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.
SIAM, Philadelphia (2000)
6 Pith papers cite this work, alongside 4,404 external citations. Polarity classification is still indexing.
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A quantum algorithm encodes probability densities in state amplitudes and uses QFT plus phase rotations to propagate Fokker-Planck drift exactly and diffusion approximately via a Wick-rotated unitary surrogate, achieving numerical agreement with the classical solution.
SS-POD augments standard POD-Galerkin with a spectral-subspace partition and local POD to achieve lower out-of-sample error than either plain POD or pure spectral-Galerkin when only a handful of snapshots are available.
Derives a corrected boundary condition that enforces exact total surfactant mass conservation in nonlinear reduced models of soluble-surfactant-laden falling films, resolving an inconsistency in prior surface transport reductions.
A Strang splitting plus Fourier collocation scheme for the fifth-order KBF equation is shown to converge at second order in time and spectrally in space under suitable regularity assumptions.
Linear stability analysis shows the algebraic-hyperbolic formulation of constraint equations is unstable near FLRW but can be stable for Gowdy spacetimes and subclasses with Fourier-based methods.
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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Quantum Prediction of Transport Dynamics in Discretized State Spaces
A quantum algorithm encodes probability densities in state amplitudes and uses QFT plus phase rotations to propagate Fokker-Planck drift exactly and diffusion approximately via a Wick-rotated unitary surrogate, achieving numerical agreement with the classical solution.
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A spectral-subspace-augmented POD-Galerkin method for parametrized PDEs with limited snapshot data
SS-POD augments standard POD-Galerkin with a spectral-subspace partition and local POD to achieve lower out-of-sample error than either plain POD or pure spectral-Galerkin when only a handful of snapshots are available.
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A conservation-consistent boundary condition for nonlinear models of soluble-surfactant-laden falling films
Derives a corrected boundary condition that enforces exact total surfactant mass conservation in nonlinear reduced models of soluble-surfactant-laden falling films, resolving an inconsistency in prior surface transport reductions.
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Fully discrete scheme for the fifth-order KdV-Burgers-Fisher equation using Strang splitting and Fourier collocation methods
A Strang splitting plus Fourier collocation scheme for the fifth-order KBF equation is shown to converge at second order in time and spectrally in space under suitable regularity assumptions.
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Numerical stability of the Hyperbolic Formulation of the Constraint equations for $\mathbb{T}^3$ cosmological space-times
Linear stability analysis shows the algebraic-hyperbolic formulation of constraint equations is unstable near FLRW but can be stable for Gowdy spacetimes and subclasses with Fourier-based methods.