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 …
Graph neural networks for temporal graphs: State of the art, open challenges, and opportunities
Graph Neural Networks (GNNs) have become the leading paradigm for learning on (static)
graph-structured data. However, many real-world systems are dynamic in nature, since the …
graph-structured data. However, many real-world systems are dynamic in nature, since the …
Physics-informed machine learning: A survey on problems, methods and applications
Recent advances of data-driven machine learning have revolutionized fields like computer
vision, reinforcement learning, and many scientific and engineering domains. In many real …
vision, reinforcement learning, and many scientific and engineering domains. In many real …
CAN-PINN: A fast physics-informed neural network based on coupled-automatic–numerical differentiation method
In this study, novel physics-informed neural network (PINN) methods for coupling
neighboring support points and their derivative terms which are obtained by automatic …
neighboring support points and their derivative terms which are obtained by automatic …
Transfer learning based physics-informed neural networks for solving inverse problems in engineering structures under different loading scenarios
Recently, a class of machine learning methods called physics-informed neural networks
(PINNs) has been proposed and gained prevalence in solving various scientific computing …
(PINNs) has been proposed and gained prevalence in solving various scientific computing …
Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads
A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk
network is devised to predict full-field highly nonlinear elastic–plastic stress response for …
network is devised to predict full-field highly nonlinear elastic–plastic stress response for …
Physics-informed PointNet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries
We present a novel physics-informed deep learning framework for solving steady-state
incompressible flow on multiple sets of irregular geometries by incorporating two main …
incompressible flow on multiple sets of irregular geometries by incorporating two main …
Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics
Traditional data-driven deep learning models often struggle with high training costs, error
accumulation, and poor generalizability in complex physical processes. Physics-informed …
accumulation, and poor generalizability in complex physical processes. Physics-informed …
[HTML][HTML] A graph convolutional autoencoder approach to model order reduction for parametrized PDEs
The present work proposes a framework for nonlinear model order reduction based on a
Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) …
Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) …
Hydrogen jet and diffusion modeling by physics-informed graph neural network
Abstract Renewable Power-to-Hydrogen (P2H2) system is an emerging decarbonization
strategy for achieving global carbon neutrality. However, the propensity of hydrogen to leak …
strategy for achieving global carbon neutrality. However, the propensity of hydrogen to leak …