LiL-Q applies quasilinearization to nonlinear PDEs and solves each resulting linear problem by convex least-squares collocation on Linear-in-Learnables trial spaces, achieving fast convergence and high accuracy on multiple benchmarks.
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When and why pinns fail to train: A neural tangent kernel perspective
14 Pith papers cite this work. Polarity classification is still indexing.
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An adaptive KAN-based PINN framework for axisymmetric pulsar magnetosphere achieves O(1e-6) PDE residual errors, under-20-minute convergence, smaller stellar radii, and a correction to the flux-T-point equation.
The curvature-aware precision controller adapts between FP32 and FP64 during PINN training to match double-precision accuracy at reduced computational cost.
A coupled LSTM-GNN model reconstructs local elasto-plastic stress fields from macroscopic loading paths on a plate-with-hole microstructure, achieving 1000x speedup and mesh transferability with 1.9% error.
PINN-AFE uses multi-head attention and input convex networks to solve Monge-Ampère equations with claimed accuracy, efficiency, and extensions to image enhancement and medical registration.
P-GONE applies generative ML to optimize Trotter-Suzuki decompositions, reporting up to 19.4x circuit depth reduction at F >= 0.95 versus Qiskit baselines on structured Hamiltonians.
An adaptive anisotropic composite quadrature strategy combined with refresh-based training narrows the gap between training and reference losses in neural residual minimization for PDEs while using quadrature points more efficiently.
Bio-PINNs with a near-to-far curriculum and deformation-uncertainty proxy recover cell-induced densified phases and tether morphologies more reliably than standard adaptive PINN baselines in single-cell and multicellular settings.
ActNet is a new KST-based neural network that outperforms KANs and competes with MLPs in PINN benchmarks for PDE simulation tasks.
INI-VPINN is a new weak-form PINN formulation that implicitly enforces Neumann and interface conditions for Poisson and Laplace problems in multi-material domains with geometric singularities.
RBF-RLS outperforms PINNs on PDEs with Dirac deltas via weak-form integration, delivering consistent forward and inverse solutions for linear transport problems in porous media and rivers.
A heteroscedastic uncertainty PINN with warm-start and deep ensembles for SAR flood inference claims 25% IoU gain by relaxing physics constraints in high-noise regions.
StableGrad applies scale correction to weight gradients after backpropagation to enable stable optimization of deep BatchNorm-free networks including PINNs.
An attention-based physics-guided CNN surrogate is trained to predict long-time microstructural evolution under the Cahn-Hilliard equation for both critical and off-critical mixtures while preserving composition and matching Lifshitz-Slyozov domain growth.
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Deep Learning Alternatives of the Kolmogorov Superposition Theorem
ActNet is a new KST-based neural network that outperforms KANs and competes with MLPs in PINN benchmarks for PDE simulation tasks.