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.
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Cite this article
APA 7
Chapagain, N., Raj, R., Shine, B. K., & S, A. A. (2026). Component-Level Evaluation of Adaptive PINN Training for CFD-Oriented Crystal Growth Simulation. https://omanscience.com/en/articles/component-level-evaluation-of-adaptive-pinn-training-for-cfd-oriented-crystal-growth-simulation
MLA 9
Chapagain, Niruta, et al. "Component-Level Evaluation of Adaptive PINN Training for CFD-Oriented Crystal Growth Simulation." https://omanscience.com/en/articles/component-level-evaluation-of-adaptive-pinn-training-for-cfd-oriented-crystal-growth-simulation.
Chicago (author–date)
Chapagain, Niruta, Rohit Raj, Bertwin Kurisinkal Shine, and Aditya A S. 2026. "Component-Level Evaluation of Adaptive PINN Training for CFD-Oriented Crystal Growth Simulation." https://omanscience.com/en/articles/component-level-evaluation-of-adaptive-pinn-training-for-cfd-oriented-crystal-growth-simulation.
Harvard
Chapagain, N., Raj, R., Shine, B. K. and S, A. A. (2026) 'Component-Level Evaluation of Adaptive PINN Training for CFD-Oriented Crystal Growth Simulation', Available at: https://omanscience.com/en/articles/component-level-evaluation-of-adaptive-pinn-training-for-cfd-oriented-crystal-growth-simulation.
Vancouver
Chapagain N, Raj R, Shine BK, S AA. Component-Level Evaluation of Adaptive PINN Training for CFD-Oriented Crystal Growth Simulation. https://omanscience.com/en/articles/component-level-evaluation-of-adaptive-pinn-training-for-cfd-oriented-crystal-growth-simulation
IEEE
N. Chapagain, R. Raj, B. K. Shine, and A. A. S, "Component-Level Evaluation of Adaptive PINN Training for CFD-Oriented Crystal Growth Simulation," https://omanscience.com/en/articles/component-level-evaluation-of-adaptive-pinn-training-for-cfd-oriented-crystal-growth-simulation.