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Many computer vision and image processing problems can be posed as solving partial differential equations (PDEs). However, designing PDE system usually requires high mathematical skills and good insight into the problems. In this paper, we…

Computer Vision and Pattern Recognition · Computer Science 2011-09-07 Risheng Liu , Zhouchen Lin , Wei Zhang , Kewei Tang , Zhixun Su

Spacecraft are vital to space exploration and are often equipped with lightweight, flexible appendages to meet strict weight constraints. These appendages pose significant challenges for modeling and control due to their inherent…

Systems and Control · Electrical Eng. & Systems 2025-02-14 Huanqing Wang , Kaixiang Zhang , Amin Vahidi-Moghaddam , Haowei An , Nan Li , Daning Huang , Zhaojian Li

Recently deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we…

Machine Learning · Computer Science 2023-08-25 Zhiwei Fang , Sifan Wang , Paris Perdikaris

This paper introduces a novel approach to PDE boundary control design using neural operators to alleviate stop-and-go instabilities in congested traffic flow. Our framework leverages neural operators to design control strategies for traffic…

Machine Learning · Computer Science 2023-12-19 Yihuai Zhang , Ruiguo Zhong , Huan Yu

Effectively controlling systems governed by Partial Differential Equations (PDEs) is crucial in several fields of Applied Sciences and Engineering. These systems usually yield significant challenges to conventional control schemes due to…

Machine Learning · Computer Science 2024-11-07 Florian Wolf , Nicolò Botteghi , Urban Fasel , Andrea Manzoni

Systems modeled by partial differential equations (PDEs) are at least as ubiquitous as systems that are by nature finite-dimensional and modeled by ordinary differential equations (ODEs). And yet, systematic and readily usable…

Optimization and Control · Mathematics 2025-09-11 Rafael Vazquez , Jean Auriol , Federico Bribiesca-Argomedo , Miroslav Krstic

Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the…

Machine Learning · Computer Science 2026-02-20 Yilong Dai , Shengyu Chen , Ziyi Wang , Xiaowei Jia , Yiqun Xie , Vipin Kumar , Runlong Yu

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

Machine Learning · Computer Science 2021-09-29 Pongpisit Thanasutives , Masayuki Numao , Ken-ichi Fukui

The goal of this paper is to make a strong point for the usage of dynamical models when using reinforcement learning (RL) for feedback control of dynamical systems governed by partial differential equations (PDEs). To breach the gap between…

Machine Learning · Computer Science 2023-03-14 Stefan Werner , Sebastian Peitz

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

Machine Learning · Computer Science 2022-11-21 Shudong Huang , Wentao Feng , Chenwei Tang , Jiancheng Lv

We consider the joint design and control of discrete-time stochastic dynamical systems over a finite time horizon. We formulate the problem as a multi-step optimization problem under uncertainty seeking to identify a system design and a…

Machine Learning · Computer Science 2022-01-07 Adrien Bolland , Ioannis Boukas , Mathias Berger , Damien Ernst

We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…

Machine Learning · Computer Science 2025-12-01 Eduardo Soares , Emilio Vital Brazil , Victor Shirasuna , Breno W. S. R. de Carvalho , Cristiano Malossi

Initial boundary value problems arise commonly in applications with engineering and natural systems governed by nonlinear partial differential equations (PDEs). Operator learning is an emerging field for solving these equations by using a…

Machine Learning · Computer Science 2025-05-15 Sumanth Kumar Boya , Deepak Subramani

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…

Machine Learning · Computer Science 2021-11-17 Zhao Chen , Yang Liu , Hao Sun

A fundamental problem in science and engineering is designing optimal control policies that steer a given system towards a desired outcome. This work proposes Control Physics-Informed Neural Networks (Control PINNs) that simultaneously…

Machine Learning · Computer Science 2022-08-22 Jostein Barry-Straume , Arash Sarshar , Andrey A. Popov , Adrian Sandu

Many engineering and scientific fields have recently become interested in modeling terms in partial differential equations (PDEs) with neural networks, which requires solving the inverse problem of learning neural network terms from…

Machine Learning · Computer Science 2026-03-30 Konstantin Riedl , Justin Sirignano , Konstantinos Spiliopoulos

Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations…

Machine Learning · Computer Science 2021-08-19 Karl Otness , Arvi Gjoka , Joan Bruna , Daniele Panozzo , Benjamin Peherstorfer , Teseo Schneider , Denis Zorin

Through many recent successes in simulation, model-free reinforcement learning has emerged as a promising approach to solving continuous control robotic tasks. The research community is now able to reproduce, analyze and build quickly on…

Machine Learning · Computer Science 2018-09-21 A. Rupam Mahmood , Dmytro Korenkevych , Gautham Vasan , William Ma , James Bergstra

Recently, researchers have made significant progress combining the advances in deep learning for learning feature representations with reinforcement learning. Some notable examples include training agents to play Atari games based on raw…

Machine Learning · Computer Science 2016-05-30 Yan Duan , Xi Chen , Rein Houthooft , John Schulman , Pieter Abbeel

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…

Numerical Analysis · Mathematics 2025-07-10 Dimitrios Gazoulis , Ioannis Gkanis , Charalambos G. Makridakis