Tensor neural networks with projection solve quasiperiodic elliptic equations after proving regularity under Diophantine conditions and a source-term restriction.
Tensor neural network and its numerical integration.arXiv preprint arXiv:2207.02754v4, 2023
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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.
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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.