Neural Inverse Operators for Solving PDE Inverse Problems

• URL: http://arxiv.org/abs/2301.11167v2
• Date: Sat, 3 Jun 2023 18:34:05 GMT
• Title: Neural Inverse Operators for Solving PDE Inverse Problems
• Authors: Roberto Molinaro, Yunan Yang, Bj\"orn Engquist, Siddhartha Mishra
• Abstract summary: We propose a novel architecture termed Neural Inverse Operators (NIOs) to solve these PDE inverse problems. A variety of experiments are presented to demonstrate that NIOs significantly outperform baselines and solve PDE inverse problems robustly, accurately and are several orders of magnitude faster than existing direct and PDE-constrained optimization methods.
• Score: 5.735035463793008
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a novel architecture termed Neural Inverse Operators (NIOs) to solve these PDE inverse problems. Motivated by the underlying mathematical structure, NIO is based on a suitable composition of DeepONets and FNOs to approximate mappings from operators to functions. A variety of experiments are presented to demonstrate that NIOs significantly outperform baselines and solve PDE inverse problems robustly, accurately and are several orders of magnitude faster than existing direct and PDE-constrained optimization methods.

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