Recovering Sharp Conductivity Features in the Finite-Data Calder\'on Problem with Physics-Informed Neural Networks
arXiv:2606.28158v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have recently emerged as a promising framework for addressing the Calder\'on inverse problem from limited boundary data. In this work, we revisit neural Calder\'on inversion by introducing multiscale boundary excitations based on randomized wavelet functions and investigating the role of Fourier-feature encoding (FFE) for representing sharp conductivity variations. We propose a physics-informed reconstruction framework that represents the unknown conductivity and the associated family of electric potential
The proliferation of AI and advanced computational methods is driving innovation in solving complex inverse problems, enhancing capabilities in fields like medical imaging and geophysical exploration.
This research advances the practical application of physics-informed AI for critical scientific and engineering challenges, potentially improving diagnostic accuracy and resource discovery.
The ability to accurately recover sharp conductivity features with limited data using AI will enable more precise and efficient analysis in various scientific and industrial applications.
- · Medical imaging companies
- · Geophysical exploration firms
- · AI research institutions
- · Material science engineers
- · Traditional inverse problem solvers
- · Data-intensive diagnostic methods
Improved resolution and efficiency in non-invasive diagnostic techniques and subsurface imaging.
Reduced need for extensive data collection in certain fields, lowering costs and accelerating research.
Potential for new AI-driven sensor technologies that leverage minimal data for comprehensive analysis.
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Read at arXiv cs.LG