Stochastic dynamics on large networks: Prediction and inference

Workshop Report

Stochastic dynamical systems are increasingly playing a central role across many disciplines,
with applications in elds as diverse as systems biology, meteorology, computational neuros-
cience and the quantitative social sciences. Statistical physics has a long tradition of developing
approximate methods for forward prediction of the dynamics of a given model. However, re-
searchers are often faced with inverse problems, where parameters of the models may not be
known or there are di erent models competing to explain the same phenomenon. Hence ecient
methods of statistical inference, i.e. the estimation of unobserved states and parameters, are
highly relevant in elds such as experimental biology, nance and other areas where very large
data sets are available but there is a shortage of modern theoretical techniques for analysing

There is a close relationship between statistical inference and the statistical physics of disor-
dered systems, which can be characterized as large systems of simple units linked by a complex
network of interactions. This relationship has so far mainly been exploited in the area of de-
veloping equilibrium tools that can be used to analyse data from systems at stationarity. More
recently, the community has seen a growing awareness of the importance of moving beyond this
towards dynamic models, for two main reasons: (a) Many interesting systems for which statistical
analysis techniques are required, e.g. networks of biological neurons, gene regulatory networks,
protein-protein interaction networks, stock markets, exhibit very rich temporal or spatiotempo-
ral dynamics; ignoring this can lose iinteresting information or lead to even qualitatively wrong
conclusions. (b) Current technological breakthroughs in collecting data from complex systems
are yielding ever increasing temporal resolution, allowing the fundamental temporal aspects
of their functioning to be analysed if combined with strong theoretical methods. The last few
years have seen an increasing development of such methods in computational statistics, machine
learning and statistical physics. DyNet18 was set up to exploit the resulting opportunities for
cross-fertilisation between ideas and techniques that have up to now been largely developed in
distinct communities, with the potential for broad impact across a number of application do-
mains. Its goal was to bring together researchers from di erent elds such as statistical physics,
statistics, numerical mathematics, machine learning and their applications in order to discuss
the new challenges originating from dynamical data and how recently developed techniques can
be used to tackle them.

DyNet18 successfully provided a forum for exploring possible synergies between solutions
to inference problems studied in di erent communities, with topics ranging across state and
parameter estimation in stochastic di erential equations; inference in spatio{temporal e.g. re-
action di usion models; path integral approaches; Monte Carlo methods, particle lter based
inference; inferring networks from dynamical data; inference and stochastic control/rare event
simulations; and agent systems and trac models.

The workshop brought together a number of successful senior and young scientists, the for-
mer including Eric vanden Eijnden (Courant Institute, US), Ron Meir (Technion, Israel), David
Saad (Aston University, UK), Sebastian Reich (Potsdam, DE) and Ben Leimkuhler (Edinbur-
gh, UK). PhD students and postdoctoral researchers were particularly encouraged to present
their results, both as 20-minute talks and at poster sessions to give them maximal exposure to
interaction and scienti c discussion. Interesting insights arose for example on the links between
non-equilibrium (driven, irreversible) dynamics in physical systems and Monte Carlo samplers
that mix more rapidly by breaking detailed balance; on the connections between optimal trans-
port problems and data assimilation; on applications of inference and simulation to crowded
stochastic systems; and on new perspectives on the complexity of learning with large neural
networks provided by the theory of stochastic dynamical systems.