# Swarm Characteristics Classification
Using Neural Networks

Donald W. Peltier III, Isaac Kaminer, Abram Clark, Marko Orescanin Authors are
with the Naval Postgraduate School, Monterey, CA, 93943.D. Peltier is with the
Department of Mechanical & Aerospace Engineering.I. Kaminer is with the
Department of Mechanical & Aerospace Engineering.A. Clark is with the
Department of Physics.M. Orescanin is with the Department of Computer Science.

(March 26, 2024)

###### Abstract

Understanding the characteristics of swarming autonomous agents is critical
for defense and security applications. This article presents a study on using
supervised neural network time series classification (NN TSC) to predict key
attributes and tactics of swarming autonomous agents for military contexts.
Specifically, NN TSC is applied to infer two binary attributes - communication
and proportional navigation - which combine to define four mutually exclusive
swarm tactics. We identify a gap in literature on using NNs for swarm
classification and demonstrate the effectiveness of NN TSC in rapidly deducing
intelligence about attacking swarms to inform counter-maneuvers. Through
simulated swarm-vs-swarm engagements, we evaluate NN TSC performance in terms
of observation window requirements, noise robustness, and scalability to swarm
size. Key findings show NNs can predict swarm behaviors with 97% accuracy
using short observation windows of 20 time steps, while also demonstrating
graceful degradation down to 80% accuracy under 50% noise, as well as
excellent scalability to swarm sizes from 10 to 100 agents. These capabilities
are promising for real-time decision-making support in defense scenarios by
rapidly inferring insights about swarm behavior.

###### Index Terms:

swarms, onboard intelligence, fleet coordination, uav interactions

##  I Introduction

The advent of autonomous vehicles in military and civilian sectors presents
new challenges and opportunities. Military engagements involving multiple
autonomous systems, in particular, have become increasingly significant in
various domains, including air, sea, and land operations. The United States
Department of Defense (DoD) recognizes the importance of developing strategies
to defend against groups of autonomous enemy agents, commonly referred to as
swarms [1]. In parallel, the increasing deployment of autonomous agents in
civilian applications, notably in transportation, underscores a similar need
for advanced tracking and conflict avoidance techniques. This convergence of
military and civilian interests highlights the need for sophisticated methods
capable of real-time characterization and behavior prediction for scenarios
involving numerous autonomous agents.

This need is particularly acute when dealing with swarming tactics, where
individual agents collaborate to exhibit complex collective behaviors. Prior
studies have explored machine learning applications in classifying
trajectories, yet there is a gap in research focusing on real-time inference
of individual agent attributes and overall swarm tactics [2, 3, 4].

Central to addressing these challenges is the field of Time Series
Classification (TSC), which has emerged as a crucial tool for understanding
the temporal dynamics of swarming agents. TSC facilitates the prediction of
categorical labels for time-ordered data, a capability vital for interpreting
the actions of autonomous swarms. The adoption of machine learning neural
network (NN) models like Multi-layer Perceptrons, Convolutional Neural
Networks (CNN), Long-Short Term Memory Recurrent Neural Networks (LSTM), and
Transformers with attention mechanisms has shown promise in TSC. However, the
application of these models specifically to swarm behavior remains an
uncharted area of exploration [5, 6, 7, 8, 9, 10, 11, 12, 13].

This study introduces an approach using supervised neural network TSC to
predict communication and navigation attributes of swarming agents rapidly. By
focusing on these attributes, our research aims to discern swarm tactics over
brief observation windows, addressing the critical need for real-time analysis
in defensive scenarios. Our methodology, tested in simulated swarm-on-swarm
engagements, is designed to offer insights into model performance in terms of
accuracy, speed, noise tolerance, and scalability, thereby contributing
significantly to the understanding of autonomous swarm dynamics.

The key contributions of this research are threefold: (1) it demonstrates the
application of NN TSC in predicting the behavior of swarming autonomous
agents, (2) it evaluates the performance of various neural network models in
this context, and (3) it presents real-time swarm intelligence gathering that
balances model accuracy with operational constraints like speed and noise
tolerance.

##  II Methodology

###  II-A Scenario & Notation

Swarm on swarm simulations were conducted in Matlab to generate data for NN
TSC. As shown in Figure 1 the simulation scenario features an attacking swarm
of enemy agents starting in the upper right, shown in red, that is perturbed
by a defending swarm of friendly agents starting in the lower left, shown in
blue.

Figure 1: Simulation example showing velocity vectors at initialization time =
0.

In this scenario, the defenders are weaponless and aim to motivate the
attacking swarm to maneuver, thereby revealing their characteristics.
Conversely, the attacking swarm employs one of four tactics. Each tactic, a
combination of two binary attributes, is represented in Figure 2, with each
attribute being either active (1) or inactive (0). Tactics are numerically
labeled (0, 1, 2, or 3), and also correlate to a specific attribute
combination ([0,0], [0,1], [1,0], or [1,1]). During each simulation, all
attacker’s attributes and tactics are identical and remain constant; there is
no switching of tactics.

Figure 2: Two binary attacker attributes combine to create four mutually
exclusive swarm tactics.

Our goal is to classify these tactics and attributes using supervised NN TSC.
From a computational complexity perspective, the addition of each binary
attribute exponentially increases the number of tactics
($\text{Tactics}=2^{\text{Attributes}}$), adding to the classification
complexity. Thus, in this foundational study, we focus on two pivotal
attributes: communication and proportional navigation [14]. These attributes
were identified as key performance indicators in prior research, including the
Aerial Combat Swarms competition [15, 16] and the Service Academies Swarm
Challenge [17].

For this investigation, we consider a two-dimensional (2D) battlespace. The
number of attackers and defenders are denoted by $N_{A}$ and $N_{D}$,
respectively. The positions and velocities of each agent in 2D space are
characterized by their $x$ and $y$ components, $P_{x}$, $P_{y}$, $V_{x}$, and
$V_{y}$. Each agent is indicated by a subscript: $i$ for attackers and $j$ for
defenders. The progression of the scenario is parameterized by time, $t$.
Therefore, an attacker’s position and velocity at any time $t$ can be
expressed as $[P_{x}(t)_{i},P_{y}(t)_{i},V_{x}(t)_{i},V_{y}(t)_{i}]$. These
time series data serve as the multivariate input for training and evaluating
the machine learning models. Specifically, we use only the attacker positions
and velocities as input data.

The following assumptions are made:

  1. 1.

All attackers use identical tactics/attributes.

  2. 2.

No tactics/attributes switching.

  3. 3.

All attacker full trajectories are known.

  4. 4.

If trajectories overlap, agents are distinguishable; no shuffling of data
order.

  5. 5.

No collision if agents overlap; collision avoided using third-dimension (3D)
separation.

For the initial study, the defensive strategy is randomized. Each defensive
agent has a unique, randomly assigned constant velocity $V_{j}$ and heading
$\theta_{j}$, constrained within specific bounds. The defender velocity
$V_{j}$ is kept between 5-40% of the attacker speed, providing the attackers a
speed advantage to prevent endless chases and shorten engagement time.
Additionally, the defender heading $\theta_{j}=\text{Uniform}(0,\pi/2)$ is
bounded between North and East to expedite swarm interaction. The initial
position for each defender is set near the origin with a spread parameter
$S_{D}=\text{Uniform}(0,5)$, influencing initial dispersion.

In contrast to the fixed trajectories of defenders, attacker dynamics are
modeled through Newton’s second law. The force on each agent comprises a
thrust force directed towards a virtual leader, and a drag-like term limits
the attacker’s velocity. Attacker $i$ equation of motion is given by (1).

$m_{i}\ddot{\mathbf{r}}_{i}=K_{i}\frac{\mathbf{r}_{i}-\mathbf{r}_{vl}^{(i)}}{|\mathbf{r}_{i}-\mathbf{r}_{vl}^{(i)}|}-B_{i}\dot{\mathbf{r}}_{i}$
(1)

Here, subscripts or superscripts $i$ refer to attacker $i$, dots denote time
derivatives, $m$ is the inertial mass, $K$ is a thrust force magnitude, $B$ is
damping parameter, $\mathbf{r}$ is position, and $\mathbf{r}_{vl}$ is the
position of a virtual leader (aim point). We note that $K/B=1$ sets the
typical velocity scale and $m/B=10$ sets a time scale for acceleration up to
this velocity, indicating that it takes 10 time steps for attackers to reach
the maximum velocity. These equations represent a simplified dynamics model,
but are sufficient to generate adversarial swarming engagements that are the
focus of this paper.

Equation (1) represents a system of $N_{A}$ uncoupled second-order ordinary
differential equations. At each time step all attacker accelerations are
calculated using this equation, based on all virtual leader positions, and we
then numerically integrate using a modified velocity Verlet algorithm with a
time step $\Delta t$, which we choose as sufficiently small that it does not
affect our results. Attacker initial velocities and accelerations are zero,
and initial positions include a spread parameter $S_{A}=\text{Uniform}(0,5)$
influencing random dispersion around a starting point centroid to the
Northeast of the defenders at a range of $40$ distance units in both $x$ and
$y$ directions.

As introduced earlier the attacking agents followed one of four tactics
(Greedy, Greedy+, Auction, Auction+) where each tactic is a binary combination
of two attributes (Comms and ProNav), which will be explained and formally
presented below.

The proportional navigation (ProNav) attribute determines algorithm used to
calculate each attacker aim point, or virtual leader $\mathbf{r}^{(i)}_{vl}$.
If this attribute is inactive, each attacking agent uses pursuit navigation.
For pursuit navigation, current target position is used for
$\mathbf{r}^{(i)}_{vl}$, which typically results in a tail-chase for moving
targets because the aim point is guaranteed to lag the target at future time.

Conversely, if the ProNav attribute is active, each attacking agent uses a
proportional navigation approximation where the constant velocity vector of
the targeted defender and the maximum velocity vector of the attacker are used
to calculate an intercept point which is assigned to $\mathbf{r}^{(i)}_{vl}$.
This intercept point is calculated every time step, such that if an attacker’s
velocity is not currently at its maximum speed, then $\mathbf{r}^{(i)}_{vl}$
will change with time. As the attacker’s velocity approaches its limiting
maximum velocity, $\mathbf{r}^{(i)}_{vl}$ changes become very small over time.
Regarding notation, the two tactics using ProNav are appended with a plus sign
to indicate improvement (Greedy+ and Auction+), as they are more efficient
than their pursuit tactic counterpart.

The communication (Comms) attribute refers to an agents ability to communicate
with other team members, and is considered linked to target assignment
technique employed by the attackers. More specifically, it’s typical for a
swarm of agents that can communicate to conduct target allocation, or
auctioning, to ensure each agent is assigned a different target for
efficiency. Tactics with the Comms attribute activated are denoted using the
prefix Auction. However, if communications are not available, the attackers
would conduct an inefficient attack where each agent engages the closest
target without deconflicting target allocation, resulting in multiple agents
targeting the same target. Tactics with the Comms attribute inactive are
represented with the prefix Greedy.

Targets for Greedy attackers are assigned based purely on attacker-defender
pairwise separation, summarized by Algorithm 1. Each defender is assigned as
target for the closest attacker at that instant in time. This process is
repeated such that each defender is targeted by the closest attacker to its
position.

Algorithm 1 GREEDY Targeting Algorithm

1:list of defenders, list of attackers

2:assignments of attackers to defenders

3:for each timeStep do

4: for each defender in defenders do

5: Find closest attacker to defender

6: Assign this attacker to defender

7: end for

8:end for

Conversely, targets for attackers using Auction are chosen globally according
to Algorithm 2. Defenders are assigned as targets to the closest unassigned
attacker at that instant in time. This process is repeated such that each
defender is targeted by the attacker closest to its position from the pool of
unassigned attackers. In the case where there are more attackers than
defenders, leftover unassigned attackers target the closest defender. Thus,
multiple attackers can target the same defender, but only in the case where
there are more attackers than defenders. This highlights an important aspect:
after each defender is removed the Auction tactics will increasingly resemble
the Greedy tactics, as attackers double-up on defenders. This nuance will be
discussed further in the results section. Additionally, we note that such a
global algorithm requires perfect communication among all defenders or perfect
knowledge of the entire scenario, such that each defender can run the
algorithm independently and know what all other defenders would be doing.

Algorithm 2 AUCTION Targeting Algorithm

1:list of defenders, list of attackers

2:assignments of attackers to defenders

3:for each timeStep do

4: Initialize unassignedAttackers to all attackers

5: for each defender in defenders do

6: Find closest unassignedAttacker

7: Assign this attacker to defender

8: Remove attacker from unassignedAttackers

9: end for

10: if unassignedAttackers is not empty then

11: for remaining unassignedAttackers do

12: Find closest defender to this attacker

13: Assign attacker to the defender

14: end for

15: end if

16:end for

For both Auction and Greedy, the targeting process is repeated at every time
step, meaning target assignments can (and do) change before the current target
is eliminated. This creates a small but important difference between Greedy
and Greedy+. As seen in Figure 3, specifically comparing Greedy and Greedy+ in
the 40 and 58 time step frames, Greedy+ formations increasingly tighten as
they travel due to an aim point that shifts less than Greedy aim points, which
reduces last minute target shifting (and overshoot).

Unlike the weaponless defenders, the attackers are able to eliminate and
remove defenders from the simulation based on a maximum weapons range $R=1$.
We track each defenders binary survival $S_{j}$ at time $t$ according to the
attacker-defender pairwise survival function shown in (2). Each simulation
instance begins with all defenders alive ($S_{j}=1$), and then defenders are
removed ($S_{j}=0$) during the course of the engagement based on interactions
with enemy agents.

$S_{j}(t)=\prod_{i}^{N_{A}}\begin{cases}0&\text{, if
}|\mathbf{r}_{j}-\mathbf{r}_{i}|<R\\\ 1&\text{, if
}|\mathbf{r}_{j}-\mathbf{r}_{i}|\geq R\end{cases}.$ (2)

Figure 3 shows a simulation example comparing the four tactics over time. It’s
easily seen that regardless of navigation attribute, both Greedy tactics
initially target the closest defender, while the two Auction tactics begin to
spread out sooner as they divide the defenders amongst themselves. Note that
20 and 58 time steps were purposefully chosen, as will be discussed in section
II-C, while the 40 time step was included to highlight the distinctly
different swarm motions.

Figure 3: Simulation visualization showing all four tactics (Greedy, Greedy+,
Auction, Auction+) with identical initialization at various engagement time
steps; agent velocity vectors shown.

###  II-B Supervised Neural Network Time Series Classification

In supervised NN training, the goal is to construct an accurate predictive
model by learning from a dataset comprised of two tensors (eg.
multidimensional vectors): the input data or features, and the true output
known as labels. The process hinges on the NN’s ability to predict outputs
from the input features. The core objective during training is to minimize the
disparity between the predicted outputs and the true labels. This is
accomplished by iteratively adjusting the NN parameters to reduce prediction
errors. The underlying mathematics of NN training are well documented [18, 19,
20, 21] and involves concepts such as gradient descent, backpropagation, and
optimization algorithms. These mathematical formulations are crucial for
understanding how a NN learns from data and how it updates its parameters in
response to the calculated gradients from the cost function.

In the context of NN TSC, the features are given by time series data. Time
series data can be univariate, where the dataset is a one-dimensional vector
with each element indexed by time. This could represent, for example, a swarm
agent’s position at each time step. In contrast, multivariate time series data
involve a tensor with multiple dimensions, where each dimension represents a
different variable that changes over time. In this study, multivariate model
inputs include attacking agent 2D position and 2D velocity.

A fundamental aspect of NN classification is the differentiation between two
types of classification tasks:
\- Multiclass classification deals with problems where each instance is to be
classified into one of three or more mutually exclusive classes. In this study
classifying the swarm tactic is a multiclass task.
\- Multilabel classification allows for the association of each instance with
multiple binary labels simultaneously. In this study classifying the attacking
agent attributes is a multilabel task.

Multihead classification refers to a model architecture where the NN has
multiple output layers, or “heads,” each responsible for a different
prediction tasks. This can be advantageous when there are distinct types of
outputs to predict from the same set of features, such as classifying both
agent attributes and swarm tactics.

An important facet that Time Series Classification (TSC) adds is the output
format [18]. Many TSC NN models are only capable of producing vector output,
which is a single prediction at the end of the time series. However, recurrent
models and transformers specifically designed for sequential data can produce
sequence output, providing predictions for each time step.

To gauge the performance of a NN and guide its training, cost functions and
metrics are employed. The cost function, also known as loss function,
quantifies the difference between the predicted values and the true labels.
The goal during training is to minimize this cost function. The multiclass
loss function used was categorical cross entropy and the multilabel loss
function used was binary cross entropy.

Metrics, on the other hand, are used to evaluate the model’s performance
according to specific criteria, such as accuracy, precision, recall, or F1
score, which can be more interpretative than raw cost values. Accuracy, which
is the percentage of correct predictions, is intuitively easy to understand.
However, if the possible classifications are not equally represented (ie. more
Greedy instances then Auction+ instances), then metrics such as precision,
recall, and their representative combination F1 score, provide a more accurate
reflection of model performance. Fortunately, in this study all possible
labels (tactics and attributes) are equally represented, so accuracy is the
primary metric discussed. Additionally, validation loss is also used as a
primary metric as it estimates a model’s ability to generalize, or predict, on
data is has never seen.

For noise impact analysis adjusted accuracy $Acc_{A}$, which is accuracy
shifted for random guess accuracy, is used for a fair comparison, as random
accuracy is different for four and two labels. This is based on equally
represented random accuracy $Acc_{R}$ equaling 0.25 for four tactics, or 0.50
for two attributes. Adjusted accuracy (3) is used to calculate a normalized
error rate (4), which ranges from 0 for perfect accuracy to 100 for random
accuracy.

$Acc_{A}=\text{Accuracy}-Acc_{R}$ (3)

$\text{Normalized Error Rate}=1-\frac{Acc_{A}}{1-Acc_{R}}$ (4)

###  II-C Experimental Setup

The experimental approach entailed a structured three-step methodology.
Initially, the process began with constructing various neural network models.
Next, a baseline dataset was generated by using a sensitivity analysis to
understand the dataset’s most significant adjustable parameters impact on
model performance. Finally, model training involved establishing a baseline
for initial comparison, and thereafter tuning the models to minimize
validation loss and maximize accuracy.

Machine learning models were developed using Python packages including
TensorFlow, Scikit Learn, Numpy, and Keras Tune. Model input data used for
this research was synthetically generated using Matlab swarm-on-swarm
engagement simulations originally developed at Naval Postgraduate School and
only included three tactics [22]. An additional tactic (Greedy+) was created
for this research. Lastly, code development was conducted using Naval
Postgraduate School high power computing
resources111https://github.com/DWPeltier3/Swarm-NN-TSC.

####  II-C1 Build Models

The models considered include those listed in Section I. For models capable of
both vector and sequence output (LSTM and TR), both outputs were tested for
each model and annotated with a “V” or “S” postfix (ie. TRV and TRS for
transformer). Additionally, traditional non-NN machine learning classifiers
including Random Forest and Logistic Regression were evaluated for comparison.
For in-depth model descriptions and diagrams of these well documented NN
models, numerous resources are available [18, 10, 5, 6, 8].

Pertinent to this discussion are two benefits of certain model types and
outputs. First, all models except the Fully Connected model embed, or
transform, the inputs into a preset-dimensional representation, meaning that
the exact input dimensions are not important. This allows any input size,
accounting for different time series lengths or different number of swarm
agents and features. Second, an intriguing potential benefit of sequence
output is where tactics switching during operations could be identified.

Estimating that the relationships learned for multiclass and multilabel
classification were similar, and therefore NN model weights would be similar,
a multihead (MH) classifier was constructed for each NN type. This allowed one
model to output both the tactic prediction and attribute predictions
simultaneously. Furthermore, as will be discussed in the results section,
because the attribute predictions were more accurate than the tactic
prediction, attribute prediction loss was weighted heavier (80%), and the
attribute predictions were concatenated as additional features during the
final stage of the tactic prediction. This architecture resulted in improved
performance, as will be discussed. Figure 4 shows the basic concept of the MH
classifier.

Figure 4: Multihead classifier.

A total of 42 model configurations were examined. These configurations came
from five NN architectures capable of vector output (FC, CNN, FCN, LSTMV, and
TRV), and two architectures capable of sequence output (LSTMS and TRS),
equating to seven architectures examined (5 vector and 2 sequence).
Furthermore, each of these seven architectures were evaluated at two different
observation window time step lengths, 20 and 58 (“full”), equating to 14
models examined. Lastly, three output types were used: multiclass (MC),
multilabel (ML), and multihead (MH = MC & ML); thus all 14 models were trained
on 3 output types, equaling 42 configurations.

####  II-C2 Generate Dataset

A sensitivity analysis was conducted on a typical two hidden layer Fully
Connected NN classifier to correlate key data generation parameters to model
performance, as shown in Figure 5, in order to establish a baseline input
dataset for model comparison during training. Parameters varied included
number of agents, number of engagements (also known as instances), and
observation window time steps. Table I shows the finalized baseline dataset
parameters. It should be noted that the second best line in Figure 5, 10v10,
was chosen to allow a buffer for possible improvement above 98% accuracy.
Lastly, the noticeable performance spike at 20 time steps led to testing the
models at 20 time steps in addition to the full 58 time steps.

Figure 5: Data generation parameters varied to develop baseline dataset for model comparison. TABLE I: Baseline Dataset Parameters Parameter | Details
---|---
$N_{D}$ vs. $N_{A}$ | 10 vs. 10
Instances | 4800 total = 1200 per tactic
Time Steps | 58
Training Split |  60% total (80% training) 2880 total = 720 per tactic
Validation Split |  15% total (20% training) 720 total = 180 per tactic
Test Split |  25% total 1200 total = 300 per tactic

The generation of the dataset involved several steps to ensure features and
labels were correctly sized for each specific model input and output. The
dataset was initially created using a Numpy array, and then converted into a
TensorFlow dataset, which accelerated model training. The features were stored
in a 3D tensor format given by [batch, time, feature], and the labels were
stored in a similar format for sequence output [batch, time, label]. However,
for the vector output, the labels were in a 2D tensor format [batch, label].

##### Features

Attacker trajectory data was generated in Matlab, ensuring equal number of
engagement instances for each tactic to avoid bias. Next, the data was
imported into Python as a Numpy array, which required uniform time lengths.
Therefore, all instance time lengths were truncated to the shortest instance
time length of 58 steps. Following this, the features were processed following
standard neural network data preparation steps including splitting the data
into training, validation, and test sets, shuffling for randomness, and
scaling the data for normalization, which accelerates gradient decent
optimization. The final step was to reshape the data as required. For example,
if less than 58 time steps were used (eg: 20 time steps would shorten all
instances), or if a Fully Connected NN was used, which required flattened 1D
input for each instance.

An interesting and important aspect of this study is that not all time steps
from each engagement were used. As noted above the feature array was uniform
across dimensions for simplicity. Though it is possible to import non-uniform
(ragged) time series data with varying engagement time lengths, it requires
significantly longer NN training times. More importantly, this study wanted to
use initial attacker actions during engagement to make the classification.
This was for two reasons. First, the most likely scenario is one where the
classification is desired quickly. Second, it’s hypothesized that towards the
end of engagements all tactics would appear similar as defenders are
eliminated and attackers team up on remaining defenders, which would lead to a
loss of meaningful information encoded in the NN model. Figure 6 shows the
statistical break down of generated engagement time lengths, which highlights
that 58 time steps is approximately half the mean engagement time of 133 time
steps.

Figure 6: Histogram of time lengths for all generated engagements. All
engagements were truncated to the shortest length (58).

Swarm size scalability analysis required additional datasets with more agents.
Datasets were created using 25v25, 50v50, 75v75, and 100v100 agents. For these
larger swarm datasets, the number of engagement instances and dataset split
percentages shown in Table I were used for consistency. However, the shortest
engagement instance varied between 62 and 64 time steps, and the mean
engagement length varied between 124 and 144 time steps. When compared to the
10v10 dataset, these ratios of shortest engagement to mean engagement length
remained approximately constant providing a fair comparison as swarm size
increased.

For noise impact analysis, we augmented our 10v10 dataset by adding zero mean
Gaussian white noise to the input features. Recall that the first half of the
features are positions, and the second half of the features are velocities,
with position and velocity characteristic lengths equal to 40 and 1
respectively. To assess the impact of varying noise levels, we adjusted the
noise scaling factor from 1 to 50, which represents the percentage of each
feature characteristic length that becomes the noise standard deviation. This
method allows us to introduce varying levels of noise into our dataset to test
the resilience and performance of the neural network models under different
noise conditions.

##### Labels

Each engagement instance was given a numerical label representing one of the
four categorical tactics, and if the output type included multilabel the
labels were adjusted to match the attribute combinations, as shown in Figure
2. For example, the auction tactic label [2] would equate to an attribute
label of [1,0], indicating “Comms” are on, but “ProNav” is off. Furthermore,
if the output was multihead, then both tactic and attribute labels were
required, leading to each instance having two labels, one for each output
head. Finally, if the output length was sequence, a label was required for
each time step. Therefore, each instance label was replicated equal to the
number of time steps characterizing the dataset being used.

##### Data Visualization

Only attacker position and velocity were used as input data. Feature
engineering other potential inputs such as separation distance, velocity
gradient, and using defender information were omitted to maintain the
simplicity of this baseline research. Figure 7 shows the normalized position
and velocity features for one agent during one engagement for each tactic.

Figure 7: All features (Px,Py,Vx,Vy) versus time for one attacker shown for
each tactic.

Furthermore, Figure 8 shows 2D and 3D Principle Component Analysis (PCA)
representations of the 40 input features (ie. 10 agents $\times$ 4 features
per agent), allowing visualization of all features across all engagements.
Principle Component Analysis representations require 2D input, and were
generated using input tensor of shape [batch * time, features], which
maintained feature separation. Additionally, this input representation shows
time steps along principal component 1 axis, highlighting feature spread at
each time step, allowing comparison amongst the four tactics at each time
step. Figure 8 highlights that the “smarter” tactics (Auction and Auction+),
which represent more efficient attack strategies and generally have shorter
engagements lengths, are less spread out and more tightly grouped.

Figure 8: Principle component 2D and 3D visualizations of the high dimensional
input features. Top: 20 time steps. Bottom: 58 time steps.

####  II-C3 Train Models

Initial model training used the baseline dataset and hyperparameters (HP)
which showed typical performance in previous studies [10]. A small amount of
manual tuning was performed to gauge initial impact from certain HP. This
resulted in using kernel initialization technique HeNormal and using no kernel
regularization for all models [18]. Table II list the baseline HP for each
model.

TABLE II: Model hyperparameters (HP) varied showing initial “Baseline” values, allowable tuning window values {min:step:max}, and final best performing “Tuned” values for the multihead full time window configurations. Model | HP | Baseline | {min:step:max} | Tuned
---|---|---|---|---
FC | # Units | 2 | {1:1:6} | 3
# Neurons | 100,20 | {10:10:100} | 100,100,60
Dropout | 0.2 | {0.2:0.1:0.5} | 0.2
CNN | # Filters | 3 | {1:1:6} | 4
Filter | 64,64,64 | {32:32:256} | 64,32,192,96
Kernel | 3,3,3 | {3:2:7} | 3,3,5,7
Pool | 2 | {2:1:5} | 3
Dropout | 0.4 | {0:0.1:0.5} | 0.1
FCN | # Filters | 3 | {1:1:6} | 2
Filter | 64,128,256 | {32:32:256} | 96,32
Kernel | 8,5,3 | {3:2:7} | 7,5
LSTMV | # Units | 2 | {1:1:6} | 1
Units | 40,20 | {10:10:100} | 120
LSTMS | # Units | 2 | {1:1:6} | 1
Units | 40,20 | {10:10:100} | 150
TRV | # Enc | 4 | {1:1:4} | 2
# Heads | 4 | {1:1:4} | 4
Dim Embed | 128 | {100:100:600} | 500
Dim FF | 512 | {400:100:600} | 400
Dropout | 0.2 | {0:0.1:0.5} | 0
TRS | # Enc | 4 | {1:1:4} | 2
# Heads | 4 | {1:1:4} | 4
Dim Embed | 128 | {100:100:600} | 500
Dim FF | 512 | {400:100:600} | 600
Dropout | 0.2 | {0:0.1:0.5} | 0

##### Hyperparameter Tuning

After baseline training, a hyperparameter optimization search (also known as
“tuning”) was conducted to enhance model performance using Keras Tune. Two
types of tuners were used; Random and Hyperband. Hyperband is a more advanced
tuning algorithm [23], but requires a significant amount of memory. Therefore
all models except the transformer were optimized using hyperband tuner; the
transformer models were by far the largest configurations which necessitated
using random tuner due to hardware memory constraints. Regardless of tuner
used, the tuning metric minimized was validation loss. Following tuning, all
models were re-trained using their respective optimized hyperparameters. Table
II shows the tuned HP for the multihead full window configurations.

##  III Results & Analysis

###  III-A Neural Network Performance

For baseline comparison, the non-neural network machine learning models
achieved the following test set accuracy: Random Forrest 84% and Logistic
Regression 32%. Comparatively, the neural network (NN) models demonstrated
higher accuracy and low loss in predicting both tactic and attributes.

Amoungst the NN models, attribute predictions consistently outperformed tactic
predictions, likely attributed to fewer labels and double the training
instances (1200 per tactic, amounting to 2400 per attribute). Furthermore, not
only did the implementation of a multihead (MH) model facilitate simultaneous
prediction of tactic and attributes, it also enhanced 11 out of 14 combined
model configurations (separately improved 8 tactic configurations and 10
attribute configurations). This improvement was evidenced by almost
universally lower validation losses and higher test accuracies. Additionally,
tuning efforts improved 28 out of 42 configurations (67%), underscoring the
importance of model optimization. Lastly, between the two sequence output
models explored, the transformer-based model TRS significantly outperformed
the LSTM-based model LSTMS. All of these points are summarized in Figure 9.

Figure 9: Best test accuracy and validation loss versus model type; each model
shows two observation windows, 20 and 58 (full) time steps.

Further illustrations provide insights into NN explainability, which is the
ability to describe how a NN is making predictions and how well it is being
trained. One example of NN explainability is feature importance, showing which
features (inputs) are heavily weighted when models make classification
predictions [10]. For instance, Random Forrest and Logistic Regression machine
learning models provide feature coefficients used to make predictions, as
shown in Figure 10. Larger magnitude coefficients equate to greater feature
importance, indicating that velocity is a more pivotal feature compared to
position. This was a key observation; the significant role of velocity as a
feature, in contrast to the position. In fact, when position inputs were
removed, NN training smoothed and performance showed no degradation. This
pattern reinforces the strong correlation between attributes being classified
and features provided. It’s intuitive that attributes used in this study would
be correlated to velocity vectors. This was further highlighted by a Class
Activation Map (CAM) analysis conducted to explain the temporal importance on
model classification, showing which time steps weighted more heavily when
making predictions. The CAM showed a strong connection between attacking swarm
total acceleration magnitude changes (ie. velocity vector changes) and time
step importance.

Figure 10: Logistic Regression model feature importance shows position inputs
are irrelevant.

Another example of NN explainability is the dimensionality reduction technique
t-distributed Stochastic Neighbor Embedding (t-SNE) which is a statistical
method for visualizing high-dimensional data by giving each datapoint a
location in a two or three-dimensional mapping. The tSNE visualization in
Figure 11 effectively demonstrates the transformation from disordered input
data to ordered output embedding just prior to the model prediction layer,
where clear tactic groupings are indicative of model learning.

Figure 11: tSNE: disordered input data becomes ordered output, indicating
model learning.

###  III-B Observation Window Impact

When evaluating the effect of observation window length, the 58 time step
(full) window offered equal or improved performance for all models except the
Fully Connected. Specifically, using 58 time steps improved accuracy for 9
configurations by less than 4%, as seen in Figure 9. More importantly, all
models except FC and LSTM displayed a decrease in validation loss (6-8%),
which is indicative of improved generalization during future inference on
unseen data.

An essential point to reiterate is that both the 20 and 58 time step windows
are both relatively short when compared to the mean engagement time of 133
time steps, respectively equalling 15% and 40% of the mean. Therefore, it is
especially interestingly that such a marginal performance increase resulted
from training models using 58 versus 20 time steps, which is approximately
three times as many time steps. In time critical applications, performing
inference three times quicker for a small performance decrease may be a
desirable trade off.

Figure 12: Best accuracy versus model size.

As seen in Figure 9, except for the LSTMS architecture all configurations
performed approximately the same, with accuracy between 90-97%. This led to
the analysis of model size versus accuracy in order to compare the
computational resources and power storage density required to deploy each
model on an edge device. A general trend of increasing model size with longer
observation windows was observed. Figure 12 shows the transformer models were
significantly larger (50MB) than other models, while the CNN models were the
smallest (0.1MB).

As will be shown shortly in Section III-D, the five best models were
determined to be the full time window configuration for CNN, FCN, LSTMV, TRV,
and TRS. Therefore, Figure 12 has these models highlighted in non-grey color,
and they will be the focus for the remaining results analysis.

###  III-C Swarm Size Scalability

All models exhibited scalability, which is an ability to be successfully
applied to swarms of different size. There is clear improvement for all models
as the swarm size increases, as shown by the decreasing validation loss in
Figure 13. The “best” model was TRV, and the “worst” was FCN; however,
difference was small across all models. However, the best improved was the
LSTMV model, indicating that the apparent information deficit previously
restricting better performance was overcome by providing more information in
the form of increased number of input features; more agents means more
information.

Figure 13: Tactic validation loss vs. swarm size across top five models.

Another interesting result is model accuracy remains about constant, or
improves, as the swarm size increases, as shown in Figure 14. This is great,
indicating that once a model is performing well, it will continue to perform
well as swarm size is increased. This trend implies that one can save time and
resources by tuning a model on small swarms knowing that scaling to larger
swarms will only improve performance.

Figure 14: Tactic test accuracy vs. swarm size across top five models.

###  III-D Noise Robustness

Figure 15 shows a canvasing of input features in the presence of increasing
noise, as well as the PCA representations which helps visualize the impact of
noise on the data.

Figure 15: Input data with increasing noise.

The models’ performance under varying noise conditions revealed interesting
patterns. Noise lightly affected the Comm (targeting) attribute, but
significantly affected the ProNav (navigation) attribute, driving tactic error
rate similar to ProNav error rate as shown in Figure 16. This is somewhat
intuitive, knowing that the velocity vector was the dominant feature.
Specifically, the velocity vector difference between Greedy and Auction
targeting was significant, allowing more resistance to noise, whereas the
difference between pursuit and ProNav navigation velocity vectors was smaller,
making the ProNav attribute more sensitive to noise.

Additionally, the already small velocity vector difference between Pursuit and
ProNav decreased further as each attacker closed separation with its target,
exacerbating the noise induced prediction degradation. This difficulty in
distinguishing navigation method, combined with the observation made in
Section II-A, where over time as defenders are eliminated the Auction tactics
begin to resemble the Greedy tactics, causes a compound effect which manifest
as it being most difficult to distinguish the Greedy+ tactic.

Overall, the Fully Connected (FC) model degraded rapidly in the presence of
noise, showing it would be an unrealistic choice for real world applications,
while the other four models displayed graceful degradation. The Fully
Convolutional Network (FCN) had the best robustness to noise, with all other
models trailing closely within 5-10%, offering some ability to rank the top
models, but not much.

Figure 16: Tactic and attribute prediction error (normalized for random guess)
as noise increases.

###  III-E Results Summary

The top five models (all using full observation window) - CNN, FCN, LSTMV,
TRV, TRS - showcased closely matched performance. The key discriminators among
these models were their sequence output capabilities and model size, with the
transformer models excelling in sequence output, but at the cost of large
model size. Conversely, the CNN models were very small, but only capable of
vector output. Noise resistance and swarm size scalability offered marginal
performance separation between the models, with FCN being most noise
resistant, but trailing in scalability. Velocity emerged as the most important
feature across all models. Additionally, all of the top models embed, or
transform, input information into a latent space of arbitrary dimension, which
is important because any input size, along both time and feature dimension,
can be accommodated. Lastly, slight to moderate overfitting during training
was observed in all models, which was mitigated using early stopping based on
minimum validation loss.

##  IV Conclusion

###  IV-A Summary of Main Findings

Throughout the course of this study, several key findings emerged. Neural
networks exhibited a strong capability to predict both the underlying
characteristic attributes and overall tactics of swarms. Not only were they
accurate, but they also achieved this with low loss, leading to robust
generalization across various test scenarios. Furthermore, there was a clear
trend observed with the volume of data: as the amount of data increased (in
terms of more agents leading to more input features, and extended time
frames), there was a general improvement in the results. However, a nuanced
finding was that while more time data generally contributed to improved
results, the increment was often marginal. This suggests an important trade-
off in defense scenarios where time is a critical resource. A slightly less
accurate classification, which is available faster, might be more practical
and desired than waiting for a marginally more accurate one.

###  IV-B Potential Applications

The implications of these findings are profound, particularly in the context
of defense. If there’s ample training data, this research strongly indicates
that essential information about an attacking swarm can be swiftly deduced
using neural networks. This rapid inference is invaluable as it can provide
crucial intelligence in real-time, leading to better-informed defense
decisions.

###  IV-C Future Work

Future work for enhancing the classification of swarms using neural networks
holds a plethora of promising directions, especially considering the
constraints and complexities of real-world scenarios. A critical avenue is the
focus on utilizing locally observable information, which is vital when sensors
have a limited range and cannot rely on global information due to unreliable
communications. This constraint presents a more realistic operational
environment where the system must act with incomplete knowledge.

Addressing this real-world challenge necessitates the exploration of a more
extensive set of attributes and tactics for classification. Realistically, in
real-world scenarios there could be an even greater number of tactics,
comprised of more binary attribute combinations. With numerous attributes
identified that could potentially classify an individual agent, the next step
is to investigate the relationship between model performance and the increased
complexity resulting from a larger number of attribute and tactic labels.
Feature engineering will be pivotal in this phase, as the development of more
meaningful inputs—whether through additional data or the combination of
existing inputs—could significantly enhance model accuracy.

Further, considering the dynamics of engagement, different orientations,
starting positions, and swarm spreads must be examined. These factors, coupled
with the effect of varying distance scales, raise the question of how to
appropriately normalize input data to feed into the neural network. A
promising approach could be the use of ragged tensors to incorporate all time
steps from each engagement instance into the model. This is a departure from
current methods that only utilize the first 15-40% of time steps for training
and prediction. A comprehensive study is warranted to determine if models
trained on entire engagements outperform those trained on partial data, even
when inference is made using a short time window. Investigating different
stages of the engagement, such as the start, middle, or end, could reveal
critical insights into optimal prediction windows.

Incorporating tactics switching into the modeling process is another
interesting frontier. By simulating tactics changes, such as shifting from
pursuit to proportional navigation (ProNav) mid-engagement, researchers can
evaluate whether sequence output models can accurately detect these
transitions. Following a similar line of thinking, removing the assumption of
all attackers using the same tactics and allowing attacking swarms to be a
heterogeneous mixture of agents would provide the opportunity to evaluate
classification of a more realistic scenario, as well as considering the
applications of Group Activity Recognition to possibly parse out the different
subgroups of attackers. Alongside this, deliberate perturbations by the
defender, as opposed to random, offer a controlled method to study the
attackers’ responses and how different defender formations and movements
impact classification speed and accuracy.

Finally, addressing the effects of input data non-uniformities, such as data
gaps from a neutralized attacking agent, scenarios with fewer agents than the
model was trained on, or fewer time steps, are crucial. Additionally, the
shuffling of input data order, which could arise from crossing trajectories
and the difficulty in distinguishing tracks, must be examined to ensure model
reliability under various data inconsistencies.

In conclusion, the proposed future work aims to significantly advance the
state-of-the-art in swarm classification using neural networks by tackling
real-world challenges and enhancing the robustness and accuracy of such
systems.

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