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.
Quadratic approximation manifold for mitigating the Kolmogorov barrier in nonlinear projection- based model order reduction,
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FastQM rotates a candidate basis of singular vectors on the Stiefel manifold to maximize quadratic manifold approximation quality, with feature-space cost independent of full dimension, shown on turbulent airfoil-wake data.
A dynamic subspace method parameterizes low-dimensional bases as geodesic paths on the Grassmannian to track evolving physics in nonlinear systems, achieving higher accuracy than static approximations at the same rank.
citing papers explorer
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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.
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Fast Quadratic Manifold Learning For Nonlinear Dimensionality Reduction in Large-scale Systems using Riemannian Optimization
FastQM rotates a candidate basis of singular vectors on the Stiefel manifold to maximize quadratic manifold approximation quality, with feature-space cost independent of full dimension, shown on turbulent airfoil-wake data.
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A Dynamic Subspace Approach for Low-rank Approximation of Large-scale Nonlinear Systems
A dynamic subspace method parameterizes low-dimensional bases as geodesic paths on the Grassmannian to track evolving physics in nonlinear systems, achieving higher accuracy than static approximations at the same rank.