arXiv：cs.LG· Chun-Wun Cheng, Bingcheng Hu, Angelica I. Aviles-Rivero·· 3 小时前AI 评分39
物理信息神经可塑性：能自我重塑的 PDE 求解器
Physics-Informed Neural Plasticity: PDE Solvers That Reshape Themselves
AI 导读
研究人员提出"物理信息神经可塑性"范式，让 PDE 求解器的表示结构在优化过程中随未解物理动态重塑，并据此实现 ReCAP——一种高斯局部化求解器，通过局部增强、残差导向分裂、门控剪枝和函数感知合并动态重新分配容量。在 5 个 3D 和 4D PDE 基准上对比 11 种物理信息求解器，ReCAP 在所有问题上取得最低相对 $L^2$ 误差，较最强竞品结果降低 10.7%–27.5%。
正文
Abstract:Physics-informed neural PDE solvers adapt their parameters to satisfy governing equations, yet their representational structure typically remains fixed throughout training. This rigidity is poorly matched to PDE solutions with strongly heterogeneous complexity across space and space--time, leaving capacity insufficient where the physics is difficult and redundant where it is simple. We introduce physics-informed neural plasticity, a paradigm in which the representation itself reshapes during optimization in response to unresolved physics. We instantiate this principle with Representation Capacity Adaptation for PDEs (ReCAP), a Gaussian-localized solver that dynamically redistributes capacity through local enrichment, residual-directed splitting, gate-based pruning, and function-aware merging. ReCAP uses responsibility-weighted error indicators and the geometry of residual energy to determine where and how to refine. To limit the disturbance introduced by splitting, we introduce quiet-child refinement, which initializes new components by transporting the parent representation while controlling instantaneous functional perturbation. We further establish conditional a posteriori reliability and structural-stability guarantees linking localized physics residuals to solution error and stable refinement. Across five challenging 3D and 4D PDE benchmarks against 11 physics-informed solvers, ReCAP achieves the lowest relative $L^2$ error on every problem, reducing error by $10.7\%$--$27.5\%$ relative to the strongest competing result. These results suggest that physics-informed solvers need not merely learn their parameters---they can learn how their representational capacity should be organized.
| Subjects: | Machine Learning (cs.LG); Numerical Analysis (math.NA) |
| Cite as: | arXiv:2610.09510 [cs.LG] |
| (or arXiv:2610.09510v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.09510 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Bingcheng Hu [view email]
[v1]
Wed, 7 Oct 2026 06:07:21 UTC (16,080 KB)
来源：arXiv：cs.LG · arxiv.org