Promising directions of machine learning for partial differential equations
SL Brunton, JN Kutz - Nature Computational Science, 2024 - nature.com
Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …
descriptions of natural physical laws, capturing a rich variety of phenomenology and …
Modern Koopman theory for dynamical systems
The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …
algorithms emerging from modern computing and data science. First-principles derivations …
Multi-level convolutional autoencoder networks for parametric prediction of spatio-temporal dynamics
J Xu, K Duraisamy - Computer Methods in Applied Mechanics and …, 2020 - Elsevier
A data-driven framework is proposed towards the end of predictive modeling of complex
spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural …
spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural …
MaxwellNet: Physics-driven deep neural network training based on Maxwell's equations
Maxwell's equations govern light propagation and its interaction with matter. Therefore, the
solution of Maxwell's equations using computational electromagnetic simulations plays a …
solution of Maxwell's equations using computational electromagnetic simulations plays a …
DeepGreen: deep learning of Green's functions for nonlinear boundary value problems
Boundary value problems (BVPs) play a central role in the mathematical analysis of
constrained physical systems subjected to external forces. Consequently, BVPs frequently …
constrained physical systems subjected to external forces. Consequently, BVPs frequently …
Artificial neural networks for photonic applications—from algorithms to implementation: tutorial
This tutorial–review on applications of artificial neural networks in photonics targets a broad
audience, ranging from optical research and engineering communities to computer science …
audience, ranging from optical research and engineering communities to computer science …
Parsimony as the ultimate regularizer for physics-informed machine learning
JN Kutz, SL Brunton - Nonlinear Dynamics, 2022 - Springer
Data-driven modeling continues to be enabled by modern machine learning algorithms and
deep learning architectures. The goals of such efforts revolve around the generation of …
deep learning architectures. The goals of such efforts revolve around the generation of …
Koopman neural operator as a mesh-free solver of non-linear partial differential equations
The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to
a series of computational techniques for numerical solutions. Although numerous latest …
a series of computational techniques for numerical solutions. Although numerous latest …
[HTML][HTML] Machine learning for nonintrusive model order reduction of the parametric inviscid transonic flow past an airfoil
Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in
the design of commercial air transportation vehicles. Computational fluid dynamics models …
the design of commercial air transportation vehicles. Computational fluid dynamics models …
Machine learning for partial differential equations
SL Brunton, JN Kutz - arXiv preprint arXiv:2303.17078, 2023 - arxiv.org
Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and multi …
descriptions of natural physical laws, capturing a rich variety of phenomenology and multi …