Results 311 to 320 of about 217,226 (371)

Fourier Neural Operator with Learned Deformations for PDEs on General Geometries

Journal of machine learning research, 2022
Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a variety of PDEs ...
Zong-Yi Li, D. Huang, Burigede Liu, Anima Anandkumar   +3 more
semanticscholar   +1 more source

Convolutional Neural Operators for robust and accurate learning of PDEs

Neural Information Processing Systems, 2023
Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of PDEs. Here, we
Bogdan Raoni'c, R. Molinaro, T. D. Ryck, Tobias Rohner, Francesca Bartolucci, Rima Alaifari, Siddhartha Mishra, Emmanuel de B'ezenac   +7 more
semanticscholar   +1 more source

LIE REMARKABLE PDEs

Asymptotic Methods in Nonlinear Wave Phenomena, 2007
Within the context of the inverse Lie problem the question whether there exist PDEs that are characterized by their Lie point symmetries may be addressed. In a recent paper the authors called these equations Lie remarkable. In this paper we exhibit various examples of Lie remarkable equations, including some multidimensional Monge-Ampere type equations.
G. MANNO, OLIVERI, Francesco, R. VITOLO
openaire   +3 more sources

Extremum seeking boundary control for PDE–PDE cascades

Systems & Control Letters, 2021
The manuscript addresses the problem of extremum seeking for wave equations evolving in the one-dimensional spatial interval~\((0,1)\subset\mathbb R\). \par The input control acts on the right spatial boundary point~\(x=1\); see Eqs.~(4)--(7). The authors also consider the case where such input is subject to the solution of a heat equation; see Eqs ...
Oliveira, Tiago Roux, Krstic, Miroslav
openaire   +1 more source

Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

IMA Journal of Numerical Analysis, 2020
Physics-informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for partial differential equations (PDEs).
Siddhartha Mishra, R. Molinaro
semanticscholar   +1 more source

On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs

Journal of Computational Physics, 2017
Víctor Bayona, Natasha Flyer, Bengt Fornberg   +2 more
exaly   +2 more sources

Transolver: A Fast Transformer Solver for PDEs on General Geometries

International Conference on Machine Learning
Transformers have empowered many milestones across various fields and have recently been applied to solve partial differential equations (PDEs). However, since PDEs are typically discretized into large-scale meshes with complex geometries, it is ...
Haixu Wu, Huakun Luo, Haowen Wang, Jianmin Wang, Mingsheng Long   +4 more
semanticscholar   +1 more source

Parabolic PDE-PDE Loops

2018
This chapter of the book is devoted to the study of parabolic–parabolic PDE loops by means of the small-gain methodology. The results contained in the present chapter allow the existence of non-local reaction terms (both distributed terms and boundary terms) as well as distributed and boundary inputs.
Iasson Karafyllis, Miroslav Krstic
openaire   +1 more source

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

International Conference on Machine Learning
Although deep models have been widely explored in solving partial differential equations (PDEs), previous works are primarily limited to data only with up to tens of thousands of mesh points, far from the million-point scale required by industrial ...
Huakun Luo, Haixu Wu, Hang Zhou, Lanxiang Xing, Yichen Di, Jianmin Wang, Mingsheng Long   +6 more
semanticscholar   +1 more source

Hyperbolic PDE-PDE Loops

2018
The chapter is devoted to the development of the small-gain methodology for coupled 1-D, hyperbolic, first-order PDEs under the presence of external inputs. Our aim is the derivation of sufficient conditions that guarantee ISS for a given system of coupled hyperbolic PDEs. Globally, Lipschitz nonlinear, non-local terms are allowed to be present both in
Iasson Karafyllis, Miroslav Krstic
openaire   +1 more source