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.
Tensor neural networks with projection solve quasiperiodic elliptic equations after proving regularity under Diophantine conditions and a source-term restriction.
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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Regularity Analysis and Tensor Neural Network Methods for Quasiperiodic Elliptic Equations
Tensor neural networks with projection solve quasiperiodic elliptic equations after proving regularity under Diophantine conditions and a source-term restriction.
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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.