Solving high-dimensional partial differential equations using tensor neural network and a posteriori error estimators
DOI10.1007/S10915-024-02700-4MaRDI QIDQ6639507
Author name not available (Why is that?), Yangfei Liao, Hehu Xie, Yifan Wang, Zhongshuo Lin
Publication date: 15 November 2024
Published in: Journal of Scientific Computing (Search for Journal in Brave)
eigenvalue problema posteriori error estimatesmachine learningsecond-order elliptic operatortensor neural networkhigh-dimensional boundary value problems
Artificial neural networks and deep learning (68T07) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems
- Weak adversarial networks for high-dimensional partial differential equations
- Optimized tensor-product approximation spaces
- Inferring solutions of differential equations using noisy multi-fidelity data
- The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
- Complementarity based a posteriori error estimates and their properties
- DGM: a deep learning algorithm for solving partial differential equations
- Structure probing neural network deflation
- Solving many-electron Schrödinger equation using deep neural networks
- The finite element methods for elliptic problems.
- Proof of the fundamental gap conjecture
- Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Reaction-Diffusion Problems
- Sparse grids for the Schrödinger equation
- Computing Multi-Eigenpairs of High-Dimensional Eigenvalue Problems Using Tensor Neural Networks
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