A hybrid solver-neural framework achieves global error O(τ^γ ln(1/τ)) for nonlinear dispersive equations by training a lightweight network on the residual defect inside the solver loop while preserving uniform stability.
Mathematics of Computation , year =
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A relaxed generalized scalar auxiliary variable exponential integrator is proposed for the modified Landau-de Gennes model of smectic-A phases, with proofs of unconditional energy stability, solution boundedness, and optimal error estimates.
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Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations
A hybrid solver-neural framework achieves global error O(τ^γ ln(1/τ)) for nonlinear dispersive equations by training a lightweight network on the residual defect inside the solver loop while preserving uniform stability.
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Relaxed Generalized Scalar Auxiliary Variable Exponential Integrator for A Modified Landau-de Gennes Theory for Smectic Liquid Crystals
A relaxed generalized scalar auxiliary variable exponential integrator is proposed for the modified Landau-de Gennes model of smectic-A phases, with proofs of unconditional energy stability, solution boundedness, and optimal error estimates.