Real-Time Inference of Defects and Impedance Using Deep Operator Networks

The advent of big data is revolutionizing scientific discovery, enabling the development of novel models, refinement of existing frameworks, and precise uncertainty quantification. Simultaneously, advancements in scientific machine learning have unlocked powerful tools for solving inverse problems, especially in scenarios involving complex systems with sparse or noisy data, where traditional methods often falter.
In this work, we present a novel operator learning framework for tackling inverse scattering and impedance problems. Our approach leverages Deep Operator Networks (DeepONets) to efficiently learn mappings between functional spaces. Once trained, the framework operates as a surrogate model, directly inferring both the shape of defects (D) and the impedance function (lambda) in real-time from the far-field patterns of time-harmonic acoustic or E-polarized electromagnetic plane waves.
We validate our method through extensive experiments on 2D benchmark problems, demonstrating its remarkable ability to reconstruct arbitrary defect shapes and fault geometries while maintaining physical consistency. Importantly, the framework excels in scenarios with limited data, addressing a critical challenge in real-world applications. By uniting operator learning with physics-informed insights, this approach advances the state of the art in solving inverse problems and paves the way for practical applications in acoustics, electromagnetics, and beyond.