# Component-Level Evaluation of Adaptive PINN Training for CFD-Oriented Crystal Growth Simulation

arXiv: https://arxiv.org/abs/2610.05127 · HTML: https://mlsanity.com/paper/2610.05127/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 7 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 1 of 1)

- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)

## Abstract (arXiv)

Physics-informed neural network (PINN) training minimizes a weighted combination of partial differential equation (PDE), boundary-condition, and initial-condition losses. Because adaptive methods modify these weights during training, their weighted total losses are not always directly comparable. We compare fixed-weight PINN, gradient-normalized PINN (GNPINN), and a rule-based adaptive controller (AgenticPINN) under matched settings on a heat-equation benchmark and a simplified Czochralski-oriented thermal-fluid problem. In the crystal-growth MLP experiment, adaptive control reduced the PDE residual from the order of 10-5 to 10-6, while the boundary-condition loss increased from the order of 10-5 to 10-2. On the heat-equation benchmark, GNPINN achieved the lowest relative L2 field error (0.054), whereas AgenticPINN obtained the smallest PDE residual but a relative L2 error of 1.368. Gaussian-process surrogates were additionally evaluated using case-wise holdout tests on corrected Czochralski CFD parameter sweeps. The temperature-field error for the temperature sweep was approximately 6%, whereas the axial-velocity error for the crystal-rotation sweep was approximately 42%. These findings show that adaptive control can improve equation satisfaction while weakening other physical constraints. PINN training should therefore be evaluated using separate PDE, boundary-condition, and solution-error metrics rather than weighted total loss alone.