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.
LeVeque,Finite Difference Methods for Ordinary and Partial Differential Equations, Society for Industrial and Applied Mathematics (2007), 10.1137/1.9780898717839
5 Pith papers cite this work. Polarity classification is still indexing.
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Derives ADSC directional edge-diffusion correction via modal rectification of centered-stencil Fourier symbol, proving consistency and stability for regularized operator and existence/qualitative convergence for nonlinear implementation.
Introduces a quantum-analogue cloud-function model for large-scale sensory processing in the brain and uses it to account for post-decisional changes of mind via interplay of fast and slow neural dynamics.
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
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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Modal-Rectification-Based Directional Edge Diffusion for Cartesian Convection--Diffusion Problems
Derives ADSC directional edge-diffusion correction via modal rectification of centered-stencil Fourier symbol, proving consistency and stability for regularized operator and existence/qualitative convergence for nonlinear implementation.
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A Quantum-Analogue Formalism for Modeling Supraliminal Information Processing
Introduces a quantum-analogue cloud-function model for large-scale sensory processing in the brain and uses it to account for post-decisional changes of mind via interplay of fast and slow neural dynamics.
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Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
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