Neural networks regress oversized subspaces for parametric problems using subspace-specific losses, with theory and experiments showing improved accuracy and smoother mappings.
Preprint, arXiv:2404.18841 [math.NA] (2024)
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Two new DOD-based reduced-order models (DOD-DL-ROM and DOD+DFNN) are introduced for hybrid-type parabolic PDEs, with rigorous error bounds linking performance to optimal map regularity and conditions for outperforming POD methods.
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Deep Learning for Subspace Regression
Neural networks regress oversized subspaces for parametric problems using subspace-specific losses, with theory and experiments showing improved accuracy and smoother mappings.
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A New Adaptive Deep Learning based Reduced Order Model for Hybrid-Type Parabolic PDEs: Rigorous Error Analysis and Applications
Two new DOD-based reduced-order models (DOD-DL-ROM and DOD+DFNN) are introduced for hybrid-type parabolic PDEs, with rigorous error bounds linking performance to optimal map regularity and conditions for outperforming POD methods.