Physics-Informed Neural Plasticity: PDE Solvers That Reshape Themselves

Key points

• We introduce physics-informed neural plasticity, a paradigm in which the representation itself reshapes during optimization in response to unresolved physics.1
• 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.1
• 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.1
• We further establish conditional a posteriori reliability and structural-stability guarantees linking localized physics residuals to solution error and stable refinement.1

Sources (1)

• [1]Physics-Informed Neural Plasticity: PDE Solvers That Reshape Themselves
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 06:07 AM

  Physics-informed neural PDE solvers adapt their parameters to satisfy governing equations, yet their representational structure typically remains fixed throughout training.

  We introduce physics-informed neural plasticity, a paradigm in which the representation itself reshapes during optimization in response to unresolved physics.

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