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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,786 papers · 148 categories

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5 results for “advection-dominated”

Using recurrent neural networks for nonlinear component computation in advection-dominated reduced-order modelscs.LG

Paper uses neural networks to speed up simulations of complex systems.

problem Rapid simulations of advection-dominated problems in engineering and geophysics.

method Recurrent neural network for approximating nonlinear component of ROM.

result The proposed framework accurately recovers transient dynamics without full nonlinear computations.

neural networks advection-dominated reduced-order models partial differential equations transient dynamics

2019-09-18abs ↗pdf ↗

Neural tangent kernel analysis of PINN for advection-diffusion equationphysics.comp-ph

This work analyzes PINNs for advection-diffusion equations using NTK theory.

problem Understanding and resolving the training difficulties of PINNs for advection-diffusion equations.

method Neural Tangent Kernel (NTK) analysis of PINNs for the linear advection-diffusion equation (LAD).

result PINNs struggle due to spectral bias and convergence rate disparity, especially in advection-dominated and diffusion-dominated regimes.

PINNs advection-diffusion equation NTK analysis spectral bias convergence rate disparity

2022-11-21abs ↗pdf ↗

Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulationphysics.comp-ph

A novel algorithm uses Gaussian process regression to interpret non-intrusive ROMs.

problem Lack of interpretability in non-intrusive ROMs.

method Latent-space interpolation using Gaussian process regression.

result Interpretability of ROMs improved with continuous time evolution.

Gaussian process non-intrusive ROMs interpretability shallow water equations

2020-07-23abs ↗pdf ↗

Flux-Corrected Diagonal Frog: second order and positivity at all time stepsmath.NA

Improved solver maintains positivity and accuracy across all time steps.

problem Linear second-order schemes for Fokker-Planck equation cannot preserve positivity.

method Flux-Corrected Diagonal Frog (FCDF) framework using nonlinear extension and iterative limiter.

result FCDF schemes are unconditionally positive across all time steps and maintain second-order accuracy.

Fokker-Planck equation positivity finite-difference schemes Flux-Corrected Diagonal Frog

2026-07-22abs ↗pdf ↗

Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equationsmath.NA

Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations

problem Positivity-preserving discretizations for anisotropic Fokker-Planck equations

method Diagonal Frog discretization

result Second-order accuracy and mass conservation

Fokker-Planck positivity-preserving FD schemes anisotropic Krylov subspace

2026-06-22abs ↗pdf ↗