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Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspectivehttps://arxiv.org/abs/2502.00604
Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networkshttps://epubs.siam.org/doi/10.1137/20M1318043
When and Why PINNs Fail to Train: A Neural Tangent Kernel Perspectivehttps://www.sciencedirect.com/science/article/pii/S002199912100663X?casa_token=YlzVQK6hGy8AAAAA:bKwMNg70UoeEuisR1cd1KZnR20xspdvYp1dM4jLkl_wfVDX7O1j2IOlGZsYnC4esu7YcMaO_WOIC
Respecting Causality for Training Physics-informed Neural Networkshttps://www.sciencedirect.com/science/article/pii/S0045782524000690
Random Weight Factorization Improves the Training of Continuous Neural Representationshttps://arxiv.org/abs/2210.01274
On the Eigenvector Bias of Fourier Feature Networks: From Regression to Solving Multi-Scale PDEs with Physics-Informed Neural Networkhttps://www.sciencedirect.com/science/article/abs/pii/S0045782521002759
PirateNets: Physics-informed Deep Learning with Residual Adaptive Networkshttps://arxiv.org/abs/2402.00326
Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainshttps://arxiv.org/abs/2006.10739
A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networkshttps://www.sciencedirect.com/science/article/abs/pii/S0021999121001376
Characterizing Possible Failure Modes in Physics-Informed Neural Networkshttps://arxiv.org/abs/2109.01050
Deep Learning Alternatives of the Kolmogorov Superposition Theoremhttps://arxiv.org/abs/2410.01990
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