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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.

168,695 papers · 148 categories

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6 results for “meshfree”

Convergence analysis of kernel learning FBSDE filtercs.LG

Kernel learning FBSDE filter improves nonlinear filtering efficiency.

problem Nonlinear filtering problem in high-dimensional systems.

method Iterative and adaptive meshfree approach using forward backward SDE and KDE.

result Rigorous convergence analysis provided, supporting empirical results.

kernel learning FBSDE filter nonlinear filtering convergence analysis meshfree method

2024-05-22abs ↗pdf ↗

INEUS: Iterative Neural Solver for High-Dimensional PIDEscs.LG

INEUS solves high-dimensional PIDEs efficiently with neural networks.

problem Solving high-dimensional partial integro-differential equations (PIDEs) efficiently.

method INEUS uses iterative neural networks to replace nonlocal integrals with sampling and reformulates PIDE solving as recursive regression.

result INEUS delivers accurate and scalable solutions for high-dimensional linear and nonlinear PIDEs.

neural networks PIDEs high-dimensional Physics-Informed Neural Networks nonlocal terms

2026-05-07abs ↗pdf ↗

Partition of unity networks: deep hp-approximationcs.LG

POUnets combine partitions of unity and monomials for efficient deep learning.

problem Efficiently approximating functions with deep neural networks in high dimensions.

method Integrates partitions of unity and monomials into neural network architecture.

result POUnets achieve hp-convergence for smooth functions and outperform MLPs for discontinuous functions.

deep learning neural networks approximation theory partitions of unity monomials

2021-01-27abs ↗pdf ↗

Geometry-informed neural atlas for boundary value problems of complex 3D geometriesphysics.comp-ph

A neural atlas simplifies 3D geometry simulation by avoiding meshing.

problem Simulation of complex 3D geometries with thin features or non-trivial topology.

method Learned geometric representation of overlapping volumetric coordinate charts, trained from point-cloud or level-set data.

result The learned atlas enables different solvers without re-meshing or re-parametrization.

geometry neural atlas 3D simulation mesh-free inverse analysis

2026-03-31abs ↗pdf ↗

MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Frameworkcs.LG

MeshfreeFlowNet generates high-resolution spatio-temporal solutions from low-resolution inputs.

problem Generating high-resolution spatio-temporal solutions from low-resolution inputs.

method Physics-constrained deep learning framework using fully convolutional encoders.

result Significantly outperforms existing baselines in super-resolution of turbulent flows.

super-resolution deep learning turbulent flows meshfree partial differential equations

2020-05-01abs ↗pdf ↗

DGM: A deep learning algorithm for solving partial differential equationsq-fin.MF

High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial condition, and boundary conditions. Our algorithm is meshfree, which is key since mesh…

2017-08-24abs ↗pdf ↗