Holomorphic neural networks enforce exact satisfaction of harmonic PDEs for 3D Laplace and elasticity problems using Whittaker representations and boundary-only training.
Machine Learning for Computational Science and Engineering 1
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An auto-adaptive sampling technique for PINNs is introduced and tested on Allen-Cahn equations to better resolve interfacial regions compared to residual-adaptive methods.
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A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials
Holomorphic neural networks enforce exact satisfaction of harmonic PDEs for 3D Laplace and elasticity problems using Whittaker representations and boundary-only training.
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Auto-Adaptive PINNs with Applications to Phase Transitions
An auto-adaptive sampling technique for PINNs is introduced and tested on Allen-Cahn equations to better resolve interfacial regions compared to residual-adaptive methods.