Image inversion and uncertainty quantification for constitutive laws of pattern formation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:436

Article

Zhao, Hongbo¹  Braatz, Richard D.¹  Bazant, Martin Z.^1,2 

[1] MIT, Dept Chem Engn, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] MIT, Dept Math, 77 Massachusetts Ave, Cambridge, MA 02139 USA

关键词: PDE-constrained optimization;    Uncertainty quantification;    MCMC;    Pattern formation;    Inverse problem;    Phase field model;   

DOI  :  10.1016/j.jcp.2021.110279

来源: Elsevier

【 摘 要 】

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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free