Scientific machine learning through physics–informed neural networks: Where we are and what's next
Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …
model equations, like Partial Differential Equations (PDE), as a component of the neural …
Physics-guided, physics-informed, and physics-encoded neural networks in scientific computing
Recent breakthroughs in computing power have made it feasible to use machine learning
and deep learning to advance scientific computing in many fields, including fluid mechanics …
and deep learning to advance scientific computing in many fields, including fluid mechanics …
A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data
Neural operators can learn nonlinear mappings between function spaces and offer a new
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
Partial differential equations (PDEs) play a central role in the mathematical analysis and
modeling of complex dynamic processes across all corners of science and engineering …
modeling of complex dynamic processes across all corners of science and engineering …
A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials
Failure trajectories, probable failure zones, and damage indices are some of the key
quantities of relevance in brittle fracture mechanics. High-fidelity numerical solvers that …
quantities of relevance in brittle fracture mechanics. High-fidelity numerical solvers that …
On universal approximation and error bounds for Fourier neural operators
Fourier neural operators (FNOs) have recently been proposed as an effective framework for
learning operators that map between infinite-dimensional spaces. We prove that FNOs are …
learning operators that map between infinite-dimensional spaces. We prove that FNOs are …
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 …
Reliable extrapolation of deep neural operators informed by physics or sparse observations
Deep neural operators can learn nonlinear mappings between infinite-dimensional function
spaces via deep neural networks. As promising surrogate solvers of partial differential …
spaces via deep neural networks. As promising surrogate solvers of partial differential …
Error estimates for deeponets: A deep learning framework in infinite dimensions
S Lanthaler, S Mishra… - … of Mathematics and Its …, 2022 - academic.oup.com
DeepONets have recently been proposed as a framework for learning nonlinear operators
mapping between infinite-dimensional Banach spaces. We analyze DeepONets and prove …
mapping between infinite-dimensional Banach spaces. We analyze DeepONets and prove …
Model reduction and neural networks for parametric PDEs
We develop a general framework for data-driven approximation of input-output maps
between infinitedimensional spaces. The proposed approach is motivated by the recent …
between infinitedimensional spaces. The proposed approach is motivated by the recent …