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MS-PINN: A physics-informed neural network for multi-field coupled evolution modeling in metal solidification.

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Title: MS-PINN: A physics-informed neural network for multi-field coupled evolution modeling in metal solidification.
Authors: Bai, Chen1 (AUTHOR) baichen@shu.edu.cn, Zhang, Yunhu2 (AUTHOR) zhangyunhu.zyh@163.com, Zheng, Hongxing2,3 (AUTHOR) hxzheng@shu.edu.cn, Qian, Quan1,4,5 (AUTHOR) qqian@shu.edu.cn
Source: Computers & Mathematics with Applications. Apr2026, Vol. 207, p60-78. 19p.
Subjects: Rapid solidification processing of metals, Artificial neural networks, Resampling (Statistics), Fluid dynamics, Partial differential equations
Abstract: Simulating the metal solidification process is crucial for improving product quality, optimizing manufacturing processes, and developing new materials. Traditional numerical methods like the Finite Element Method (FEM) and Physics-Informed Neural Networks (PINNs) face significant challenges when applied to metal solidification simulations due to inefficiencies and inaccuracies in dealing with multiphysics coupling, nonlinearity, and spatio-temporal complexity. Despite their potential, PINNs require further optimization to accurately capture complex physical phenomena in practical simulations. In this study, we propose a novel method based on PINNs, termed MS-PINN, which integrates Fourier Feature Embedding (FFE), Residual-based Adaptive Resampling (RAD), and Self-adaptive Loss Balanced methods (SAL) to significantly enhance simulation accuracy and efficiency. FFE improves the model's ability to capture high-frequency features, RAD increases learning efficiency in high-gradient regions, and SAL dynamically adjusts loss function weights to optimize the training process. Experimental results show that MS-PINN outperforms traditional PINNs and other advanced approaches, achieving average error reductions of approximately 81.00% compared to Conv-LSTM, 77.11% compared to TCN, and 61.56% compared to PINN in reconstruction experiments. In predictive experiments, MS-PINN reduces errors by 53.23%, 68.81%, and 72.54% compared to PINN, TCN, and CONV-LSTM methods, respectively. Additionally, we developed a general PDE-solving software, NeuroPDE, based on this method. NeuroPDE has demonstrated success not only in the solidification process of Cu-1wt.%Ag alloy but also in solving Burgers, diffusion, and Navier-Stokes (NS) equations, including turbulent datasets characterized by high Reynolds numbers, and their inverse problems. This highlights NeuroPDE's versatility and broad applicability in solving complex forward and inverse problems in fluid dynamics and other fields. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Simulating the metal solidification process is crucial for improving product quality, optimizing manufacturing processes, and developing new materials. Traditional numerical methods like the Finite Element Method (FEM) and Physics-Informed Neural Networks (PINNs) face significant challenges when applied to metal solidification simulations due to inefficiencies and inaccuracies in dealing with multiphysics coupling, nonlinearity, and spatio-temporal complexity. Despite their potential, PINNs require further optimization to accurately capture complex physical phenomena in practical simulations. In this study, we propose a novel method based on PINNs, termed MS-PINN, which integrates Fourier Feature Embedding (FFE), Residual-based Adaptive Resampling (RAD), and Self-adaptive Loss Balanced methods (SAL) to significantly enhance simulation accuracy and efficiency. FFE improves the model's ability to capture high-frequency features, RAD increases learning efficiency in high-gradient regions, and SAL dynamically adjusts loss function weights to optimize the training process. Experimental results show that MS-PINN outperforms traditional PINNs and other advanced approaches, achieving average error reductions of approximately 81.00% compared to Conv-LSTM, 77.11% compared to TCN, and 61.56% compared to PINN in reconstruction experiments. In predictive experiments, MS-PINN reduces errors by 53.23%, 68.81%, and 72.54% compared to PINN, TCN, and CONV-LSTM methods, respectively. Additionally, we developed a general PDE-solving software, NeuroPDE, based on this method. NeuroPDE has demonstrated success not only in the solidification process of Cu-1wt.%Ag alloy but also in solving Burgers, diffusion, and Navier-Stokes (NS) equations, including turbulent datasets characterized by high Reynolds numbers, and their inverse problems. This highlights NeuroPDE's versatility and broad applicability in solving complex forward and inverse problems in fluid dynamics and other fields. [ABSTRACT FROM AUTHOR]
ISSN:08981221
DOI:10.1016/j.camwa.2026.01.015