert Systems with Applications, 40(8):2941–2946.
  * Lenz et al., (2021) Lenz, S., Hackenberg, M., and Binder, H. (2021).  The JuliaConnectoR: A functionally oriented interface for integrating Julia in R.  arXiv:2005.06334 [cs, stat].
  * Lessmann et al., (2015) Lessmann, S., Baesens, B., Seow, H.-V., and Thomas, L. C. (2015).  Benchmarking state-of-the-art classification algorithms for credit scoring: An update of research.  European Journal of Operational Research, 247(1):124–136.
  * McCulloch and Pitts, (1943) McCulloch, W. S. and Pitts, W. (1943).  A logical calculus of the ideas immanent in nervous activity.  The bulletin of mathematical biophysics, 5(4):115–133.
  * Miettinen, (2012) Miettinen, K. (2012).  Nonlinear Multiobjective Optimization, volume 12.  Springer Science & Business Media.
  * Molnar et al., (2020) Molnar, C., Casalicchio, G., and Bischl, B. (2020).  Interpretable Machine Learning – A Brief History, State-of-the-Art and Challenges.  In Koprinska, I., Kamp, M., Appice, A., Loglisci, C., Antonie, L., Zimmermann, A., Guidotti, R., Özgöbek, Ö., Ribeiro, R. P., Gavaldà, R., Gama, J., Adilova, L., Krishnamurthy, Y., Ferreira, P. M., Malerba, D., Medeiros, I., Ceci, M., Manco, G., Masciari, E., Ras, Z. W., Christen, P., Ntoutsi, E., Schubert, E., Zimek, A., Monreale, A., Biecek, P., Rinzivillo, S., Kille, B., Lommatzsch, A., and Gulla, J. A., editors, ECML PKDD 2020 Workshops, Communications in Computer and Information Science, pages 417–431, Cham. Springer International Publishing.
  * Montgomery, (2017) Montgomery, D. C. (2017).  Design and Analysis of Experiments.  John wiley & sons.
  * Muralidhar et al., (2018) Muralidhar, N., Islam, M. R., Marwah, M., Karpatne, A., and Ramakrishnan, N. (2018).  Incorporating Prior Domain Knowledge into Deep Neural Networks.  In 2018 IEEE International Conference on Big Data (Big Data), pages 36–45.
  * Nosratabadi et al., (2020) Nosratabadi, S., Mosavi, A., Duan, P., Ghamisi, P., Filip, F., Band, S. S., Reuter, U., Gama, J., and Gandomi, A. H. (2020).  Data Science in Economics: Comprehensive Review of Advanced Machine Learning and Deep Learning Methods.  Mathematics, 8(10):1799.
  * Ozbayoglu et al., (2020) Ozbayoglu, A. M., Gudelek, M. U., and Sezer, O. B. (2020).  Deep learning for financial applications : A survey.  Applied Soft Computing, 93:106384.
  * Paszke et al., (2019) Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S. (2019).  PyTorch: An imperative style, high-performance deep learning library.  In Wallach, H., Larochelle, H., Beygelzimer, A., dAlché-Buc, F., Fox, E., and Garnett, R., editors, Advances in Neural Information Processing Systems 32, pages 8024–8035. Curran Associates, Inc.
  * Platt and Platt, (2002) Platt, H. D. and Platt, M. B. (2002).  Predicting corporate financial distress: Reflections on choice-based sample bias.  Journal of economics and finance, 26(2):184–199.
  * R Core Team, (2020) R Core Team (2020).  R: A Language and Environment for Statistical Computing.  R Foundation for Statistical Computing, Vienna, Austria.
  * Rao and Frtunikj, (2018) Rao, Q. and Frtunikj, J. (2018).  Deep learning for self-driving cars: Chances and challenges.  In Proceedings of the 1st International Workshop on Software Engineering for AI in Autonomous Systems, SEFAIS ’18, pages 35–38, New York, NY, USA. Association for Computing Machinery.
  * Rosenblatt, (1958) Rosenblatt, F. (1958).  The perceptron: A probabilistic model for information storage and organization in the brain.  Psychological Review, 65(6):386–408.
  * Rudin, (2019) Rudin, C. (2019).  Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead.  Nature Machine Intelligence, 1(5):206–215.
  * Rumelhart et al., (1986) Rumelhart, D. E., McClelland, J. L., and Group, P. R. (1986).  Parallel Distributed Processing: Explorations in the Microstructure of Cognition: Foundations, volume 1.  A Bradford Book, Cambridge, MA, USA.
  * Saad, (1998) Saad, D., editor (1998).  On-Line Learning in Neural Networks.  Publications of the Newton Institute. Cambridge University Press, Cambridge, [Eng.] ; New York.
  * Simonyan et al., (2014) Simonyan, K., Vedaldi, A., and Zisserman, A. (2014).  Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps.  arXiv:1312.6034 [cs].
  * Sundararajan et al., (2017) Sundararajan, M., Taly, A., and Yan, Q. (2017).  Axiomatic Attribution for Deep Networks.  arXiv:1703.01365 [cs].
  * Venables and Ripley, (1999) Venables, W. N. and Ripley, B. D. (1999).  Modern Applied Statistics with S-PLUS.  Statistics and Computing. Springer-Verlag, New York, third edition.
  * Vinyals et al., (2019) Vinyals, O., Babuschkin, I., Czarnecki, W. M., Mathieu, M., Dudzik, A., Chung, J., Choi, D. H., Powell, R., Ewalds, T., Georgiev, P., Oh, J., Horgan, D., Kroiss, M., Danihelka, I., Huang, A., Sifre, L., Cai, T., Agapiou, J. P., Jaderberg, M., Vezhnevets, A. S., Leblond, R., Pohlen, T., Dalibard, V., Budden, D., Sulsky, Y., Molloy, J., Paine, T. L., Gulcehre, C., Wang, Z., Pfaff, T., Wu, Y., Ring, R., Yogatama, D., Wünsch, D., McKinney, K., Smith, O., Schaul, T., Lillicrap, T., Kavukcuoglu, K., Hassabis, D., Apps, C., and Silver, D. (2019).  Grandmaster level in StarCraft II using multi-agent reinforcement learning.  Nature, 575(7782):350–354.
  * von Kurnatowski et al., (2021) von Kurnatowski, M., Schmid, J., Link, P., Zache, R., Morand, L., Kraft, T., Schmidt, I., and Stoll, A. (2021).  Compensating data shortages in manufacturing with monotonicity knowledge.  arXiv:2010.15955 [cs, math].
  * von Rueden et al., (2021) von Rueden, L., Mayer, S., Beckh, K., Georgiev, B., Giesselbach, S., Heese, R., Kirsch, B., Pfrommer, J., Pick, A., Ramamurthy, R., Walczak, M., Garcke, J., Bauckhage, C., and Schuecker, J. (2021).  Informed Machine Learning – A Taxonomy and Survey of Integrating Knowledge into Learning Systems.  IEEE Transactions on Knowledge and Data Engineering, pages 1–1.
  * Wickham et al., (2019) Wickham, H., Averick, M., Bryan, J., Chang, W., McGowan, L. D., François, R., Grolemund, G., Hayes, A., Henry, L., Hester, J., Kuhn, M., Pedersen, T. L., Miller, E., Bache, S. M., Müller, K., Ooms, J., Robinson, D., Seidel, D. P., Spinu, V., Takahashi, K., Vaughan, D., Wilke, C., Woo, K., and Yutani, H. (2019).  Welcome to the tidyverse.  Journal of Open Source Software, 4(43):1686.
  * Zhang et al., (2019) Zhang, D., Cao, D., and Chen, H. (2019).  Deep learning decoding of mental state in non-invasive brain computer interface.  In Proceedings of the International Conference on Artificial Intelligence, Information Processing and Cloud Computing, AIIPCC ’19, pages 1–5, New York, NY, USA. Association for Computing Machinery.
  * Zhang et al., (2018) Zhang, Q., Yang, L. T., Chen, Z., and Li, P. (2018).  A survey on deep learning for big data.  Information Fusion, 42:146–157.
  * Zikeba et al., (2016) Zikeba, M., Tomczak, S. K., and Tomczak, J. M. (2016).  Ensemble boosted trees with synthetic features generation in application to bankruptcy prediction.  Expert Systems with Applications.

##  Appendix A Dataset indicators

Table 4: Dataset financial indicators with corresponding description.

ID | Description | ID | Description
---|---|---|---
Attr 1 | net profit / total assets | Attr 33 | operating expenses / short-term liabilities
Attr 2 | total liabilities / total assets | Attr 34 | operating expenses / total liabilities
Attr 3 | working capital / total assets | Attr 35 | profit on sales / total assets
Attr 4 | current assets / short-term liabilities | Attr 36 | total sales / total assets
Attr 5 | [(cash + short-term securities + receivables - short-term liabilities) / (operating expenses - depreciation)] * 365 | Attr 37 | (current assets - inventories) / long-term liabilities
Attr 6 | retained earnings / total assets | Attr 38 | constant capital / total assets
Attr 7 | EBIT / total assets | Attr 39 | profit on sales / sales
Attr 8 | book value of equity / total liabilities | Attr 40 | (current assets - inventory - receivables) / short-term liabilities
Attr 9 | sales / total assets | Attr 41 | total liabilities / ((profit on operating activities + depreciation) * (12/365))
Attr 10 | equity / total assets | Attr 42 | profit on operating activities / sales
Attr 11 | (gross profit + extraordinary items + financial expenses) / total assets | Attr 43 | rotation receivables + inventory turnover in days
Attr 12 | gross profit / short-term liabilities | Attr 44 | (receivables * 365) / sales
Attr 13 | (gross profit + depreciation) / sales | Attr 45 | net profit / inventory
Attr 14 | (gross profit + interest) / total assets | Attr 46 | (current assets - inventory) / short-term liabilities
Attr 15 | (total liabilities * 365) / (gross profit + depreciation) | Attr 47 | (inventory * 365) / cost of products sold
Attr 16 | (gross profit + depreciation) / total liabilities | Attr 48 | EBITDA (profit on operating activities - depreciation) / total assets
Attr 17 | total assets / total liabilities | Attr 49 | EBITDA (profit on operating activities - depreciation) / sales
Attr 18 | gross profit / total assets | Attr 50 | current assets / total liabilities
Attr 19 | gross profit / sales | Attr 51 | short-term liabilities / total assets
Attr 20 | (inventory * 365) / sales | Attr 52 | (short-term liabilities * 365) / cost of products sold)
Attr 21 | sales (n) / sales (n-1) | Attr 53 | equity / fixed assets
Attr 22 | profit on operating activities / total assets | Attr 54 | constant capital / fixed assets
Attr 23 | net profit / sales | Attr 55 | working capital
Attr 24 | gross profit (in 3 years) / total assets | Attr 56 | (sales - cost of products sold) / sales
Attr 25 | (equity - share capital) / total assets | Attr 57 | (current assets - inventory - short-term liabilities) / (sales - gross profit - depreciation)
Attr 26 | (net profit + depreciation) / total liabilities | Attr 58 | total costs /total sales
Attr 27 | profit on operating activities / financial expenses | Attr 59 | long-term liabilities / equity
Attr 28 | working capital / fixed assets | Attr 60 | sales / inventory
Attr 29 | logarithm of total assets | Attr 61 | sales / receivables
Attr 30 | (total liabilities - cash) / sales | Attr 62 | (short-term liabilities *365) / sales
Attr 31 | (gross profit + interest) / sales | Attr 63 | sales / short-term liabilities
Attr 32 | (current liabilities * 365) / cost of products sold | Attr 64 | sales / fixed assets


11institutetext: Software Systems for Digitalization, German Aerospace Center
(DLR), Mälzerstraße 3, 07745 Jena, Germany 11email:
<EMAIL_ADDRESS>
22institutetext: Software for Space Systems and Interactive Visualization,
German Aerospace Center (DLR), Lilienthalplatz 7, 38108 Braunschweig, Germany
22email<EMAIL_ADDRESS>
# Digital Availability of Product Information for Collaborative Engineering of
Spacecraft

Diana Peters 11 0000-0002-5855-2989 Philipp M. Fischer 22 0000-0003-2918-5195
Philipp M. Schäfer 11 0000-0003-3931-6670 Kobkaew Opasjumruskit 11
0000-0002-9206-6896 Andreas Gerndt 22 0000-0002-0409-8573

###### Abstract

In this paper, we introduce a system to collect product information from
manufacturers and make it available in tools that are used for concurrent
design of spacecraft. The planning of a spacecraft needs experts from
different disciplines, like propulsion, power, and thermal. Since these
different disciplines rely on each other there is a high need for
communication between them, which is often realized by a Model-Based Systems
Engineering (MBSE) process and corresponding tools. We show by comparison that
the product information provided by manufacturers often does not match the
information needed by MBSE tools on a syntactic or semantic level. The
information from manufacturers is also currently not available in machine-
readable formats. Afterwards, we present a prototype of a system that makes
product information from manufacturers directly available in MBSE tools, in a
machine-readable way.

###### Keywords:

Model-Based Systems Engineering Product Information Spacecraft Concurrent
Engineering.

##  1 Introduction

Complex systems can not be realized by a single person or discipline due to
the systems size and heterogeneity. The field of Systems Engineering (SE) aims
to find solutions how to realize such systems successfully. One approach
emerging in the SE field is Model-Based SE (MBSE), which “can be described as
the formalized application of modeling principles, methods, languages, and
tools to the entire lifecycle of large, complex, interdisciplinary,
sociotechnical systems.” [28]. By MBSE tool, we denote any software
application that supports the development of a model by participants from
different disciplines. The spacecraft components specified in an MBSE tool we
denote as Equipment, while spacecraft components built or offered by
manufacturers are denoted as products.

The sources of information that engineers enter in MBSE tools for spacecraft
design are PDF data sheets, spreadsheets, and engineers’ implicit knowledge.
Even if information is stored and transmitted digitally, it is often not
machine-readable and especially not automatically available in an MBSE tool.
Instead, a human has to take the information from a document to enter it into
another system. This manual process is both slow and error-prone. Furthermore,
every manufacturer uses a different format and a different vocabulary to
represent information. Sometimes, not even PDF data sheets are
available—Jahnke and Martelo found, that ”From the 34 found suppliers of
Cubesat related hardware, 62 % do publish detailed specifications and
datasheets on their website.” [22], which means that more than one third of
the suppliers do not make this information available on their website.

As spacecraft are not anymore always one-of-a-kind products,
CubeSats111CubeSats are mini satellites made of 10cm x 10cm x 10cm units and
often use COTS (commercial off-the-shelf) products and small series of
satellites become more common. According to Lange et al. [23], it becomes also
more important to reuse information from former missions. This does not only
include the MBSE models themselves, but also for example spacecraft component
databases, where engineers could, additionally to the information from
manufacturers, also add their own data, e.g. ”template components” for
different size categories of spacecraft.

Jahnke and Martelo also pointed out that ”[…] the task during the CE sessions
of the single domain expert is shifted from actual design of the sub-system
and estimation of key-parameters towards the selection of the most suiting
existing solution from e.g. a database and interface cross-check to other sub-
systems.” [22]. So it becomes more important to find a product that fits
certain requirements, including interface compatibility to other products,
then to design a product from scratch.

In this paper we point out the problems with the current product information
exchange between manufacturer and customer, collect requirements for a system
to overcome these problems, and present a prototype system that makes product
information available in the in-house MBSE tool of Virtual Satellite.

##  2 Related Work

Several approaches exist to make the whole MBSE process or phases of it
possible or easier. This includes software applications, standards, and models
of space systems.

The life cycle of a space system, as described by the European Cooperation for
Space Standardization (ECSS), the European Space Agency (ESA), and the
National Aeronautics and Space Administration (NASA), consists of phases 0 and
A through F [2][25], where in this paper we focus of the early planning phases
0 and A. Virtual Spacecraft Design (VSD) by ESA [9], Virtual Satellite by the
German Aerospace Center (DLR) [14], RangeDB by Airbus Defense and Space [8],
and Open Concurrent Design Tool (OCDT) [13] as well as CDP4 [1] by RHEA Group
all aim to support an MBSE process following the suggestions made by ECSS in
two Technical Memorandums, ECSS-E-TM-10-23A [12] and ECSS‐E‐TM‐10‐25A [10].
These tools have an internal model of the spacecraft and its subsystems. They
all require manual input of Equipment data. They all support at least either
the import or export of Excel spreadsheets. Though following similar ideas and
guidelines, the parameters provided by these tools, and especially the names
used for those parameters, vary. Table 1 shows an overview of the mass and
structure parameters of most of the mentioned MBSE tools. We selected mass and
structure parameters, because those are among the most relevant parameters for
the early planning phases.

MBSE Tool | Virtual Satellite 4 | VSD | OCDT/CDP4
---|---|---|---
Mass | massPerUnit (kg) | Weigth [sic!] (gram) | mass (kg)
Parameters |  |  | mass margin
Structure | radius (m) |  | diameter (m)
Parameters | shape |  | shape
| sizeX (m) | Height (millimetre) | height (m)
| sizeY (m) | Length (millimetre) | length (m)
| sizeZ (m) | Width (millimetre) | width (m)
Table 1: Mass and structure parameters of equipment at different MBSE tools
(units in braces). The parameter names for Virtual Satellite 4 and VSD were
taken from installations of the tools. OCDT and CDP4 directly implement the
ParameterType concept from ECSS-E-TM-10-25. At Virtual Satellite, the margin
parameters are not defined at Equipment level, but above.

The aim of standards and formats is to provide a base for interfaces, so
systems can exchange information directly, reliably, and without human
interaction. For the small field of Spacecraft Onboard Interface Services the
Consultative Committee for Space Data Systems (CCSDS) developed a standard for
Electronic Data Sheets (EDS) [30]. EDS allow the exchange of information in a
machine-readable format; no manual data transformation is necessary. Units,
like ”gram” or ”inch” are defined in the EDS dictionary of terms, as are
quantity kinds, like ”massQK” or ”lengthQK”. But there is no definition that
connects ”gram” with ”massQK” or that states that every physical component
must have a mass.

ISO 10303 (STEP) [26] is an ISO standard for product manufacturing
information, i.e., how a product is supposed to be produced, but it can be
used for the whole life cycle of a product. Regarding space engineering, the
technical report ECSS-E-TM-10-20A [11] lists what part of the STEP standard
should be used for information exchange between which disciplines. This
regards mostly computer-aided design (CAD) and physical structure contexts
while other parts of the standard, like electronics, are neglected. A rather
simple format to store 3D information is STL (STereoLithographie, also
Standard Triangulation/Tesselation Language) [29], which is supported by most
CAD tools and used for additive manufacturing.

The specification of information exchange between manufacturers and MBSE tools
does not only include technical protocols but also the information on which
data is relevant in which context and what is its semantic meaning. Tailored
modeling languages and tools are required to describe the semantic model of a
spacecraft. Hennig et al. looked into existing languages and tools that can be
used to describe Conceptual Data Models (CDMs). They conclude that none of
them are ideal for this task [15]. In the same year, Ait-Ameur et al.
introduced a special ontology modeling language (PLIB) for engineering in
general [4]. Following their former analysis, Hennig et al. developed a
conceptual data modeling language, SCDML [16], and also an ontology to
describe space system design data [17]. Hoppe et al. also mentioned the
benefits of ontologies and Web Ontology Language (OWL) together with the
Eclipse Modeling Framework (EMF) for the MBSE process [19][18][21]. On top of
that, they built the Semantic Engineering Modeling Framework (SEMF) [20].
MARVL CIP [6] is a platform that aims to support the information exchange
between agencies and manufacturers across the whole life cycle of the
spacecraft.

All these approaches target at the models in the MBSE process itself and
sometimes at the question of how to use the same model across different phases
or how to map between models of different phases. They should be taken into
account to generate a ”product data model” in a way that is compatible to the
existing tools. But none of them can be used directly to model product data.

We looked into the previously mentioned EDS [30] and STEP [26] as potential
carriers of product data. Both address the exchange of data sheet information,
but they either focus on a small topic (EDS) or are used only for a certain
area in practice (STEP—for 3D information). So far, no standards or practices
exist to cover all relevant information for the data exchange between supplier
and customer in the space sector. However, EDS and/or STEP could become a
starting point for the development of a data exchange format for product data,
especially with the planned new definition of the EDS standard [27].

PDF data sheets are meant to describe a product technically but there is no
standard regarding the syntax or semantic of this description. There are
several approaches to extract (semantic) information from data sheets, e.g. by
[7], [3], [5], and [24], but we do not know of an accessible tool that
performs that task reliably.

##  3 Methods

As CubeSats become more common and products for those are already offered in
online shops, we compared the information offered by such shops with the
information required by the above mentioned MBSE tools. As with the MBSE
tools, we focused on parameters for mass and structure. Since the outer
dimensions of CubeSats are restricted by the form factor (1U, 2U, …), we
expected to find similar presentations of the structure parameters between the
different shops. Besides the parameter names we were also interested in the
formats the information were offered in.

To use product information directly in MBSE tools, we see the following
requirements for an exchange format:

  * •

_machine readable_ \- so humans do not have to enter or copy information
manually

  * •

_uniform / standardized_ \- so no transformations between different formats
are necessary

  * •

_automatically comparable_ \- so search for a product that fits certain
requirements becomes easier

  * •

_all values for one product from a single source (optional)_ \- so it is not
necessary to request multiple sources for the information about a single
product

The results of our search and the comparison with parameters at MBSE tools are
discussed in the next section.

##  4 Results

For each of the six CubeSat shops, the formats in which information was
presented are summarized in Table 2. We were looking for information in tables
(or bullet points in the format $<$key$>$:$<$value$>$), PDF data sheets, and
STEP files. Shop B offered information mostly in free text222that is, running
text, as opposed to bullet points, tables, or figures, little in tables, and
PDF or STEP files only upon request. Shop E offered parameters only in free
text or in text bullet points like ”Mass is ca. XYg”; Shop D offered only very
few bullet points in the format $<$key$>$:$<$value$>$ and STEP files only
after login. None of the shops offered an API (application programming
interface) to read the data—we asked all of them via e-mail. One of the shops
is working on an API to request the PDF data sheets, but no machine-readable
data.

Shop | A | B | C | D | E | F
---|---|---|---|---|---|---
table on website | X | (X) | X | X | - | (X)
PDF data sheet | X | - | X | X | X | X
STEP file | X | - | - | X | X | (X)
Table 2: Formats of Information Presentation at CubeSat Shops

For each shop, we picked the first search result for ”solar panel” to compare
the parameters presented directly by the shops (not in the data sheets of the
manufacturers).

The mass and structure parameters of each shop are compared in Table 3; Shops
B, E, and F did not provide any mass or structure related parameters in a
table or table-like format.

Shop | A | C | D
---|---|---|---
Mass | Mass | Very low solar cell mass | Mass (exact mass
Parameters |  | Side solar panel weight | depends on configuration)
Structure | Nominal thickness | Solar cells thickness | Panel Thickness
Parameters | Dimensions (PCB | PCB Thickness |
| \+ Solar Cells) |  |
Table 3: Mass and structure parameters at CubeSat shops. Both parameters in
Shop D were followed by lists with the actual values.

Even though our sample of CubeSat shops is small, it becomes obvious that
neither between the different shops nor between the shops and MBSE tools the
same parameter names are used. ”Mass” and ”thickness” are reoccurring names,
but the additional texts at the shops (see Table 3) make it clear that the
semantics of those names vary (e.g., ”thickness” sometimes refers to the cells
only, sometimes to cells plus PCB).

##  5 Prototype: Product Information in MBSE Tool

We built a small prototype to make product information available in MBSE
tools, including a plugin for the DLR in-house MBSE tool Virtual Satellite.
Figure 1 shows an overview of the architecture.

Manufacturers [Software System] Contains product data; accessible via an API
Engineers [Person] Crawler [Container] Requests data from supplier API and
creates or updates database entries Database [Container] Storage of product
data according to our data model MBSE Tool [Software System] Tool to
collaboratively create the model of a spacecraft requestproductsupdate oradd
entrysearchmatchingentriesuses Product Data Hub
---
[ Software System]
Software System: | one standalone software application
---|---
Container: | data storage with an interface to store, update, delete,
| and search data
Person: | a human being
Figure 1: Architecture of Product Data System

The main component is the Product Data Hub (PDH) that consists of a crawler
and a database. The database stores product information independently of
manufacturers; this bridges temporary unavailability of single shops and
provides a single access point for the MBSE tools. The database is filled by a
crawler that request the manufacturers regularly and updates or adds entries.
Here, we need only one crawler because all manufacturers provide their data in
the same format. To request data from actual manufacturers (given they provide
an API) would require different crawlers since currently there is no uniform
data exchange format all manufacturers share.

The second component of the prototype is a manually created mockup of
manufacturers that provides product information in a machine-readable way via
http in a JSON (JavaScript Object Notation, a language-independent data
format)) format. The data format is the same for all manufacturers.

The last component of the prototype is a plugin for Virtual Satellite that
enables the users to do three different things:

  1. 1.

Add an _Equipment_ with the values of a product in the PDH

  2. 2.

Update an _Equipment_ with values from a product in the PDH

  3. 3.

Save an _Equipment_ as product to the PDH

To add a new _Equipment_ with the values of a product in the PDH, the user
browses a product list provided by the plugin and selects one with fitting
values (see Figure 2). The new _Equipment_ can then be used as any _Equipment_
in Virtual Satellite—changes at the _Equipment_ have no effect on the product
from which the _Equipment_ was created.

Figure 2: Screenshot of Product Selection Dialog in Virtual Satellite

The update function is rather a search function: The user specifies an
_Equipment_ and the plugin looks for products in the PDH that fit this
specification within a range of uncertainty for all values. The range of
uncertainty can be defined by the user. The user selects one product that fits
the pre-specified _Equipment_ and all values from the product are taken over
to the _Equipment_.

The last function is to add an _Equipment_ as product to the PDH. That way the
user can for example define templates (e.g. for a ”small battery”) for which
no real product from a manufacturer exists. This function can also be used to
add values for products described by PDF data sheets manually.

##  6 Conclusion and Outlook

The comparison of parameters at MBSE tools and CubeSat shops shows that there
is neither a set of parameters that is supported by everyone nor a common
understanding of the semantics of the provided parameters.

Our prototype shows how product information can be exchanged between
manufacturers and MBSE tools in principle. It also shows that for machine
readable exchange of product information between manufacturers and MBSE tools
a standardized format is needed that includes also a semantic description for
each parameter. Our prototype only worked because we had control over all
parts—to expand the concept, every party needs a common understanding of the
exchanged information. We think that over the next years it should be possible
to reach such a common understanding within the space industry, at least for
parts of the information to exchange. The attempt at ESA to find a new and
broader standard for EDS goes in that direction.

In the future we want to look more into semantic descriptions of space
products and also in different phases of the spacecraft life cycle, since so
far our focus was on the early planning phase.

## References

  * [1] Designing the Future of Your Complex Engineering Projects. https://www.rheagroup.com/cdp, accessed: 2018-05-29
  * [2] Space project management - Project planning and implementation (2009)
  * [3] Agrawal, R., Ho, H., Jacquenet, F., Jacquenet, M.: Mining Information Extraction Rules from Datasheets Without Linguistic Parsing. In: Ali, M., Esposito, F. (eds.) Innovations in Applied Artificial Intelligence. pp. 510–520. Springer Berlin Heidelberg, Berlin, Heidelberg (2005)
  * [4] Ait-Ameur, Y., Baron, M., Bellatreche, L., Jean, S., Sardet, E.: Ontologies in engineering: the OntoDB/OntoQL platform. Soft Computing 21(2), 369–389 (Mar 2015). https://doi.org/10.1007/s00500-015-1633-5
  * [5] Barkschat, K.: Semantic Information Extraction on Domain Specific Data Sheets. In: Presutti, V., d’Amato, C., Gandon, F., d’Aquin, M., Staab, S., Tordai, A. (eds.) The Semantic Web: Trends and Challenges. pp. 864–873. Springer International Publishing, Cham (2014)
  * [6] Bieze, M.: MARVL - Model-based requirements-verification lifecycle. Software Systems Division (TEC-SW) and Data Systems Division (TEC-ED) Final Presentation Day - May 2018
  * [7] Castellanos, M., Chen, Q., Dayal, U., Hsu, M., Lemon, M., Siegel, P., Stinger, J.: Component Advisor: A tool for automatically extracting electronic component data from Web datasheets. on Reuse of Web-based Information p. 31 (1998)
  * [8] Eisenmann, H., Cazenave, C.: Evolving a classic SRDB into an engineering database. In: 6th International Workshop on Systems and Concurrent Engineering for Space Applications (SECESA). pp. 8–10 (2014)
  * [9] Eisenmann, H., Basso, V., Fuchs, J., De Wilde, D.: ESA virtual spacecraft design. In: Proceedings of the 4th International Workshop on System & Concurrent Engineering for Space Applications (SECESA) (2010)
  * [10] ESA-ESTEC: Space engineering - engineering design model data exchange (ecss‐e‐tm‐10‐25a). techreport ECSS‐E‐TM‐E‐10‐25A, ECSS (2010)
  * [11] ESA-ESTEC: Space engineering - product data exchange (ecss‐e‐tm‐10‐20a). techreport ECSS‐E‐TM‐E‐10‐20A, ECSS (2010)
  * [12] ESA-ESTEC: Space engineering - space system data repository (ecss-e-tm-10-23a). techreport ECSS-E-TM-10-23A, ECSS (2011)
  * [13] Ferreira, I., de Koning, H.P., Gerene, S., Pickering, A., Vennekens, J., Beyer, F.: Open Concurrent Design Tool: ESA Community Open Source Ready to Go! 6th International Workshop on System & Concurrent Engineering for Space Applications (SECESA) (Oct 2014)
  * [14] Fischer, P.M., Lüdtke, D., Lange, C., Roshani, F.C., Dannemann, F., Gerndt, A.: Implementing Model-Based System Engineering for the Whole Lifecycle of a Spacecraft. CEAS Space Journal 9(3), 351–365 (Jul 2017). https://doi.org/10.1007/s12567-017-0166-4
  * [15] Hennig, C., Eisenmann, H., Viehl, A., Bringmann, O.: On languages for conceptual data modeling in multi-disciplinary space systems engineering. In: 2015 3rd International Conference on Model-Driven Engineering and Software Development (MODELSWARD). pp. 384–393 (Feb 2015)
  * [16] Hennig, C., Hoppe, T., Eisenmann, H., Viehl, A., Bringmann, O.: SCDML: A language for Conceptual Data Modeling in Model-based Systems Engineering. In: 2016 4th International Conference on Model-Driven Engineering and Software Development (MODELSWARD). pp. 184–192 (Feb 2016)
  * [17] Hennig, C., Viehl, A., Kämpgen, B., Eisenmann, H.: Ontology-based design of space systems. In: Lecture Notes in Computer Science, pp. 308–324. Springer International Publishing (2016). https://doi.org/10.1007/978-3-319-46547-029
  * [18] Hoppe, T., Eisenmann, H., Viehl, A., Bringmann, O.: Digital Space Systems Engineering through Semantic Data Models. In: 2017 IEEE International Conference on Software Architecture (ICSA). IEEE (Apr 2017). https://doi.org/10.1109/icsa.2017.35
  * [19] Hoppe, T., Eisenmann, H., Viehl, A., Bringmann, O.: Guided systems engineering by profiled ontologies. In: 2017 IEEE International Systems Engineering Symposium (ISSE). IEEE (Oct 2017). https://doi.org/10.1109/syseng.2017.8088255
  * [20] Hoppe, T., Eisenmann, H., Viehl, A., Bringmann, O.: SEMF – the semantic engineering modeling framework - bringing semantics into the eclipse modeling framework for space systems engineering. In: Proceedings of the 5th International Conference on Model-Driven Engineering and Software Development. SCITEPRESS - Science and Technology Publications (2017). https://doi.org/10.5220/0006118702930301
  * [21] Hoppe, T., Eisenmann, H., Viehl, A., Bringmann, O.: Shifting from data handling to knowledge engineering in aerospace industry. In: 2017 IEEE International Systems Engineering Symposium (ISSE). IEEE (oct 2017). https://doi.org/10.1109/syseng.2017.8088312
  * [22] Jahnke, S.S., Martelo, A.: Special characteristics of concurrent engineering studies dealing with cubesatmissions and their impact on the CE process. In: 7th International Systems & Concurrent Engineering for Space Applications Conference (SECESA) (2016)
  * [23] Lange, C., Grundmann, J.T., Kretzenbacher, M., Fischer, P.M.: Systematic reuse and platforming: Application examples for enhancing reuse with model-based systems engineering methods in space systems development. Concurrent Engineering 26(1), 77–92 (2018)
  * [24] Murdaca, F., Berquand, A., Kumar, K., Riccardi, A., Soares, T., Gerené, S., Brauer, N.: Knowledge-based information extraction from datasheets of space parts. In: 8th International Systems & Concurrent Engineering for Space Applications Conference (September 2018), https://strathprints.strath.ac.uk/65764/
  * [25] NASA: NASA Systems Engineering Handbook. US National Aeronautics and Space Admin (2008)
  * [26] Pratt, M.J.: Introduction to ISO 10303—the STEP standard for product data exchange. Journal of Computing and Information Science in Engineering 1(1), 102 (2001). https://doi.org/10.1115/1.1354995
  * [27] Prochazka, M.: Electronic Data Sheets at ESA: Current Status and Roadmap. Flight Software Workshop 2017 (Dec 2017)
  * [28] Ramos, A.L., Ferreira, J.V., Barcelo, J.: Model-Based Systems Engineering: An Emerging Approach for Modern Systems. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews) 42(1), 101–111 (2012). https://doi.org/10.1109/tsmcc.2011.2106495
  * [29] Roscoe, L.E.: StereoLithography Interface Specification. Tech. rep., 3D Systems, Inc. (Oct 1989)
  * [30] (SANA), S.A.N.A.: Spacecraft Onboard Interface Services Electronic Data Sheets and Dictionary of Terms. https://sanaregistry.org/r/sois (May 2017), accessed: 2018-02-19