Solving Inverse Problems with Deep Learning
summary
Neural architectures encode physics: a wavelet-based PCR-net for pseudodifferential inverses and a SwitchNet/butterfly module for Fourier integral operators, assembled into end-to-end networks that map boundary data to material fields. Models train on modest datasets (8k–10k pairs typical, ~220k for travel-time experiments) and recover shapes reliably — electrical impedance tomography at about 8% error, travel-time reconstructions tolerate up to 10% noise and optical tomography remains usable at ~5% noise.
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chapters (11)
- 0:00Introduction to talk
- 1:45What is an inverse problem
- 4:57Deep learning for inverse problems
- 8:06Motivating new neural modules
- 10:12Pseudo-differential operator nets
- 16:14Fourier integral operator nets
- 20:51Applying nets to radar imaging
- 28:26Electrical impedance tomography
- 34:07Travel time tomography
- 38:59Optical tomography results
- 44:14Summary and references
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