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In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…

The paper proposes a systematic framework for building data-driven stochastic differential equation (SDE) models from sparse, noisy observations. Unlike traditional parametric approaches, which assume a known functional form for the drift,…

Understanding the training dynamics of deep learning models is perhaps a necessary step toward demystifying the effectiveness of these models. In particular, how do data from different classes gradually become separable in their feature…

In this work, we explore modeling change points in time-series data using neural stochastic differential equations (neural SDEs). We propose a novel model formulation and training procedure based on the variational autoencoder (VAE)…

Although the governing equations of many systems, when derived from first principles, may be viewed as known, it is often too expensive to numerically simulate all the interactions they describe. Therefore researchers often seek simpler…

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…

We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics. We approximate the…

Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between…

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…

Dynamical systems are essential to model various phenomena in physics, finance, economics, and are also of current interest in machine learning. A central modeling task is investigating parameter sensitivity, whether tuning atmospheric…

The reconstruction and inference of stochastic dynamical systems from data is a fundamental task in inverse problems and statistical learning. While surrogate modeling advances computational methods to approximate these dynamics, standard…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Physical computing has the potential to enable widespread embodied intelligence by leveraging the intrinsic dynamics of complex systems for efficient sensing, processing, and interaction. While individual devices provide basic data…

Simulating parameter-dependent stochastic differential equations (SDEs) presents significant computational challenges, as separate high-fidelity simulations are typically required for each parameter value of interest. Despite the success of…

When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales, stochastic noise and high-dimensionality can make simulations prohibitively expensive. The computational cost is dictated by…

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…

Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…

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 address the issue of modeling and estimating changes in the state of the spatio-temporal dynamical systems based on a sequence of observations like video frames. Traditional numerical simulation systems depend largely on…