Tensor neural networks with projection solve quasiperiodic elliptic equations after proving regularity under Diophantine conditions and a source-term restriction.
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SD-FSNN combines stochastic dimension sampling, frozen random weights, Gaussian ansatz, and structure-preserving layers to solve high-dimensional GPEs on unbounded domains with dimension-independent cost and improved accuracy over prior solvers.
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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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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Stochastic-Dimension Frozen Sampled Neural Network for High-Dimensional Gross-Pitaevskii Equations on Unbounded Domains
SD-FSNN combines stochastic dimension sampling, frozen random weights, Gaussian ansatz, and structure-preserving layers to solve high-dimensional GPEs on unbounded domains with dimension-independent cost and improved accuracy over prior solvers.
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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.