BiLO: Bilevel Local Operator Learning for PDE inverse problems

• DOI: 10.48550/arxiv.2404.17789
• Publication Date: 2024-04-27
• Authors: Zirui Zhang; Xiaohui Xie; John Lowengrub
• Keywords: Operator (biology); Bilevel optimization

We propose a new neural network based method for solving inverse problems partial differential equations (PDEs) by formulating the PDE problem as bilevel optimization problem. At upper level, we minimize data loss with respect to parameters. lower train locally approximate solution operator in neighborhood of given set parameters, which enables an accurate approximation descent direction level The function includes L2 norms both residual and its derivative apply gradient simultaneously on problems, leading effective fast algorithm. method, refer BiLO (Bilevel Local Operator learning), is also able efficiently infer unknown functions PDEs through introduction auxiliary variable. demonstrate that our enforces strong constraints, robust sparse noisy data, eliminates need balance loss, inherent soft constraints.