发表机构
Hubei University（湖北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究对照测试了PINNs的两种故障修复方案，发现二者作用场景互不重叠，需联合评估精度、架构等因素并按种子报告结果。
AI 中文摘要
物理信息神经网络（PINNs）在刚性或平流主导的偏微分方程（PDE）任务中常失效，近期两项研究提出了相互竞争的修复方案：将精度从FP32切换至FP64以修复L-BFGS的停止伪影，或用状态空间模型（SSM）骨干网络加子序列对齐替代多层感知机（MLP）以应对架构简单性偏差。我们在预注册的144次运行研究中，采用配对种子的对照设置，测试了对流、反应、波动三类场景，还开展了独立的85次对流/波动研究；成功标准为相对ℓ₂误差低于0.05。两种修复方案作用于互不重叠的场景和种子子集，无法相互替代。在难度较高的对流任务（β=50）中，对齐方案在FP32下恢复2/5的种子，在FP64下恢复3/5的种子，而未对齐的SSM在两种精度下均只能成功0/5的种子，普通MLP在精度切换后仅从0/5提升至1/5；该恢复效果源于对齐目标，而非骨干网络本身。在反应任务中，仅骨干网络就能成功3/5至4/5的种子，因此每种方案都覆盖了另一种方案未覆盖的场景。响应还具有种子特异性：同一精度切换对不同种子的影响方向相反，在波动任务中，精度切换降低了中位数误差，但未带来统计显著的成功次数提升。在独立的多步运行器中收紧内部L-BFGS容忍度也能降低中位数误差，但会大幅增加运行时间，且成功次数不变。因此，必须联合评估精度、停止规则、骨干网络和对齐方案，并按种子报告结果。
英文摘要
Physics-Informed Neural Networks (PINNs) frequently fail on stiff or advection-dominated PDEs, and two recent accounts offer competing remedies: switching from FP32 to FP64 to repair an L-BFGS stopping artifact, or replacing the MLP with a state-space-model (SSM) backbone plus sub-sequence alignment to counter architectural simplicity bias. We test both under matched, seed-paired controls in a pre-registered 144-run study spanning convection, reaction, and wave, plus an independent 85-run convection/wave study; success is relative $\ell_2$ error below $0.05$. The two remedies act on disjoint regime-and-seed slices: neither substitutes for the other. On hard convection ($β{=}50$), alignment recovers 2/5 seeds in FP32 and 3/5 in FP64, where the unaligned SSM succeeds on 0/5 seeds at either precision and the vanilla MLP moves only from 0/5 to 1/5 across the precision switch---the recoveries trace to the alignment objective, not the backbone. On reaction the backbone alone already succeeds on 3/5--4/5 seeds, so each remedy covers a regime the other does not. Responses are also seed-specific: the same precision switch flips individual seeds in opposite directions and, on wave, lowers median error with no statistically significant success gain. Tightening the inner L-BFGS tolerance in an independent repeated-step runner likewise lowers median error at a large runtime cost, with success counts unchanged. Precision, stopping, backbone, and alignment must therefore be evaluated jointly and reported per seed.
Comments11 pages, 5 figures, 6 tables; appendix with full proofs included
