Scientific Computing

2 items

RESEARCHarXiv CS.LG·14d ago

Iterative Refinement Neural Operators are Learned Fixed-Point Solvers: A Principled Approach to Spectral Bias Mitigation

This paper introduces the Iterative Refinement Neural Operator (IRNO) to mitigate spectral bias in neural operators, using a learned refinement module via fixed-point iteration. IRNO decomposes predictions into a coarse initialization followed by successive residual corrections, achieving significant error reduction across physical systems.

deep learning Neural Operators Scientific Computing Iterative Methods

RESEARCHarXiv CS.LG·4/30/2026

A Randomized PDE Energy driven Iterative Framework for Efficient and Stable PDE Solutions

This work introduces a PDE energy-driven iterative framework for solving partial differential equations efficiently and stably, without relying on traditional matrix-based discretizations or costly data-driven neural network training. It evolves random initial fields through physically constrained diffusion iterations and Gaussian smoothing, strictly enforcing boundary conditions, and demonstrates stable convergence on Poisson, Heat, and viscous Burgers equations.

Numerical Methods machine learning Scientific Computing Algorithms