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.
Gradient-enhanced physics- informed neural networks for forward and inverse PDE problems.Computer Methods in Applied Mechanics and Engineering, 393:114823, 2022
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PI-MFA optimizes tensor-product B-spline control points to balance data fidelity against PDE residuals, producing physically consistent continuous flow fields.
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NPSolver trains neural Poisson solvers label-free by supervising with a small number of preconditioned conjugate gradient steps and adds Boundary-Aware Transolver for mixed boundaries, outperforming baselines on 2D/3D irregular geometries.
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A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks
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.