NSEM solves Poisson-Nernst-Planck benchmarks to 10^-4 to 10^-7 relative error using two orders of magnitude fewer collocation points than adaptive PINNs by combining spectral differentiation matrices with neural networks and a boundary-layer coordinate map.
When and why pinns fail to train: A neural tangent kernel perspective
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Different neural architectures produce qualitatively distinct controls in PINN optimal control for RLC and Duffing systems, with Fourier versions yielding richer oscillations and smoother nets yielding more regular efficient trajectories.
A high-level outline is given for a unified theory that reduces learning to a small set of ideas from dynamical systems, geometry, and physics via definitions of solvable problems and parametrized methods.
Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
A comprehensive review of deep learning techniques for computational mechanics, including LSTM for constitutive modeling, PINNs for PDE solving, optimizers, and kernel methods.
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