Continuous time PDE prediction with different parameters and effective grid input domain

Ziquan Wang

doi:10.1117/12.2685927

28 July 2023 Continuous time PDE prediction with different parameters and effective grid input domain

Ziquan Wang

Proceedings Volume 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023); 127561H (2023) https://doi.org/10.1117/12.2685927
Event: 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), 2023, Tangshan, China

Abstract

Due to issues such as uneven spatial distribution of data sensors and data vulnerability, dynamic systems such as disease transmission and weather prediction that can be described by PDE often generate uneven spatiotemporal data. However, due to the limitations of module assumptions or convolutional calculations, existing data-driven deep learning models are often not suitable for spatiotemporal data that is not standardized in the spatiotemporal domain, and specific models are difficult to generalize to new dynamic systems. In this paper, graph neural network and method of line method are used to model the uneven spatio-temporal data modeling generated by dynamic systems, and a prediction model that allows efficient spatio-temporal input domain is proposed. It uses a differential graph network of approximate derivatives to learn the differential information in dynamic system data, combined with the dynamic system parameter information extracted from the parameter coding network, and finally realizes accurate prediction of dynamic systems through network approximate equations. The model achieves end-to-end system prediction, in which the parameter encoding network learns dynamic system parameters and other information, and is supplemented by a meta learning mechanism to improve the model's generalization ability on different PDE prediction tasks. The experimental results on the nonlinear reaction diffusion equation and heat equation show that the model can adapt to the data with spatiotemporal noise, and shows a very competitive prediction accuracy.

Citation Download Citation

Ziquan Wang "Continuous time PDE prediction with different parameters and effective grid input domain", Proc. SPIE 12756, 3rd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2023), 127561H (28 July 2023); https://doi.org/10.1117/12.2685927

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KEYWORDS

Data modeling

Neural networks

Partial differential equations

Systems modeling

Dynamical systems

Differential equations

Deep learning

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