Related papers: Learning dynamics on invariant measures using PDE-…

In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of…

We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…

The problem of continuous inverse optimal control (over finite time horizon) is to learn the unknown cost function over the sequence of continuous control variables from expert demonstrations. In this article, we study this fundamental…

Reinforcement learning algorithms typically consider discrete-time dynamics, even though the underlying systems are often continuous in time. In this paper, we introduce a model-based reinforcement learning algorithm that represents…

The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…

Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…

Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse…

Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…

We study time uncertainty-aware modeling of continuous-time dynamics of interacting objects. We introduce a new model that decomposes independent dynamics of single objects accurately from their interactions. By employing latent Gaussian…

The combination of numerical integration and deep learning, i.e., ODE-net, has been successfully employed in a variety of applications. In this work, we introduce inverse modified differential equations (IMDE) to contribute to the behaviour…

Ordinary differential equations (ODEs) are a conventional way to describe the observed dynamics of physical systems. Scientists typically hypothesize about dynamical behavior, propose a mathematical model, and compare its predictions to…

Learning or identifying dynamics from a sequence of high-dimensional observations is a difficult challenge in many domains, including reinforcement learning and control. The problem has recently been studied from a generative perspective…

Along with the practical success of the discovery of dynamics using deep learning, the theoretical analysis of this approach has attracted increasing attention. Prior works have established the grid error estimation with auxiliary…

Neural ordinary differential equations (ODEs) are widely recognized as the standard for modeling physical mechanisms, which help to perform approximate inference in unknown physical or biological environments. In partially observable (PO)…

This letter presents a high-dimensional analysis of the training dynamics for a single-layer nonlinear contrastive learning model. The empirical distribution of the model weights converges to a deterministic measure governed by a…

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when…

Model generalization of the underlying dynamics is critical for achieving data efficiency when learning for robot control. This paper proposes a novel approach for learning dynamics leveraging the symmetry in the underlying robotic system,…

This paper introduces new model parameterizations for learning discrete-time dynamical systems from data via the Koopman operator and studies their properties. Whereas most existing works on Koopman learning do not take into account the…

We address the problem of estimating the inputs of a dynamical system from measurements of the system's outputs. To this end, we introduce a novel estimation algorithm that explicitly trades off bias and variance to optimally reduce the…