勷勤数学•专家报告

题      目：Combining Physics-informed Neural Networks with the Fixed Stress Splitting for Solving Biot’s Model

报  告  人：蔡明超 教授  (邀请人：叶颀)

                                    美国马里兰摩根州立大学        

时      间：3月21日  10：00-11：00

地     点：数科院西楼111报告厅

报告人简介:

        蔡明超，美国马里兰摩根州立大学教授，博导。主要从事数值分析，流体,弹性和生物力学的计算，自2017年来，获得NSF，NIH，Army Research 0ffice等机构累计超过120万美元的科研项目资助，在SIAM J. Numer. Anal., SIAM, J. Sci. Comput.，Math. Comput. 和J. Biomechanics等有影响力的SCI期刊上发表论文30多篇，出版book chapters 2部，做大会或邀请报告共 80多次，NSF计算数学研究项目评审专家,组织并主持过大型学术会议：CBMS conference: Deep Learning and Numerical PDEs (2023).

摘      要：

       Biot's model serves as the cornerstone of poroelasticity. Our objective is to address this model using physics-informed neural networks (PINNs). By leveraging the fixed-stress splitting iterative method, we design distinct loss functions for the displacement and pressure variables. This approach enables the training of two separate, compact neural networks. The fixed-stress iterative algorithm is employed to couple these variables, enhancing the accuracy of the neural network approximations. Our numerical experiments validate the efficacy of this method, and we provide error analysis to underscore the capability of fixed-stress splitting-based PINNs in accurately approximating solutions to Biot's model. Additionally, we briefly explore the application of PINNs to inverse problems associated with Biot's model.

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