南京大学学报（自然科学版）2026，Vol.62Issue(2)：309-322,14.DOI:10.13232/j.cnki.jnju.2026.02.013
从弱非线性可解到强非线性失效:LLG方程中梯度冲突诱导的PINN失效边界
Phase transition to failure:Quantifying critical thresholds of gradient conflict in PINN for LLG dynamics
摘要
Abstract
Recent remarkable advances in machine learning(ML)have inspired the exploration of novel algorithms for solving differential equations.After nearly three decades of development,numerous ML-based solvers have emerged,demonstrating significant performance advantages in specific scenarios.However,recent studies have revealed a widespread and systematic omission of negative results in current literature,leading to an overly optimistic bias in the academic assessment of ML's capabilities for solving differential equations.Consequently,there is an urgent need for more comprehensive empirical evidence to objectively evaluate algorithmic efficacy,particularly to establish a rational understanding of failure cases and performance boundaries.This study investigates the widely used Physics-Informed Neural Network(PINN)framework for solving the Landau-Lifshitz-Gilbert(LLG)equation,the core governing equation in micromagnetics.By systematically varying the magnetocrystalline anisotropy constant(Ku)and the demagnetization factor(N)to modulate the strength of nonlinearity in the system,we comprehensively assess PINN's solution performance.Our results show that PINN can effectively solve the LLG equation only under weakly nonlinear conditions.In strongly nonlinear regimes,however,PINN fails to converge or produces inaccurate solutions,revealing an inherent limitation of such machine learning approaches when applied to strongly nonlinear differential equations.This failure mechanism is attributed to gradient conflicts induced by the strong nonlinearity during gradient descent iterations,which lead to either solution divergence or catastrophic loss of accuracy.关键词
PINN/LLG equation/非线性磁化动力学/微磁模拟Key words
PINN/LLG equation/nonlinear magnetization dynamics/micromagnetic simulation分类
信息技术与安全科学引用本文复制引用
马丁,陈丽娜,刘荣华..从弱非线性可解到强非线性失效:LLG方程中梯度冲突诱导的PINN失效边界[J].南京大学学报（自然科学版）,2026,62(2):309-322,14.基金项目
国家自然科学基金(12574125),国家重点研发计划(2023YFA1406603,2024YFA1408801) （12574125）
