News for our work about PINN for LLG dynamics, recently published in Progress in Physics
We published a paper entitled “Phase transition to failure: Quantifying critical thresholds of gradient conflict in PINN for LLG dynamics” (Chinese title: 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) in [ Progress in Physics 62(2), 309-322 (2026)]. In this work, we systematically investigated the capability of physics-informed neural networks (PINNs) for solving the Landau–Lifshitz–Gilbert (LLG) equation, the core governing equation of micromagnetics. By varying the magnetocrystalline anisotropy constant Ku and the demagnetization factor N to tune the strength of nonlinearity, we found that PINNs can solve the LLG equation only under weakly nonlinear conditions. In strongly nonlinear regimes, gradient conflicts during the training iterations lead to divergence or a catastrophic loss of accuracy, which defines a quantitative failure boundary for machine-learning solvers of nonlinear magnetization dynamics. This work provides a rational understanding of the performance boundaries of PINNs and helps to correct the overly optimistic assessment of ML-based differential-equation solvers. Congratulations to Ding Ma and Co-workers!
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