Related papers: Distributed Control of Partial Differential Equati…

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…

A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization…

Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…

The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

A properly designed controller can help improve the quality of experimental measurements or force a dynamical system to follow a completely new time-evolution path. Recent developments in deep reinforcement learning have made steep advances…

Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality…

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…

We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…

This article shows how the recent breakthroughs in Reinforcement Learning (RL) that have enabled robots to learn to play arcade video games, walk or assemble colored bricks, can be used to perform other tasks that are currently at the core…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…

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…

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…

We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…

Manipulate and control of the complex quantum system with high precision are essential for achieving universal fault tolerant quantum computing. For a physical system with restricted control resources, it is a challenge to control the…

This paper introduces a framework for regression with dimensionally distributed data with a fusion center. A cooperative learning algorithm, the iterative conditional expectation algorithm (ICEA), is designed within this framework. The…

We present a novel method for Deep Reinforcement Learning (DRL), incorporating the convex property of the value function over the belief space in Partially Observable Markov Decision Processes (POMDPs). We introduce hard- and soft-enforced…