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 …
Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
Deep neural operators can learn operators mapping between infinite-dimensional function
spaces via deep neural networks and have become an emerging paradigm of scientific …
spaces via deep neural networks and have become an emerging paradigm of scientific …
Learning the dynamical response of nonlinear non-autonomous dynamical systems with deep operator neural networks
We propose using operator learning to approximate the dynamical response of non-
autonomous systems, such as nonlinear control systems. Unlike classical function learning …
autonomous systems, such as nonlinear control systems. Unlike classical function learning …
Scalable uncertainty quantification for deep operator networks using randomized priors
We present a simple and effective approach for posterior uncertainty quantification in deep
operator networks (DeepONets); an emerging paradigm for supervised learning in function …
operator networks (DeepONets); an emerging paradigm for supervised learning in function …
A mathematical guide to operator learning
N Boullé, A Townsend - arXiv preprint arXiv:2312.14688, 2023 - arxiv.org
Operator learning aims to discover properties of an underlying dynamical system or partial
differential equation (PDE) from data. Here, we present a step-by-step guide to operator …
differential equation (PDE) from data. Here, we present a step-by-step guide to operator …
Vb-deeponet: A bayesian operator learning framework for uncertainty quantification
S Garg, S Chakraborty - Engineering Applications of Artificial Intelligence, 2023 - Elsevier
Neural network based data-driven operator learning schemes have shown tremendous
potential in computational mechanics. DeepONet is one such neural network architecture …
potential in computational mechanics. DeepONet is one such neural network architecture …
Deep learning methods for partial differential equations and related parameter identification problems
Recent years have witnessed a growth in mathematics for deep learning—which seeks a
deeper understanding of the concepts of deep learning with mathematics and explores how …
deeper understanding of the concepts of deep learning with mathematics and explores how …
Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators
Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly
critical as neural networks (NNs) are being widely adopted in addressing complex problems …
critical as neural networks (NNs) are being widely adopted in addressing complex problems …
RiemannONets: Interpretable neural operators for Riemann problems
Developing the proper representations for simulating high-speed flows with strong shock
waves, rarefactions, and contact discontinuities has been a long-standing question in …
waves, rarefactions, and contact discontinuities has been a long-standing question in …
DAE-PINN: a physics-informed neural network model for simulating differential algebraic equations with application to power networks
Deep learning-based surrogate modeling is becoming a promising approach for learning
and simulating dynamical systems. However, deep-learning methods find it very challenging …
and simulating dynamical systems. However, deep-learning methods find it very challenging …