The Neural Compiler converts symbolic programs into exact differentiable PyTorch modules for hybrid scientific machine learning, enabling precise encoding of known physics with few trainable parameters.
Understanding and mitigating gradient flow pathologies in physics-informed neural networks.SIAM Journal on Scientific Computing, 43(5):A3055–A3081
9 Pith papers cite this work. Polarity classification is still indexing.
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G-PARC embeds analytically computed differential operators via moving least squares on graphs into recurrent networks, achieving higher accuracy with 2-3x fewer parameters than prior graph PADL methods on nonlinear benchmarks.
A multi-network PINN with NTK-based adaptive weighting jointly estimates source functions, velocity, diffusion parameters, and the solution field in advection-diffusion PDEs from noisy sparse data.
Sparse RFNNs with sSVD via Lanczos-Golub-Kahan bidiagonalization maintain accuracy while improving efficiency and robustness for 1D steady convection-diffusion equations with strong advection.
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
A meta-network learns to adapt Gaussian basis geometry across parametric PDE families, which a physics-informed least-squares corrector then refines for improved accuracy.
The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.
AdamFLIP treats PDE constraint residuals in PINNs as a controlled dynamical system, computes Lagrange multipliers via feedback linearization to drive residuals to zero, and applies Adam-style adaptation to the resulting gradient for scalable hard-constrained training.
The paper surveys AI surrogates including PINNs, neural operators, and hybrid generative models as ways to reach high-Re and high-S MHD regimes beyond direct numerical simulation.
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Physics-Informed Neural Networks for Joint Source and Parameter Estimation in Advection-Diffusion Equations
A multi-network PINN with NTK-based adaptive weighting jointly estimates source functions, velocity, diffusion parameters, and the solution field in advection-diffusion PDEs from noisy sparse data.
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When PINNs Go Wrong: Pseudo-Time Stepping Against Spurious Solutions
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.