Related papers: Using machine-learning modelling to understand mac…

Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…

The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…

A machine learning technique is proposed for quantifying uncertainty in power system dynamics with spatiotemporally correlated stochastic forcing. We learn one-dimensional linear partial differential equations for the probability density…

Many systems are partially stochastic in nature. We have derived data driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous…

Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

We present a data-driven machine-learning approach for modeling space-time socioeconomic dynamics. Through coarse-graining fine-scale observations, our modeling framework simplifies these complex systems to a set of tractable mechanistic…

Coarse-graining techniques play a central role in reducing the complexity of stochastic models, and are typically characterised by a mapping which projects the full state of the system onto a smaller set of variables which captures the…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative…

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via…

Many real-valued stochastic time-series are locally linear (Gassian), but globally non-linear. For example, the trajectory of a human hand gesture can be viewed as a linear dynamic system driven by a nonlinear dynamic system that represents…

Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…

In this paper, we discuss information-theoretic tools for obtaining optimized coarse-grained molecular models for both equilibrium and non-equilibrium molecular dynamics. The latter are ubiquitous in physicochemical and biological…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…

In this paper, a general framework for the analysis of a connection between the training of artificial neural networks via the dynamics of Markov chains and the approximation of conservation law equations is proposed. This framework allows…

We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…

Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…

A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach…