Adaptive training balances physics errors in crystal growth simulations
Component-Level Evaluation of Adaptive PINN Training for CFD-Oriented Crystal Growth Simulation
Machine Learning
Summary
Simulating how crystals grow using physics rules can be tricky because the computer models try to satisfy several conditions at once, like equations and boundaries. The authors studied different ways to adjust the model’s focus on each condition during training. They found that some ways improve how well the equations are obeyed but make other conditions worse. This means we should look at each type of error separately rather than just adding them all up into one number when judging model quality.
What this means in practice
- •For computational physicists: Improve simulation accuracy by separately tracking different physical errors when training physics-informed neural networks for crystal growth models.
- •For process engineers: Use adaptive PINN training techniques to better capture thermal-fluid dynamics in crystal growth, enhancing process design and control.
Authors
Niruta Chapagain, Rohit Raj, Bertwin Kurisinkal Shine, Aditya A S
Abstract
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 $L_2$ field error (0.054), whereas AgenticPINN obtained the smallest PDE residual but a relative $L_2$ 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.