Learning continuous models for continuous physics

AS Krishnapriyan, AF Queiruga, NB Erichson… - Communications …, 2023 - nature.com
Dynamical systems that evolve continuously over time are ubiquitous throughout science
and engineering. Machine learning (ML) provides data-driven approaches to model and …

Data-driven tensor train gradient cross approximation for hamilton–jacobi–bellman equations

S Dolgov, D Kalise, L Saluzzi - SIAM Journal on Scientific Computing, 2023 - SIAM
A gradient-enhanced functional tensor train cross approximation method for the resolution of
the Hamilton–Jacobi–Bellman (HJB) equations associated with optimal feedback control of …

Learning optimal feedback operators and their sparse polynomial approximations

K Kunisch, D Vásquez-Varas, D Walter - Journal of Machine Learning …, 2023 - jmlr.org
A learning based method for obtaining feedback laws for nonlinear optimal control problems
is proposed. The learning problem is posed such that the open loop value function is its …

Leveraging multitime Hamilton–Jacobi PDEs for certain scientific machine learning problems

P Chen, T Meng, Z Zou, J Darbon… - SIAM Journal on Scientific …, 2024 - SIAM
Hamilton–Jacobi partial differential equations (HJ PDEs) have deep connections with a wide
range of fields, including optimal control, differential games, and imaging sciences. By …

Approximation of compositional functions with ReLU neural networks

Q Gong, W Kang, F Fahroo - Systems & Control Letters, 2023 - Elsevier
The power of DNN has been successfully demonstrated on a wide variety of high-
dimensional problems that cannot be solved by conventional control design methods. These …

Sympocnet: Solving optimal control problems with applications to high-dimensional multiagent path planning problems

T Meng, Z Zhang, J Darbon, G Karniadakis - SIAM Journal on Scientific …, 2022 - SIAM
Solving high-dimensional optimal control problems in real-time is an important but
challenging problem, with applications to multiagent path planning problems, which have …

Feedforward neural networks and compositional functions with applications to dynamical systems

W Kang, Q Gong - SIAM Journal on Control and Optimization, 2022 - SIAM
In this paper we develop an algebraic framework for analyzing neural network
approximation of compositional functions, a rich class of functions that are frequently …

Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton–Jacobi PDEs

J Darbon, PM Dower, T Meng - Mathematics of Control, Signals, and …, 2023 - Springer
Solving high-dimensional optimal control problems and corresponding Hamilton–Jacobi
PDEs are important but challenging problems in control engineering. In this paper, we …

HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models

T Meng, Z Zou, J Darbon, GE Karniadakis - arxiv preprint arxiv …, 2024 - arxiv.org
The interplay between stochastic processes and optimal control has been extensively
explored in the literature. With the recent surge in the use of diffusion models, stochastic …

Neural network optimal feedback control with guaranteed local stability

T Nakamura-Zimmerer, Q Gong… - IEEE Open Journal of …, 2022 - ieeexplore.ieee.org
Recent research shows that supervised learning can be an effective tool for designing near-
optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the …