Solving PDEs with Unmeasurable Source Terms Using Coupled Physics-Informed Neural Network with Recurrent Prediction for Soft Sensors

• URL: http://arxiv.org/abs/2301.08618v3
• Date: Tue, 11 Jul 2023 14:18:08 GMT
• Title: Solving PDEs with Unmeasurable Source Terms Using Coupled Physics-Informed Neural Network with Recurrent Prediction for Soft Sensors
• Authors: Aina Wang, Pan Qin, Xi-Ming Sun
• Abstract summary: Partial equations (PDEs) are a model candidate for soft sensors in industrial processes with differential dependence. Although physics-informed neural networks (PINNs) are a promising machine learning method for solving PDEs, they are infeasible for the nonhomogeneous Ps with unmeasurable source terms. To this end, a coupled neural network (CPINN) with a recurrent prediction (RP) learning strategy (NN- RP) is proposed.
• Score: 0.9346127431927981
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Partial differential equations (PDEs) are a model candidate for soft sensors in industrial processes with spatiotemporal dependence. Although physics-informed neural networks (PINNs) are a promising machine learning method for solving PDEs, they are infeasible for the nonhomogeneous PDEs with unmeasurable source terms. To this end, a coupled PINN (CPINN) with a recurrent prediction (RP) learning strategy (CPINN- RP) is proposed. First, CPINN composed of NetU and NetG is proposed. NetU is for approximating PDEs solutions and NetG is for regularizing the training of NetU. The two networks are integrated into a data-physics-hybrid loss function. Then, we theoretically prove that the proposed CPINN has a satisfying approximation capability for solutions to nonhomogeneous PDEs with unmeasurable source terms. Besides the theoretical aspects, we propose a hierarchical training strategy to optimize and couple NetU and NetG. Secondly, NetU-RP is proposed for compensating information loss in data sampling to improve the prediction performance, in which RP is the recurrently delayed outputs of well-trained CPINN and hard sensors. Finally, the artificial and practical datasets are used to verify the feasibility and effectiveness of CPINN-RP for soft sensors.

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