2022/09/29 by Ruchi Guo, Guo, Ruchi, Shuhao Cao +3 · 4 citations
Earth and Planetary Sciences · Engineering · #35R30 #65N21 #65R10 #68T07 #Electrical and Bioimpedance Tomography #FOS: Computer and information sciences #FOS: Mathematics #Geophysical and Geoelectrical Methods #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Reservoir Engineering and Simulation Methods
paper · pdf · doi:10.48550/arxiv.2209.14977
openalex publication_date 2022/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and the reconstructed images. An effort is made to give a specific example to a fundamental question: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural networks? Specifically, inspired by direct sampling methods for inverse problems, the 1D boundary data in different frequencies are preprocessed by a partial differential equation-based feature map to yield 2D harmonic extensions as different input channels. Then, by introducing learnable non-local kernels, the direct sampling is recast to a modified attention mechanism. The new method achieves superior accuracy over its predecessors and contemporary operator learners and shows robustness to noises in benchmarks. This research shall strengthen the insights that, despite being invented for natural language processing tasks, the attention mechanism offers great flexibility to be modified in conformity with the a priori mathematical knowledge, which ultimately leads to the design of more physics-compatible neural architectures.