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.
Solving Schr¨ odinger equation using tensor neural network.arXiv preprint arXiv:2209.12572, 2022
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fTNN is a deterministic tensor neural network subspace method for fractional PDEs that decomposes the fractional Laplacian via spatially dependent integration splits and uses boundary-singularity-aware trial functions to achieve higher accuracy than fPINN and Monte Carlo methods on tested cases.
A frozen-feature neural network with a Gaussian envelope and stochastic dimension sampling produces accurate 1D–3D GPE solutions, but the 1000-dimensional claim rests on a manufactured stationary equation, not GPE dynamics.
Minimum number of terms for exact antisymmetry in a class of TPFs grows exponentially with dimension, shown via CP rank of antisymmetric tensors.
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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fTNN: a tensor neural network for fractional PDEs
fTNN is a deterministic tensor neural network subspace method for fractional PDEs that decomposes the fractional Laplacian via spatially dependent integration splits and uses boundary-singularity-aware trial functions to achieve higher accuracy than fPINN and Monte Carlo methods on tested cases.
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Stochastic-Dimension Frozen Sampled Neural Network for High-Dimensional Gross-Pitaevskii Equations on Unbounded Domains
A frozen-feature neural network with a Gaussian envelope and stochastic dimension sampling produces accurate 1D–3D GPE solutions, but the 1000-dimensional claim rests on a manufactured stationary equation, not GPE dynamics.
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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.
- Regularity Analysis and Tensor Neural Network Methods for Quasiperiodic Elliptic Equations