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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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.
RBF-RLS outperforms PINNs on PDEs with Dirac deltas via weak-form integration, delivering consistent forward and inverse solutions for linear transport problems in porous media and rivers.
An auto-adaptive sampling technique for PINNs is introduced and tested on Allen-Cahn equations to better resolve interfacial regions compared to residual-adaptive methods.
PINNSur applies PINNs to surface PDEs by neural approximation of normals and operator projection, with an added empirical test for convergence behavior.
GPU port of entropy-stable DG Euler solver with non-conservative buoyancy terms reaches nearly 70% of 64-bit peak on A100 volume kernels, delivers 10x speedup and 13x better energy efficiency versus CPU, and preserves symmetry-based flux savings.
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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Auto-Adaptive PINNs with Applications to Phase Transitions
An auto-adaptive sampling technique for PINNs is introduced and tested on Allen-Cahn equations to better resolve interfacial regions compared to residual-adaptive methods.
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GPU Performance of an Entropy-Stable Discontinuous Galerkin Euler Solver with Non-Conservative Terms
GPU port of entropy-stable DG Euler solver with non-conservative buoyancy terms reaches nearly 70% of 64-bit peak on A100 volume kernels, delivers 10x speedup and 13x better energy efficiency versus CPU, and preserves symmetry-based flux savings.