Mühendislik · 4 dk okuma · 17 Nisan 2026
Hybrid PINNs: Finite-Difference Regularization for Physics Solvers
Adding weak finite-difference gradient penalties to physics-informed neural networks improves boundary accuracy without replacing automatic-differentiation residuals.
Auxiliary finite-difference regularization of residual gradients improves PINN accuracy at boundaries without replacing core AD-based loss.
- — Standard PINNs use a single scalar loss; hybrid approach adds weak FD penalty on residual-field gradients.
- — FD regularizer stays auxiliary—governing PDE residual remains automatic-differentiation based.
- — Poisson benchmark shows trade-off: regularizer improves residual smoothness but may reduce field accuracy elsewhere.
- — 3D annular heat-conduction test uses body-fitted shell grid near outer wall to target boundary flux.
- — Shell weight 5e-4 with Kourkoutas-beta optimizer reduced outer-wall BC error from 1.22e-2 to 9.29e-4.
- — Wall-flux RMSE dropped from 9.21e-3 to 9.63e-4 across six random seeds over 100k epochs.
- — Adam optimizer requires lower learning rate (1e-3) for stability; Kourkoutas-beta shows more robust shell benefit.
- — Hybrid design most effective when FD regularizer aligns with physical quantity of interest (e.g., boundary flux).
Sık sorulanlar
- The FD regularizer is auxiliary—it only penalizes gradients of the residual field in a weak term, while the main PDE residual is still computed via automatic differentiation. A full FD PINN would replace AD entirely. The hybrid approach preserves AD's accuracy for the core residual while using FD to smooth the residual field in regions of interest, reducing computational cost and implementation complexity.