Related papers: Learning the Evolution of Correlated Stochastic Po…

In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…

System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…

Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a…

Machine learning encompasses a set of tools and algorithms which are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting…

Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…

Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…

In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…

In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…

We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed…

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…

The modeling of dynamical systems is essential in many fields, but applying machine learning techniques is often challenging due to incomplete or noisy data. This study introduces a variant of stochastic interpolation (SI) for probabilistic…

In machine learning energy potentials for atomic systems, forces are commonly obtained as the negative derivative of the energy function with respect to atomic positions. To quantify aleatoric uncertainty in the predicted energies, a widely…

Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory…

Electricity systems are experiencing increased effects of randomness and variability due to emerging stochastic assets. The increased effects introduce new uncertainties into power systems that can impact system operability and reliability.…

Machine Learning is a powerful tool to reveal and exploit correlations in a multi-dimensional parameter space. Making predictions from such correlations is a highly non-trivial task, in particular when the details of the underlying dynamics…

The analysis of dynamical systems is a fundamental tool in the natural sciences and engineering. It is used to understand the evolution of systems as large as entire galaxies and as small as individual molecules. With predefined conditions…

Extracting environmental forces from noisy data is a common yet challenging task in complex physical systems. Machine learning represents a robust approach to this problem, yet is mostly tested on simulated data with known parameters. Here…

Approaches to keeping a dynamical system within state constraints typically rely on a model-based safety condition to limit the control signals. In the face of significant modeling uncertainty, the system can suffer from important…