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.
A physics-informed deep learning framework for inversion and surrogate mod- eling in solid mechanics
5 Pith papers cite this work. Polarity classification is still indexing.
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2026 5representative citing papers
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.
Systematic benchmark of PINN architectures on 1D stiff PNP system finds BRDR loss weighting competitive with NTK at lower wall-clock time.
PINNs for first-order plane-strain elastodynamics achieve higher accuracy with soft boundary enforcement over implicit geometries but require longer training than hard enforcement.
Digi Turbine is a synthetic PINN benchmark integrating Euler-Bernoulli beam theory with Winkler foundation, Bayesian inverse identification, and FORM screening for OWT monopile monitoring, validated on synthetic data with analytical ground truth.
citing papers explorer
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A Systematic Benchmark of Physics-Informed Neural Network Architectures for the Stiff Poisson-Nernst-Planck System: Adaptive LossWeighting and Multi-Scale Resolution
Systematic benchmark of PINN architectures on 1D stiff PNP system finds BRDR loss weighting competitive with NTK at lower wall-clock time.