# On scientific understanding with artificial intelligence

Mario Krenn<EMAIL_ADDRESS>Max Planck Institute for the Science of
Light (MPL), Erlangen, Germany.  Chemical Physics Theory Group, Department of
Chemistry, University of Toronto, Canada.  Department of Computer Science,
University of Toronto, Canada.  Vector Institute for Artificial Intelligence,
Toronto, Canada.  Robert Pollice  Chemical Physics Theory Group, Department of
Chemistry, University of Toronto, Canada.  Department of Computer Science,
University of Toronto, Canada.  Si Yue Guo  Chemical Physics Theory Group,
Department of Chemistry, University of Toronto, Canada.  Matteo Aldeghi
Chemical Physics Theory Group, Department of Chemistry, University of Toronto,
Canada.  Department of Computer Science, University of Toronto, Canada.
Vector Institute for Artificial Intelligence, Toronto, Canada.  Alba Cervera-
Lierta  Chemical Physics Theory Group, Department of Chemistry, University of
Toronto, Canada.  Department of Computer Science, University of Toronto,
Canada.  Pascal Friederich  Chemical Physics Theory Group, Department of
Chemistry, University of Toronto, Canada.  Department of Computer Science,
University of Toronto, Canada.  Institute of Nanotechnology, Karlsruhe
Institute of Technology, Eggenstein-Leopoldshafen, Germany.  Gabriel dos
Passos Gomes  Chemical Physics Theory Group, Department of Chemistry,
University of Toronto, Canada.  Department of Computer Science, University of
Toronto, Canada.  Florian Häse  Chemical Physics Theory Group, Department of
Chemistry, University of Toronto, Canada.  Department of Computer Science,
University of Toronto, Canada.  Vector Institute for Artificial Intelligence,
Toronto, Canada.  Department of Chemistry and Chemical Biology, Harvard
University, Cambridge, USA.  Adrian Jinich  Division of Infectious Diseases,
Weill Department of Medicine, Weill-Cornell Medical College, New York, USA.
AkshatKumar Nigam  Chemical Physics Theory Group, Department of Chemistry,
University of Toronto, Canada.  Department of Computer Science, University of
Toronto, Canada.  Zhenpeng Yao  Chemical Physics Theory Group, Department of
Chemistry, University of Toronto, Canada.  Center of Hydrogen Science,
Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China.
The State Key Laboratory of Metal Matrix Composites, School of Materials
Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road,
Shanghai 200240, China.  Innovation Center for Future Materials, Zhangjiang
Institute for Advanced Study, Shanghai Jiao Tong University, 429 Zhangheng
Road, Shanghai 201203, China.  Alán Aspuru-Guzik<EMAIL_ADDRESS>Chemical
Physics Theory Group, Department of Chemistry, University of Toronto, Canada.
Department of Computer Science, University of Toronto, Canada.  Vector
Institute for Artificial Intelligence, Toronto, Canada.  Canadian Institute
for Advanced Research (CIFAR) Lebovic Fellow, Toronto, Canada.

###### Abstract

Imagine an oracle that correctly predicts the outcome of every particle
physics experiment, the products of every chemical reaction, or the function
of every protein. Such an oracle would revolutionize science and technology as
we know them. However, as scientists, we would not be satisfied with the
oracle itself. We want more. We want to comprehend how the oracle conceived
these predictions. This feat, denoted as scientific understanding, has
frequently been recognized as the essential aim of science. Now, the ever-
growing power of computers and artificial intelligence poses one ultimate
question: How can advanced artificial systems contribute to scientific
understanding or achieve it autonomously?

We are convinced that this is not a mere technical question but lies at the
core of science. Therefore, here we set out to answer where we are and where
we can go from here. We first seek advice from the philosophy of science to
understand scientific understanding. Then we review the current state of the
art, both from literature and by collecting dozens of anecdotes from
scientists about how they acquired new conceptual understanding with the help
of computers. Those combined insights help us to define three dimensions of
android-assisted scientific understanding: The android as a I) computational
microscope, II) resource of inspiration and the ultimate, not yet existent
III) agent of understanding. For each dimension, we explain new avenues to
push beyond the status quo and unleash the full power of artificial
intelligence’s contribution to the central aim of science. We hope our
perspective inspires and focuses research towards androids that get new
scientific understanding and ultimately bring us closer to true artificial
scientists.

##  I Introduction

Artificial Intelligence (A.I.) has recently been called a “new tool in the box
for scientists”Zdeborová (2017) and that “machine learning with artificial
networks is revolutionizing science“Fösel  _et al._ (2018). Additionally, it
has been conjectured “that machines could have a significantly more creative
role in future research.” Melnikov  _et al._ (2018). For instance, it has even
been postulated that “[t]he new goal of theoretical chemistry should be that
of providing access to a chemical ’oracle’: an A.I. environment which can help
humans solve problems, associated with the fundamental chemical questions of
the fourth industrial revolution […], in a way such that the human cannot
distinguish between this and communicating with a human expert” Aspuru-Guzik
_et al._ (2018).

Figure 1: How can Androids contribute to new scientific understanding? In
addition to scientific literature, we take inspiration from the philosophy of
science and from dozens of stories provided by active computational natural
scientists. Thereby we identify three fundamental dimensions of computer-
assisted scientific understanding. From there, we look into the future and
develop a roadmap on how to develop Androids that can contribute to
understanding – the essential aim of science.

However, this excitement has not been shared among all scientists.
Specifically, it has been questioned whether advanced computational approaches
can go beyond numerics Hoffmann and Malrieu (2020a, b, c); Marcus (2020);
Thaler (2021) and contribute fundamentally to one of the essential aims of
science, that is, gaining of new scientific understanding Potochnik (2015,
2017); De Regt (2017).

In this work, we address how artificial systems can contribute to scientific
understanding – specifically, what is the state-of-the-art and how we can push
further. Besides a thorough literature review, we surveyed dozens of
scientists at the interface of biology, chemistry or physics on the one hand,
and artificial intelligence and advanced computational methods. These personal
narratives focus on the concrete discovery process of ideas and are a vital
augmentation to the scientific literature. We put the literature and personal
accounts in the context of a philosophical theory of Scientific Understanding
recently developed by Dennis Dieks and Henk de Regt De Regt and Dieks (2005);
De Regt (2017), who was awarded the Lakatos Award in 2019 for the development
of this theory. We thereby introduce three fundamental dimensions for
scientific androids111We encapsulate all advanced artificial computational
systems under androids, independent of their working principles. In this way,
we are focusing on the operational objective rather than the methodology.
contribution towards new scientific understanding:

  1. I)

Androids acting as a microscope in the responses, i.e., akin to an instrument
revealing properties of a physical system that are otherwise difficult or even
impossible to probe. Humans then lift these insights to scientific
understanding.

  2. II)

Androids acting as muses, i.e., sources of inspiration for new concepts and
ideas that are subsequently understood and generalized by human scientists.

  3. III)

Lastly, in an ultimate dimension of android-assisted scientific understanding,
computers are the agents of understanding. While we have not found any
evidence of computers acting as true agents of understanding in science yet,
we outline important characteristics of such an artificial system of the
future and potential ways to achieve it.

In the first two dimensions, the android enables humans to gain new scientific
understanding while in the last one the machine gains understanding itself.
These classes enable us to layout a vibrant and mostly unexplored field of
research, which will hopefully manifest itself as a guiding star for future
developments of artificial intelligence in the natural sciences.

The goal of this perspective is to put Scientific Understanding back to the
limelight – where we are convinced it belongs. We hope to inspire physicists,
chemists and biologists and A.I. researchers to go beyond the status quo,
focus on these central aims of science, and revolutionize computer-assisted
scientific understanding. In that way, we believe that androids will become
true agents of understanding that contribute to science in a fundamental and
creative way.

##  II Scientific Understanding

Let us imagine an oracle providing non-trivial predictions that are always
true. While such a hypothetical system would have a very significant
scientific impact, scientists would not be satisfied. We want “to be able to
grasp how the predictions are generated, and to develop a feeling for the
consequences in concrete situations” De Regt and Dieks (2005). Colloquially,
we refer to this goal as “understanding” – But what does that really mean? Can
we find criteria for scientific understanding? To do that, we seek guidance
from the field of philosophy of science. Notably, while hardly any scientist
would argue against “understanding” as an essential aim of science (next to
explanation, description and prediction De Regt (2020)), this view was not
always accepted by philosophers. Specifically, Carl Hempel, who made
foundational contributions clarifying the meaning of scientific explanation,
argued that “understanding” is subjective and merely a psychological by-
product of scientific activity and is therefore not relevant for the
philosophy of science Hempel (1965). Other philosophers criticized these
rather unsatisfying conclusions, and they tried to formalize what scientific
understanding means. Proposals include that understanding is connected to the
ability to build causal models (Lord Kelvin said “It seems to me that the test
of ’Do we or not understand a particular subject in physics?’ is, ’Can we make
a mechanical model of it?’ ”De Regt and Dieks (2005)), connected to providing
visualizations (or Anschaulichkeit, as its strong proponent Erwin Schrödinger
called itSchrödinger (1996); De Regt (2014)) or that understanding corresponds
to providing unification Friedman (1974); Kitcher (1981).

In recent years, Henk de Regt and Dennis Dieks have developed a new theory of
scientific understanding, which is both contextual and pragmatic De Regt and
Dieks (2005); De Regt (2017, 2020). Importantly, they find that techniques
such as visualization or unification are “tools for understanding”, thereby
unifying previous ideas in one general framework. Their theory is agnostic to
the specific “tool” being used, making it particularly useful for application
in scientific disciplines. They extend crucial insights by Werner Heisenberg
Heisenberg (1927) and rather than introducing mere theoretical or hypothetical
ideas, the main motivation behind their theory is that a “satisfactory
conception of scientific understanding should reflect the actual (contemporary
and historical) practice of Science”. Put simply, they argue that:

> A phenomenon P can be understood if there exists an intelligible theory T of
> P such that scientists can recognise qualitatively characteristic
> consequences of T without performing exact calculations De Regt and Dieks
> (2005); De Regt (2017).

Concretely, de Regt and Dieks define two interlinked criteria:

  1. 1.

Criterion of Understanding Phenomena: A phenomenon P can be understood if a
theory T of P exists that is intelligible.

  2. 2.

Criterion for the Intelligibility of Theories: A scientific theory T is
intelligible for scientists (in context C) if they can recognise qualitatively
characteristic consequences of T without performing exact calculations.

We decided to use this specific theory because of one particular strength: We
can use it experimentally to evaluate whether scientists have understood new
concepts or ideas, rather than by inspecting their methodology, by simply
looking at the scientific outcome and the consequences. This also coincides
with Angelika Potochnik’s argument that “understanding requires successful
mastery, in some sense, of the target of understanding”Potochnik (2017). We
will follow this approach and, consequently, here explore its relationship to
the role of A.I. in science. Accordingly, we believe we can significantly
advance A.I.’s contribution to this central aim of Science if we have a clear
picture of how scientists gain conceptual understanding, and instil it to
artificial systems afterwards. We approach this goal by applying ideas of de
Regt and Dieks directly to android assisted science (and ultimately, to
android scientists themselves).

##  III What is next?

###  III.1 Beyond Re-Discovery

In recent years, scientists at the interface between A.I. and the natural
sciences tried to rediscover scientific laws or concepts with machines. The
question is, however, whether an android is capable of contributing to new
scientific understanding if it can rediscovers physical laws and concepts,
such as the heliocentric world view Iten  _et al._ (2020), the arrow of time
Seif  _et al._ (2021) or mechanical equations of motions Udrescu and Tegmark
(2020)? We believe that this is not guaranteed. The human creators of these
androids know what they are looking for in these case studies. Therefore, it
is unclear how both conscious and unconscious biases (in the broadest sense,
e.g., by choosing particular representations) in the code or the data analysis
can be prevented. Consequently, even if an algorithm can rediscover
interesting physical phenomena, we cannot know whether and how they can be
used to advance Science by helping to uncover new scientific understanding.

Hence, we believe we need to go beyond rediscovery tasks. Therefore we focus
explicitly on the question of how to get new scientific understanding.

###  III.2 Beyond Discovery

Importantly, other central aims of science such as prediction and discovery
can lead to scientific and technological disruptions while not directly
contributing to scientific understanding as discussed above De Regt (2020);
Potochnik (2017). For instance, imagine the hypothetical discovery of the
hitherto best material for energy storage that could revolutionize batteries.
However, this game-changing discovery would not qualify as understanding if
chemists could not use the underlying principles fruitfully in other contexts
(without computation).

Similarly, the recent breakthrough in protein folding will undoubtedly change
the landscape of biochemistry. However, so far, AlphaFold is a black box – an
oracleJumper  _et al._ (2021); Tunyasuvunakool  _et al._ (2021). As such it
does not directly provide new scientific understanding in the sense of de Regt
and Dieks (but could of course in the future enable humans to gain new
scientific understanding). Hence, we believe we must go beyond artificial
discoveries in science.

###  III.3 Where to go from here?

The ultimate goal is to get new understanding from androids. Loosely speaking,
we want to find new ideas or concepts that we can apply and use in different
situations without (complete) computations.

This article aims to explain precisely what such a goal requires, what
previous approaches have achieved, and how we can go further. We want to
clearly lay out this underappreciated but essential research question and
thereby give a clear goal for the future of A.I. in the natural sciences.

Figure 2: The future computational microscope. We envision two types of
advances in the next-generation computational microscopes which aim to advance
genuine scientific understanding. First (left), larger and more complex
computations will allow the computational observation of phenomena not
accessible so far. There, new computational paradigms will play a significant
role, such as Graphical Processor Units (GPU), Tensor Processor Units (TPU),
Optical Processor Units (OPU) and – ultimately – quantum computers. Second
(right), new ways to represent the highly complex data will advance our
ability to sense structure and recognize underlying patterns. The involvement
of all our senses could, for sensing computer-generated data, be an exciting
pathway to advanced understanding.

##  IV Three dimensions of computer-assisted understanding

We use scientific literature and personal anecdotes of dozens of scientists,
and the context of the philosophy of science, to introduce a new
classification of androids contribution to scientific understanding222We call
the classification dimensions, as they are independent and non-exclusive.. It
helps to see diverse unexplored journeys that can be investigated in the
future.

An android can act

  1. I)

as a computational microscope, providing information not (yet) attainable by
experiment

  2. II)

as a resource of inspiration or an artificial muse, expanding the scope of
human imagination and creativity.

In those two classes, the human scientist is essential to take the new insight
and inspiration and develop it to full understanding. Finally, an android can
be

  1. III)

an agent of understanding, replacing the human in generalizing observations
and transferring scientific concepts to new phenomena.

We stress that these three classes should not be understood dogmatically but
rather guide future possibilities. In the following sections, based on
concrete examples, we discuss each class in more detail and propose avenues
for pushing the boundaries of the current computational faculties.

###  IV.1 Computational microscope for scientific understanding

Microscopes are devices that enable us to investigate objects and phenomena
imperceptible to the naked eye. In a similar way, computational microscopes
enable the investigation of objects or processes that we cannot visualize or
probe in any other way. One main objective is to simulate biological, chemical
or physical processes that happen at length and time scales not perceivable by
experiment.

As we are interested in understanding, the new computer-generated data needs
to be generalized to other contexts without complete computationDe Regt and
Dieks (2005). We show now two concrete examples.

The first example is molecular dynamics simulations of the SARS-CoV-2. The
authors uncovered new biological functions that show different behaviours in
the open and closed conformations of the spike protein. This explanation
changed the view upon glycans in biological systems and inspired new ways to
analyze these systems without the need to perform full computations Casalino
_et al._ (2020).

In the second example, the authors describe how molecular dynamics simulations
helped to uncover fundamental patterns called glycoblocks. The systematic use
of glycoblocks can both be used to understand sequence-structure-property
relationships of biomolecules and can also inform the design of synthetic
structures with desired functions without the need for simulating the entire
system Fogarty  _et al._ (2020).

#### The next computational microscope

A computational microscope aims to provide data via computation that are not
(yet) accessible by experiments that humans can understand. How could we make
computational microscopes even more insightful and make it easier for human
scientists to use this data to gain scientific understanding? There are two
vibrant directions going forwards. First, more advanced computational systems
will allow to analyze of more complex physical systems. Second, representing
the information in a more interpretable way will help to lift the indications
from computers to true scientific understanding.

More Complex Systems – One obvious but nevertheless important research
direction is increasing the complexity as well as the accuracy of computer
simulationsFriederich  _et al._ (2021a). For example, increasing the size of
the systems, the time-scale of the simulations, the number of interactions
that can be modelled will significantly increase the applicability in complex
dynamic systems. In general, this can be achieved by either algorithmic
improvements or hardware improvements, or both. In that regard, we expect that
modern neural network technologies together with advanced hardware such as
GPUs, TPUs or even OPUs Gigan  _et al._ (2020); Xu  _et al._ (2021) will have
an enormous impact. Furthermore, the recent progress in experimental quantum
computing for quantum chemistry Quantum  _et al._ (2020) and physicsZhang  _et
al._ (2017); Schweizer  _et al._ (2019); Martinez  _et al._ (2016) promises
that entirely new algorithms, based on quantum mechanics itself, will play an
important role in this area Cao  _et al._ (2019); Gross and Bloch (2017).
Algorithmic improvements could involve adaptive and intelligent resolution
during simulation and advanced visualization methodsDe Regt and Dieks (2005),
which directly leads to the second future techniques:

Full spectrum of senses – We believe that human scientists can get more out of
data if the full capabilities of all our senses are addressed. At the moment,
we analyze data largely in (potentially animated) 2-dimensional pictures. As a
first step, we believe that real 3D environments (realized either via virtual
or augmented reality glasses, or holography) will significantly help in
understanding complex systems or complex data. Initial advances in that regard
have been demonstrated in the domain of chemistry O’Connor  _et al._ (2018);
Probst and Reymond (2018); Schmid  _et al._ (2020), and we expect this to
become a standard tool for scientists to advance scientific understanding. In
addition, we expect that going beyond the visual sense can open entirely new
ways to experience scientific data. For example, the auditory sense is
excellent in detecting structure or symmetries in (periodic) time-dependent
data Castelvecchi (2021). Furthermore, including the sense of touch, smell and
taste could further expand the horizon of experiences. We expect that in order
to realize that, physical scientists need to work closely together with
psychologists and neurologists (and potentially even with artists), to develop
suitable data representations that can be efficiently recognized by scientists
with all their senses. An ultimate, admittedly futuristic version of a
computational microscope could circumvent the receptors of human senses and
instead use a computer-brain interface to enhance further experiencing
computed data.

###  IV.2 Resource of inspiration for scientific understanding

Surprising and creative ideas are the foundation of Science. Computer
algorithms are a means to provoke such ideas systematically, thereby
significantly accelerating scientific and technological progress. Already 70
years ago, Alan Turing realized that computers could surprise their human
creators: “Machines take me by surprise with great frequency. This is largely
because I do not do sufficient calculation to decide what to expect them to
do, or rather because, although I do a calculation, I do it in a hurried,
slipshod fashion, taking risks.” and ”Naturally I am often wrong, and the
result is a surprise for me for by the time the experiment is done these
assumptions have been forgotten“Turing (1950).

A much more recent study provides stories by dozens of researchers of
artificial life and evolution. They demonstrate in an impressive way how
computer algorithms can surprise their human creators and lead to behaviour
that the authors would denote as creativeLehman  _et al._ (2020). Accordingly,
we believe that androids can be artificial muses of Science in a metaphorical
sense.

Those examples demonstrate that computers can indeed be used as a source of
surprises. But what are the most general ways to get inspirations from
computers? And how can they be lifted by humans to true scientific
understanding? We will outline a number of ways to develop ways to provoke
surprising behaviours of algorithms and use their solutions, internal or
external states as a source of inspiration for new scientific ideas.

Figure 3: The future re-source of inspiration:  An android could act as a
computational muse and inspire the human scientist by (A) identifying
surprises in data, (B) identifying surprises in the scientific literature, (C)
finding surprising concepts by inspecting models or (D) by probing the
behaviour of artificial agents or (E) my finding new concepts from
interpretable solutions.

#### The future resource of inspiration

Identifying surprises in data –  Exceptional data points or unexpected
regularities obtained from experiments or simulations can surprise human
scientists and inspire new ideas and concepts. Our survey shows that these
exceptional points are usually identified by humans, such as the following two
examples, which use high-throughput computations in chemistry Pickard and
Needs (2011) and quantum optics Krenn  _et al._ (2016, 2020).

The first example deals with a surprising phase of crystal structures in high-
pressure physics. There, the authors found an unexpected stable configurations
of alternating NH2 and NH4 layers, rather than a dense NH3 phase. The authors
conceptualized this phenomenon as spontaneous ionization, a common process in
acid-base chemistry, which is now a widely accepted phenomenon in the high-
pressure phase diagram of NH3. Spontaneous ionization in the high-pressure
behaviour of matter has become a more general principle that can be used
without performing any simulations Pickard and Needs (2008).

In the second example, a search for new quantum experiments uncovered a
solution with considerable larger quantum entanglement than expected. The
authors understood the underlying principles and thereby discovered a new
concept of entanglement generation Krenn  _et al._ (2017a, b). The principle
can be used without any computation and, for example, acts now as a new
representation in more advanced artificial intelligence systems for quantum
physics Krenn  _et al._ (2021), demonstrating the application of the computer-
inspired idea in more general different contexts.

In contrast to these examples and many others from literature and from
personal accounts, the anomalies could manifest themselves in a more involved
combination of variables, which might be very difficult for humans to grasp.
Accordingly, applying advanced statistical methods and machine learning
algorithms (e.g., see reference Malhotra  _et al._ (2015)) to this type of
problem will be an important future research direction. Exciting works into
the direction of autonomous anomaly detection have been applied on scientific
data from the Large Hadron Collider (LHC) at CERN Collaboration (2020, 2021);
Park  _et al._ (2021). Such techniques have the potential to identify new
physics signatures, which can then be conceptualized and understood by human
physicists Schwartz (2021); Kasieczka  _et al._ (2021). Neural networks that
autonomously discover symmetries could become an efficient discovery tool for
outliers in scientific data where the underlying rules might not be known
beforehand Yu  _et al._ (2018); Dehmamy  _et al._ (2021).

Estimating the confidence of predictions will be one method to directly search
for anomalies in data Nigam  _et al._ (2021). The ability to uncover hidden
regularities was very recently demonstrated in mathematics, where an A.I.
hinted on relations between previously unconnected invariants in knot theory,
which allowed mathematicians to conjecture and prove new theorems Davies  _et
al._ (2021). Alternatively, an A.I. capable of constructing new scientific
hypotheses could uncover outliers or unexpected patterns that are not
discernible with standard statistical methods.

It would be truly exciting to see an A.I. uncover hidden patterns or
irregularities in scientific data previously overlooked by humans, which leads
to new ideas and, ultimately, to new conceptual understanding. As of now, we
are not aware of cases like that.

The data points for these systems could be obtained from computational methods
(involving those described in section IV.1), with exciting opportunities for
mathematics or theoretical physics Douglas (2022). Alternatively, the data
could be obtained directly from experiments. Here we can imagine a closed-loop
approach where an algorithm tries to explore the environment and steer the
exploration into unexpected regions. If the data-source is an experiment, this
future system will require access to complex lab automation with large
parameter spaces to explore, as demonstrated recently in biology King  _et
al._ (2009), chemistry Bédard  _et al._ (2018); Steiner  _et al._ (2019);
Coley  _et al._ (2019); Burger  _et al._ (2020); Chatterjee  _et al._ (2020);
Grizou  _et al._ (2020) or physics Moon  _et al._ (2020); Dalgaard  _et al._
(2020).

Identifying surprises in the scientific literature –  The number of scientific
papers in essentially every scientific domain is growing enormouslyLarsen and
Von Ins (2010). Consequently, researchers have to specialise in narrow
subdisciplines, which makes finding new interdisciplinary ideas difficult. In
the future, we believe that computers will be able to use the scientific
literature in an automated wayEvans and Foster (2011); Clauset  _et al._
(2017); Fortunato  _et al._ (2018); Wang and Barabási (2021) and identify
exceptional and surprising phenomena for further investigation. While the
large-scale automated analysis of the scientific literature, to our knowledge,
has not yet been able to induce new scientific understanding, there is
significant progress in the field. One promising approach towards this goal is
unsupervised word embedding of a large corpus of scientific papers. In that
technique, the content of the scientific literature is transformed into a
high-dimensional vector space. Recently, this technique has been applied in
the domain of material science Tshitoyan  _et al._ (2019) and rediscovered
central scientific concepts such as the periodic table of the elements.
Additionally, the results also suggested the existence of previously
undiscovered structure-property relationships. Examples include new candidates
for thermoelectric materials. Moreover, several other advanced computational
techniques are being developed in material science to extract knowledge from
the scientific literature and investigate it systematically by A.I.
technologiesOlivetti  _et al._ (2020), and can lead to complex scientific
conclusions as demonstrated for instance on zeolite transformations Schwalbe-
Koda  _et al._ (2019).

An alternative approach aims to build semantic knowledge networks from large
bodies of scientific literature. In these networks, scientific concepts are
nodes, and edges carry relational information. In the simplest case, that
means two scientific concepts are mentioned in the same scientific paper
Rzhetsky  _et al._ (2015); Krenn and Zeilinger (2020). Thus, scientific
knowledge is represented as an evolving network, which can be used to identify
both islands and unexplored regions of the scientific literature. This type of
network was used in biochemistry to identify efficient global research
strategies Rzhetsky  _et al._ (2015) and in quantum physics to predict and
suggest future research directions Krenn and Zeilinger (2020). Advances in
A.I. technology could improve this type of system significantly. For example,
natural language processing architectures such as BERT Devlin  _et al._
(2018), or GPT3 Brown  _et al._ (2020) could help extract more scientific
knowledge from research papers, and large graph-based neural networks could
improve the prediction of new research topics from semantic networks Hamilton
_et al._ (2017).

Surprising concepts by inspecting models – We also expect considerable
progress by rationalising what A.I. algorithms have learned in order to solve
a specific problem, i.e., explainable or interpretable A.I. Montavon  _et al._
(2018); Samek  _et al._ (2019); Roscher  _et al._ (2020); Lundberg  _et al._
(2020). One idea towards this goal is inspired by DeepDreaming, a method first
used in computer vision Mahendran and Vedaldi (2015); Mordvintsev  _et al._
(2015). Put simply, the idea is to invert a neural network and probe its
behaviour. Recently, this approach has been applied to rediscover
thermodynamical properties Seif  _et al._ (2021), and design principles for
functional molecules Shen  _et al._ (2021). An alternative and remarkable
application is the disentanglement of variables in neural networks Burgess
_et al._ (2018). The goal is to understand the internal representation the
neural network has learned. Recently, astronomical data, represented in
geocentric coordinates, was used to train a neural network and disentanglement
of variables enabled the rediscovery of heliocentric coordinates via the
internal representation of the model Iten  _et al._ (2020). In a related
study, using gradient boosting with decision trees, feature importance has
been used to explain properties of molecules, and quantum optics circuits
Friederich  _et al._ (2021b). Related to this is a study where the internal
representation of an unsupervised deep generative model for quantum
experiments has been inspected to understand the model’s internal
worldviewFlam-Shepherd  _et al._ (2021). In the chemical domain,
counterfactual explanations for machine learning models have been demonstrated
to produce rationale behind a model’s prediction. Counterfactual explanations
illustrate what differences to an event or instance would generate a change in
an outcome. Wellawatte et al. Wellawatte  _et al._ (2022) showed how this can
be achieved in a model-independent way (it has been demonstrated for random
forest, sequence models and graph neural networks), indicating great future
potentials for opening the black-box of AI in science. Albeit not in science,
recent work has investigated what the chess-playing A.I AlphaZero has learned
about chess and how human-like knowledge is encoded in the internal
representation McGrath  _et al._ (2021). The concepts rediscovered in all of
those works were not new, and thus the most important challenge for the future
is to learn how to extract previously unknown concepts. Progress towards
resolving that challenge will be essential in the near future to inspire new
scientific ideas.

New concepts from interpretable solutions – Rather than getting inspirations
from the A.I. algorithms themselves, scientists can also be surprised by the
corresponding solutions. When solutions are represented in an interpretable
way, they can provoke new ideas and lead to new concepts. An example of
interpretable representations is a mathematical formula. Thus, scientists can
inspect formulae derived by computer algorithms to solve mathematical problems
directly and derive more general solution strategies. Several publications
demonstrated extracting symbolic models from experimental data of mechanical
systems Schmidt and Lipson (2009); Udrescu and Tegmark (2020), of quantum
systems Gentile  _et al._ (2021) and in astronomy Cranmer  _et al._ (2020a).
It will be exciting to see how these approaches, e.g., combined with methods
such as causal inference Cranmer  _et al._ (2020b), can be improved to propose
reasonable physical models of unknown systems that advance scientific
understanding. Altogether, exciting advances have been achieved in the field
of mathematicsRaayoni  _et al._ (2021); Wagner (2021), and we foresee similar
approaches making a significant impact in the physical sciences as well.

One concrete, recent example in astronomy is the rediscovery of Newton’s law
of gravitation from real-world observational data of planets and moons in our
solar system from the last 30 years Lemos  _et al._ (2022). The application of
graph neural networks allowed for the high-quality prediction of the object’s
motion. Furthermore, a symbolic regression technique called PySR (introduced
in Cranmer  _et al._ (2020a)) was able to extract reasonable mathematical
expressions for the learned behaviour. Interestingly, besides the equations of
motions, the method simultaneously predicts the masses of the planetary
objects correctly. The technique required the assumption of several symmetries
and other physical laws. It will be interesting to see whether these
prerequisites can be reduced further and how related approaches can be applied
to modern physics questions.

Another concrete example of this methodology has been showcased in the field
of quantum optics Krenn  _et al._ (2021). There, an A.I. algorithm with a
graph-theoretical representation of quantum optical setups designs
configurations for previously unknown quantum systems. The final solutions
were represented in a physically-interpretable graph-theoretical
representation. From there, human scientists can quickly interpret the
underlying reasons why the solutions work and apply it in other contexts
without further computation. Accordingly, developing interpretable
representations and methods to extract underlying concepts in other domains
will be an important future research direction.

Probing the behaviour of artificial agents – Another only rarely explored
opportunity is interpreting the behaviour of machines when tasked to solve a
scientific problem Rahwan  _et al._ (2019). Algorithms that take actions such
as genetic algorithms or reinforcement learning agents adopt policies to
navigate the problem space. Human scientists can observe how they navigate
this space. Instead of following a strict external reward, e.g., maximise a
specific property of a physical system, intrinsic rewards such as artificial
curiosity can be implemented Schmidhuber (2008); Pathak  _et al._ (2017).
Instead of maximizing directly some functions, the artificial agent tries to
learn and predict the behaviour of the environment. It then chooses actions
that lead to situations it cannot predict well, thus maximizing its own
understanding of the environment. It has been shown using curious agents in
simulated virtual universes Thiede  _et al._ (2020) and robot agents in real
laboratories Grizou  _et al._ (2020) that curiosity is an efficient
exploration strategy. Alternative intrinsic rewards for artificial agents are
computational creativityVarshney  _et al._ (2020, 2019) and surprise Itti and
Baldi (2009). These intrinsic rewards can produce exceptional and unexpected
solutions, ultimately inspiring human scientists.

###  IV.3 Agent of Understanding

The third and final class we consider are algorithms that can autonomously
acquire new scientific understanding, a feat that has neither been described
by the respondents of our survey nor in the scientific literature. Therefore,
we will approach this class by listing the requirements of these agents,
proposing tests to detect their successful realization and speculating what
such computer programs could look like.

First, it is important to realize that finding new scientific understanding is
context-dependent. What is new depends on whether we consider an individual
scientist and their field of expertise, a scientific domain, the whole
scientific community or even the entire scientific endeavour throughout
history. Hence, true agents of understanding must be able to evaluate whether
an insight is new, at least in the context of a specific scientific domain
that requires access to the knowledge of a scientific field.

Secondly, de Regt emphasized the importance of underlying scientific theories
that allow us to recognize qualitatively characteristic consequences De Regt
(2017). It is not enough to simply interpolate data points or predict new ones
using advanced statistical methods such as machine learning. Thus, even though
such methods can approximate complex and expensive computations, naïve
applications of neural networks cannot be agents of understanding. Scientific
understanding requires more than mere calculation. To illustrate this point
even further, let us consider one concrete example in quantum physics from the
literature: A computational method solved an open question about the
generation of important resource states for quantum computing. Then it
extracted the conceptual core of the solution in the form of a new quantum
interference effect in such a fashion that human scientists can both
understand the results and apply the acquired understanding in different
contexts Krenn  _et al._ (2021). Even if the computer itself was able to apply
the conceptual core to other situations, it would not be a priori clear
whether the computer truly acquired scientific understanding. What is still
missing is an explanation of the discovered technique in the context of a
scientific theory. In this particular example, the android and the human
scientist would need to recognize the underlying quantum interference in the
context of the theory of quantum physics. Thus, we can propose the first
sufficient condition for agents of understanding:

> Condition for Scientific Understanding I: An android gained scientific
> understanding if it can recognize qualitatively characteristic consequences
> of a theory without performing exact computations and use them in a new
> context.

This condition closely follows the ideas of de Regt and Dieks De Regt and
Dieks (2005). Let us go one step further and imagine that there is an android
capable of explaining discoveries in the context of scientific theories. How
could human scientists recognize that the machine acquired new scientific
understanding? We argue that human scientists would do it in the exact same
way they can recognize that other human scientists acquired new scientific
understanding. That is, let the other human scientists transfer the newly
acquired understanding to themselves. This allows us to propose the second
sufficient condition for agents of understanding:

> Condition for Scientific Understanding II: An android gained scientific
> understanding if it can transfer its understanding to a human expert.

We argue that one can only recognize indirectly whether a computer (or human)
has gained scientific understanding. Therefore, finally, we propose a test in
the spirit of the Turing test Turing (1950) or the Feigenbaum testFeigenbaum
(2003) (or adaptations thereof in the natural sciences such as the Chemical
Turing Test or the Feynman Test Aspuru-Guzik  _et al._ (2018)):

> The Scientific Understanding Test:
>
> A human (the student) interacts with a teacher, either a human or an android
> scientist. The teacher’s goal is to explain a scientific theory and its
> qualitative, characteristic consequences to the student. Another human (the
> referee) tests both the student and the teacher independently333In
> principle, there is no reason for the student or the referee not to be
> androids. However, to keep the test as simple as possible, we want to keep
> the number of possible variations small.. If the referee cannot distinguish
> between the qualities of their non-trivial explanations in various contexts,
> we argue that the teacher has scientific understanding.

This implies that humans need to understand the new concepts that androids
devised. If a machine truly understands something, it will be able to explain
it and transfer the understanding to someone else.444We leave aside the
question whether the explanation of the android is true or false. It has been
argued that also false theories can lead to genuine understanding De Regt and
Gijsbers (2017). We believe that this should always be possible, even if the
understanding is far beyond what human experts know at this point. We envision
that computers will use advanced human-computer interaction techniques
together with the tools we described for (future) computational microscopes.

Additionally, scientific discussions between a human and a computer could be
realized using advanced queries in natural language processing tools such as
BIRD Devlin  _et al._ (2018) or GPT-3 Brown  _et al._ (2020). That way, the
scientist could probe the computer with scientific questions. Suppose the
scientist gains new scientific understanding by communicating with the
algorithm, as judged by our scientific understanding test. In that case, they
can confirm that the computer truly acquired understanding.555We would like to
point out that our test, like the ones originated by Turing and Feigenbaum,
are not clear-cut, leaving room for situations that do not allow a clear
judgement. We are optimistic that more efforts will be directed at developing
the necessary technologies, which will lead to ever more convincing
demonstrations of android scientists acting as true agents of understanding in
the future.

##  V Conclusion

Undoubtedly, advanced computational methods in general and artificial
intelligence specifically will further revolutionize how scientists
investigate the secrets of our world. We outline how these new methods can
directly contribute to one of the main aims of science, namely acquiring new
scientific understanding. We suspect that significant future progress in the
use of androids to acquire scientific understanding will require
multidisciplinary collaborations between natural scientists, computer
scientists and philosophers of science. Thus, we firmly believe that these
research efforts can – within our lifetimes – transform androids into true
agents of understanding that will directly contribute to one of the most
essential aims of science, namely Scientific Understanding.

## Acknowledgements

The authors thank Anastassia Alexandrova, Rommie Amaro, Curtis Berlinguette,
Lillian Chong, Gerardo Cisneros, Andy Cooper, Graeme Day, Francois-Xavier
Coudert, Lee Cronin, Elisa Fadda, Rafael Gomez-Bombarelli, Leticia Gonzalez,
Johannes Hachmann, Roald Hoffmann, Jan Halborg Jensen, Erin R. Johnson, Lynn
Kamerlin, Heather J. Kulik, Jean-Paul Malrieu, Anat Milo, Frank Noe, Jens
Kehlet Nørskov, Artem Oganov, Juan Perez-Mercader, Chris Pickard, Markus
Reiher, Jean-Louis Reymond, Dennis Salahub, Stefano Sanvito, Franziska
Schoenebeck, Ilja Siepmann, Alex Sodt, Isaac Tamblyn, Donald Truhlar,
Alexandre Tkatchenko, Koji Tsuda, Alexandre Varnek, Tejs Vegge, Anatole von
Lilienfeld and Eva Zurek for answering our questions on understanding, Xuemei
Gu for Figure 2 and 3, and Nora Tischler and Robert Fickler for valueable
comments on the manuscript. A.A.-G. and his group acknowledge generous support
from the Canada 150 Research Chairs Program, the University of Toronto, and
Anders G. Frøseth. M.K. acknowledges support from the FWF (Austrian Science
Fund) via the Erwin Schrödinger fellowship No. J4309. R.P. acknowledges
funding through a Postdoc.Mobility fellowship by the Swiss National Science
Foundation (SNSF, Project No. 191127).

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