Image inversion and uncertainty quantification for constitutive laws of pattern formation
The forward problems of pattern formation have been greatly empowered by extensive theoretical studies and simulations, however, the inverse problem is less well understood. It remains unclear how accurately one can use images of pattern formation to learn the functional forms of the nonlinear and n...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier BV
2021
|
| Online Access: | https://hdl.handle.net/1721.1/135663 |
| _version_ | 1826205075019661312 |
|---|---|
| author | Zhao, Hongbo Braatz, Richard D Bazant, Martin Z |
| author_facet | Zhao, Hongbo Braatz, Richard D Bazant, Martin Z |
| author_sort | Zhao, Hongbo |
| collection | MIT |
| description | The forward problems of pattern formation have been greatly empowered by
extensive theoretical studies and simulations, however, the inverse problem is
less well understood. It remains unclear how accurately one can use images of
pattern formation to learn the functional forms of the nonlinear and nonlocal
constitutive relations in the governing equation. We use PDE-constrained
optimization to infer the governing dynamics and constitutive relations and use
Bayesian inference and linearization to quantify their uncertainties in
different systems, operating conditions, and imaging conditions. We discuss the
conditions to reduce the uncertainty of the inferred functions and the
correlation between them, such as state-dependent free energy and reaction
kinetics (or diffusivity). We present the inversion algorithm and illustrate
its robustness and uncertainties under limited spatiotemporal resolution,
unknown boundary conditions, blurry initial conditions, and other non-ideal
situations. Under certain situations, prior physical knowledge can be included
to constrain the result. Phase-field, reaction-diffusion, and
phase-field-crystal models are used as model systems. The approach developed
here can find applications in inferring unknown physical properties of complex
pattern-forming systems and in guiding their experimental design. |
| first_indexed | 2024-09-23T13:06:20Z |
| format | Article |
| id | mit-1721.1/135663 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:06:20Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1356632021-10-28T03:56:38Z Image inversion and uncertainty quantification for constitutive laws of pattern formation Zhao, Hongbo Braatz, Richard D Bazant, Martin Z The forward problems of pattern formation have been greatly empowered by extensive theoretical studies and simulations, however, the inverse problem is less well understood. It remains unclear how accurately one can use images of pattern formation to learn the functional forms of the nonlinear and nonlocal constitutive relations in the governing equation. We use PDE-constrained optimization to infer the governing dynamics and constitutive relations and use Bayesian inference and linearization to quantify their uncertainties in different systems, operating conditions, and imaging conditions. We discuss the conditions to reduce the uncertainty of the inferred functions and the correlation between them, such as state-dependent free energy and reaction kinetics (or diffusivity). We present the inversion algorithm and illustrate its robustness and uncertainties under limited spatiotemporal resolution, unknown boundary conditions, blurry initial conditions, and other non-ideal situations. Under certain situations, prior physical knowledge can be included to constrain the result. Phase-field, reaction-diffusion, and phase-field-crystal models are used as model systems. The approach developed here can find applications in inferring unknown physical properties of complex pattern-forming systems and in guiding their experimental design. 2021-10-27T20:24:31Z 2021-10-27T20:24:31Z 2021 2021-06-08T16:36:51Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135663 en 10.1016/j.jcp.2021.110279 Journal of Computational Physics Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Zhao, Hongbo Braatz, Richard D Bazant, Martin Z Image inversion and uncertainty quantification for constitutive laws of pattern formation |
| title | Image inversion and uncertainty quantification for constitutive laws of pattern formation |
| title_full | Image inversion and uncertainty quantification for constitutive laws of pattern formation |
| title_fullStr | Image inversion and uncertainty quantification for constitutive laws of pattern formation |
| title_full_unstemmed | Image inversion and uncertainty quantification for constitutive laws of pattern formation |
| title_short | Image inversion and uncertainty quantification for constitutive laws of pattern formation |
| title_sort | image inversion and uncertainty quantification for constitutive laws of pattern formation |
| url | https://hdl.handle.net/1721.1/135663 |
| work_keys_str_mv | AT zhaohongbo imageinversionanduncertaintyquantificationforconstitutivelawsofpatternformation AT braatzrichardd imageinversionanduncertaintyquantificationforconstitutivelawsofpatternformation AT bazantmartinz imageinversionanduncertaintyquantificationforconstitutivelawsofpatternformation |