MIONet: Learning Multiple-Input Operators via Tensor Product
From MaRDI portal
Publication:5048574
DOI10.1137/22M1477751MaRDI QIDQ5048574
Lu Lu, Shuai Meng, Pengzhan Jin
Publication date: 16 November 2022
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2202.06137
neural networksuniversal approximation theoremtensor productoperator regressionscientific machine learningMIONetmultiple-input operators
Computational learning theory (68Q32) Artificial neural networks and deep learning (68T07) Algorithms for approximation of functions (65D15) Nonlinear operators and their properties (47H99) Computational methods for problems pertaining to operator theory (47-08)
Related Items
Deep learning methods for partial differential equations and related parameter identification problems, Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness, Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads, Reliable extrapolation of deep neural operators informed by physics or sparse observations, Transferable neural networks for partial differential equations, Variationally mimetic operator networks, A nonlinear-manifold reduced-order model and operator learning for partial differential equations with sharp solution gradients
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Tensor Decompositions and Applications
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Machine learning in cardiovascular flows modeling: predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
- DGM: a deep learning algorithm for solving partial differential equations
- A physics-informed operator regression framework for extracting data-driven continuum models
- DeepM\&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks
- DeepM\&Mnet for hypersonics: predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Banach space theory. The basis for linear and nonlinear analysis
- A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials
- Tensor rank is NP-complete
- The Random Feature Model for Input-Output Maps between Banach Spaces
- Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- A seamless multiscale operator neural network for inferring bubble dynamics
- Physics-Informed Neural Networks with Hard Constraints for Inverse Design
- fPINNs: Fractional Physics-Informed Neural Networks