Related papers: Stochastic Physics-Informed Neural Ordinary Differ…

We propose a novel Stochastic Differential Equation (SDE) framework to address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODEs) have shown…

Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each…

Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the governing equations are unknown and observational data are…

Stochastic regularization of neural networks (e.g. dropout) is a wide-spread technique in deep learning that allows for better generalization. Despite its success, continuous-time models, such as neural ordinary differential equation (ODE),…

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

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…

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…

Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to…

We present a framework and algorithms to learn controlled dynamics models using neural stochastic differential equations (SDEs) -- SDEs whose drift and diffusion terms are both parametrized by neural networks. We construct the drift term to…

This paper proposes the use of spectral element methods \citep{canuto_spectral_1988} for fast and accurate training of Neural Ordinary Differential Equations (ODE-Nets; \citealp{Chen2018NeuralOD}) for system identification. This is achieved…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

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…

Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…

Understanding and modeling nonlinear dynamical systems is a fundamental challenge across science and engineering. Deep learning has shown remarkable potential for capturing complex system behavior, yet achieving models that are both…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

It is critical yet challenging for deep learning models to properly characterize uncertainty that is pervasive in real-world environments. Although a lot of efforts have been made, such as heteroscedastic neural networks (HNNs), little work…

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…

Neural differential equations offer a powerful framework for modeling continuous-time dynamics, but forecasting stiff biophysical systems remains unreliable. Standard Neural ODEs and physics informed variants often require orders of…