PRISM enables zero-shot parameterized high-dimensional high-order neural PDE solvers via implicit stochastic modulation that decouples parameters from the differentiation graph while preserving unbiased estimators.
Tensor neural network and its numerical integration.arXiv preprint arXiv:2207.02754v4, 2023
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Tensor neural network approximation reduces high-dimensional nonlocal diffusion integrals to low-dimensional ones via separability, with L2 error estimates for Dirichlet and Neumann conditions and tests up to dimension 20.
Minimum number of terms for exact antisymmetry in a class of TPFs grows exponentially with dimension, shown via CP rank of antisymmetric tensors.
TPNet constructs multi-dimensional basis functions via tensor products of subnetwork outputs and solves for coefficients with least-squares to solve PDEs more efficiently than PINNs.
citing papers explorer
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Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers
PRISM enables zero-shot parameterized high-dimensional high-order neural PDE solvers via implicit stochastic modulation that decouples parameters from the differentiation graph while preserving unbiased estimators.
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ND-TNN: Tensor-Neural-Network Approximation for High-Dimensional Nonlocal Diffusion Models
Tensor neural network approximation reduces high-dimensional nonlocal diffusion integrals to low-dimensional ones via separability, with L2 error estimates for Dirichlet and Neumann conditions and tests up to dimension 20.
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Lower Bound on the Representation Complexity of Antisymmetric Tensor Product Functions
Minimum number of terms for exact antisymmetry in a class of TPFs grows exponentially with dimension, shown via CP rank of antisymmetric tensors.
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A Novel Tensor Product-Based Neural Network for Solving Partial Differential Equations
TPNet constructs multi-dimensional basis functions via tensor products of subnetwork outputs and solves for coefficients with least-squares to solve PDEs more efficiently than PINNs.
- Regularity Analysis and Tensor Neural Network Methods for Quasiperiodic Elliptic Equations