Related papers: Optimal high-level descriptions of dynamical syste…
A high-performance image compression algorithm is crucial for real-time information transmission across numerous fields. Despite rapid progress in image compression, computational inefficiency and poor redundancy modeling still pose…
Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and…
We recount recent history behind building compact models of nonlinear, complex processes and identifying their relevant macroscopic patterns or "macrostates". We give a synopsis of computational mechanics, predictive rate-distortion theory,…
Stochastic model-predictive control (SMPC) has evolved to a powerful framework for the control of stochastic dynamical systems. SMPC utilizes a probabilistic uncertainty description to provide a systematic trade-off between the control…
Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however,…
We consider the question of whether thermodynamic macrostates are objective consequences of dynamics, or subjective reflections of our ignorance of a physical system. We argue that they are both; more specifically, that the set of…
When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…
A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of "macrostates" (e.g. sets of "microstates"), the consequence on…
Physical models of biological systems can become difficult to interpret when they have a large number of parameters. But the models themselves actually depend on (i.e. are sensitive to) only a subset of those parameters. Rigorously…
An efficient representation of observed data has many benefits in various domains of engineering and science. Representing static data sets, such as images, is a living branch in machine learning and eases downstream tasks, such as…
The definition of complexity through Statistical Complexity Measures (SCM) has recently seen major improvements. Mostly, effort is concentrated in measures on time series. We propose a SCM definition for spatial dynamical systems. Our…
Multivariate information theory provides a general and principled framework for understanding how the components of a complex system are connected. Existing analyses are coarse in nature -- built up from characterizations of discrete…
Many real-world dynamical systems can be described as State-Space Models (SSMs). In this formulation, each observation is emitted by a latent state, which follows first-order Markovian dynamics. A Probabilistic Deep SSM (ProDSSM)…
State Space Models (SSMs), developed to tackle long sequence modeling tasks efficiently, offer both parallelizable training and fast inference. At their core are recurrent dynamical systems that maintain a hidden state, with update costs…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
The data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. They have been used to reason about beliefs, lies, and group epistemic behaviour inspired by social…
Hierarchies are of fundamental interest in both stochastic optimal control and biological control due to their facilitation of a range of desirable computational traits in a control algorithm and the possibility that they may form a core…
State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…