Learning Physics from an Imperfect Ancestor
A three-stage method uses an imperfect neural operator to steer PINNs into the correct PDE basin.
The paper addresses neural operators that fail outside their training distribution and physics-informed neural networks that can settle in the wrong solution basin despite a small residual. A three-stage method freezes a physics-informed operator's spatial basis, extrapolates its solution branch with a polynomial continuation prior, and distills the field into a fresh PINN. On Allen-Cahn, distillation recovers the non-trivial branch that a standard PINN collapses away from; on lid-driven cavity flow at Reynolds number 3200 it reaches the physical state with fewer parameters and optimization steps than recent baselines.
- An imperfect neural operator identifies the basin; the PDE residual refines it
- Tested on Burgers, Allen-Cahn, and lid-driven cavity flow
- Recovers the non-trivial Allen-Cahn branch that a scratch PINN misses
- At Reynolds number 3200, converges with fewer parameters and steps
From the original article
1 min read at arxiv.orgNeural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed neural networks avoid dependence on labeled data, yet their optimization can be basin-fragile: when the governing residual admits multiple solutions, a PINN trained from scratch may converge to a physically incorrect state despite achieving a small residual.
By S. Mohammad Mousavi · arxiv.org
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