Applications of Deep Learning to Scientific Inverse Problems
The first part of this thesis introduces an end-to-end deep learning architecture, called the wide-band butterfly network (WideBNet), which comprehensively solves the inverse wave scattering problem across all length scales. Our architecture incorporates the physics of wave propagation using tools f...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2022
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| Online Access: | https://hdl.handle.net/1721.1/139969 |
| _version_ | 1826202070337716224 |
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| author | Li, Matthew T. C. |
| author2 | Demanet, Laurent |
| author_facet | Demanet, Laurent Li, Matthew T. C. |
| author_sort | Li, Matthew T. C. |
| collection | MIT |
| description | The first part of this thesis introduces an end-to-end deep learning architecture, called the wide-band butterfly network (WideBNet), which comprehensively solves the inverse wave scattering problem across all length scales. Our architecture incorporates the physics of wave propagation using tools from computational harmonic analysis, specifically the butterfly factorization, and traditional multi-scale methods such as the Cooley-Tukey FFT algorithm. This allows WideBNet to automatically adapt to the dimension of the data so that the number of trainable parameters scales linearly, up to logarithmic factors, with the inherent complexity of the inverse problem. While our trained network provides competitive results in classical imaging regimes, most notably it also succeeds in the super-resolution regime where other comparable methods fail. This encompasses both (i) reconstruction of scatterers with sub-wavelength geometric features, and (ii) accurate imaging when two or more scatterers are separated by less than the classical diraction limit. We demonstrate these properties are retained even in the presence of strong noise and extend to scatterers not previously seen in the training set. In addition, we also demonstrate that our proposed framework outperforms both classical inversion and competing wave scattering specialized architectures across a variety of wave scattering mediums.
The second contribution of this thesis concerns scientific inverse problems in which uncontrollable experimental conditions induce nuisance variations in data and encumber inference. In particular, domain experts in these settings contend with the challenge of disambiguating whether changes in data arise from evolution of the physical quantities of interest (in eect, the signal), or from experimental fluctuations (in eect, the noise). We address this question using a bespoke auto-encoding architecture called the symmetric autoencoder (SymAE). SymAE embeds the data into explanatory latent coordinates corresponding to either coherent physical information or nuisance information. We assume weak supervision in the data and explicitly incorporate symmetries into the architecture to achieve this partitioning. As a result, this endows SymAE with the ability to align datapoints to a common nuisance variation by swapping relevant coordinates in the structured latent space. These resulting virtual datapoints can then be reliably used by domain experts for the purpose of extracting the physics retained in the coherent information. As a motivating example we consider applications to time-lapse monitoring in which geophysicists aim to determine whether changes in data arise on account of evolution in subsurface variabilities (e.g. leaks of supercritical CO2), or arise from uncontrollable conditions encountered during the seismic survey (e.g. from inherent randomness of the micro-seismic sources). We provide numerical experiments demonstrating SymAE is capable of disentangling coherent and nuisance eects in its latent space for a broad range of models for wave propagation. Furthermore, we quantify the accuracy of SymAE redatuming using examples with synthetic seismic data. |
| first_indexed | 2024-09-23T12:01:24Z |
| format | Thesis |
| id | mit-1721.1/139969 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T12:01:24Z |
| publishDate | 2022 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1399692022-02-08T03:38:20Z Applications of Deep Learning to Scientific Inverse Problems Li, Matthew T. C. Demanet, Laurent Massachusetts Institute of Technology. Department of Mechanical Engineering The first part of this thesis introduces an end-to-end deep learning architecture, called the wide-band butterfly network (WideBNet), which comprehensively solves the inverse wave scattering problem across all length scales. Our architecture incorporates the physics of wave propagation using tools from computational harmonic analysis, specifically the butterfly factorization, and traditional multi-scale methods such as the Cooley-Tukey FFT algorithm. This allows WideBNet to automatically adapt to the dimension of the data so that the number of trainable parameters scales linearly, up to logarithmic factors, with the inherent complexity of the inverse problem. While our trained network provides competitive results in classical imaging regimes, most notably it also succeeds in the super-resolution regime where other comparable methods fail. This encompasses both (i) reconstruction of scatterers with sub-wavelength geometric features, and (ii) accurate imaging when two or more scatterers are separated by less than the classical diraction limit. We demonstrate these properties are retained even in the presence of strong noise and extend to scatterers not previously seen in the training set. In addition, we also demonstrate that our proposed framework outperforms both classical inversion and competing wave scattering specialized architectures across a variety of wave scattering mediums. The second contribution of this thesis concerns scientific inverse problems in which uncontrollable experimental conditions induce nuisance variations in data and encumber inference. In particular, domain experts in these settings contend with the challenge of disambiguating whether changes in data arise from evolution of the physical quantities of interest (in eect, the signal), or from experimental fluctuations (in eect, the noise). We address this question using a bespoke auto-encoding architecture called the symmetric autoencoder (SymAE). SymAE embeds the data into explanatory latent coordinates corresponding to either coherent physical information or nuisance information. We assume weak supervision in the data and explicitly incorporate symmetries into the architecture to achieve this partitioning. As a result, this endows SymAE with the ability to align datapoints to a common nuisance variation by swapping relevant coordinates in the structured latent space. These resulting virtual datapoints can then be reliably used by domain experts for the purpose of extracting the physics retained in the coherent information. As a motivating example we consider applications to time-lapse monitoring in which geophysicists aim to determine whether changes in data arise on account of evolution in subsurface variabilities (e.g. leaks of supercritical CO2), or arise from uncontrollable conditions encountered during the seismic survey (e.g. from inherent randomness of the micro-seismic sources). We provide numerical experiments demonstrating SymAE is capable of disentangling coherent and nuisance eects in its latent space for a broad range of models for wave propagation. Furthermore, we quantify the accuracy of SymAE redatuming using examples with synthetic seismic data. Ph.D. 2022-02-07T15:16:17Z 2022-02-07T15:16:17Z 2021-09 2021-09-30T17:29:06.260Z Thesis https://hdl.handle.net/1721.1/139969 In Copyright - Educational Use Permitted Copyright MIT http://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Li, Matthew T. C. Applications of Deep Learning to Scientific Inverse Problems |
| title | Applications of Deep Learning to Scientific Inverse
Problems |
| title_full | Applications of Deep Learning to Scientific Inverse
Problems |
| title_fullStr | Applications of Deep Learning to Scientific Inverse
Problems |
| title_full_unstemmed | Applications of Deep Learning to Scientific Inverse
Problems |
| title_short | Applications of Deep Learning to Scientific Inverse
Problems |
| title_sort | applications of deep learning to scientific inverse problems |
| url | https://hdl.handle.net/1721.1/139969 |
| work_keys_str_mv | AT limatthewtc applicationsofdeeplearningtoscientificinverseproblems |