Neural operators for accelerating scientific simulations and design
Scientific discovery and engineering design are currently limited by the time and cost of
physical experiments. Numerical simulations are an alternative approach but are usually …
physical experiments. Numerical simulations are an alternative approach but are usually …
An operator learning perspective on parameter-to-observable maps
Computationally efficient surrogates for parametrized physical models play a crucial role in
science and engineering. Operator learning provides data-driven surrogates that map …
science and engineering. Operator learning provides data-driven surrogates that map …
NCDL: a framework for deep learning on non-cartesian lattices
J Horacsek, U Alim - Advances in Neural Information …, 2024 - proceedings.neurips.cc
The use of non-Cartesian grids is a niche but important topic in sub-fields of the numerical
sciences such as simulation and scientific visualization. However, non-Cartesian …
sciences such as simulation and scientific visualization. However, non-Cartesian …
Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems
Fourier Neural Operators (FNOs) excel on tasks using functional data, such as those
originating from partial differential equations. Such characteristics render them an effective …
originating from partial differential equations. Such characteristics render them an effective …
Operator Deep Smoothing for Implied Volatility
L Gonon, A Jacquier, R Wiedemann - arXiv preprint arXiv:2406.11520, 2024 - arxiv.org
We devise a novel method for implied volatility smoothing based on neural operators. The
goal of implied volatility smoothing is to construct a smooth surface that links the collection of …
goal of implied volatility smoothing is to construct a smooth surface that links the collection of …
Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids
Scientific computing using deep learning has seen significant advancements in recent
years. There has been growing interest in models that learn the operator from the …
years. There has been growing interest in models that learn the operator from the …
Operator learning based on sparse high-dimensional approximation
D Potts, F Taubert - arXiv preprint arXiv:2406.03973, 2024 - arxiv.org
We present a dimension-incremental method for function approximation in bounded
orthonormal product bases to learn the solutions of various differential equations. Therefore …
orthonormal product bases to learn the solutions of various differential equations. Therefore …
[图书][B] Statistical Foundations of Operator Learning
NH Nelsen - 2024 - search.proquest.com
This thesis studies operator learning from a statistical perspective. Operator learning uses
observed data to estimate mappings between infinite-dimensional spaces. It does so at the …
observed data to estimate mappings between infinite-dimensional spaces. It does so at the …
[PDF][PDF] PINN-TI: Physical Information embedded in Neural Networks for solving ordinary differential equations with Time-varying Inputs
X Zhao, YT Shi, K Zhao - 2024 - scholar.archive.org
Modeling and predicting the dynamics of multiphysics and multiscale systems with hidden
physics methods is often costly, requiring different formulations and complex computer …
physics methods is often costly, requiring different formulations and complex computer …
GraphDeepONet: Learning to simulate time-dependent partial differential equations using graph neural network and deep operator network
Scientific computing using deep learning has seen significant advancements in recent
years. There has been growing interest in models that learn the operator from the …
years. There has been growing interest in models that learn the operator from the …