Learning physics of pattern formation from images

Biological materials are often driven out of equilibrium and requires multiphysics coupling such as chemical and mechanical deformation fields. Advanced imaging offers the possibility of data-driven modeling of material properties and nonequilibrium physics. In this talk, I will share our work using partial-differential-equation (PDE)-constrained optimization and Bayesian inference to learn the continuum models of materials from microscopy images and diffraction data. We extracted thermodynamic and reaction kinetic models, spatial heterogeneity, and chemo-mechanical coupling, demonstrating the possibility of achieving full utilization of the dataset. In addition to experimental data, I will show recent work where we learned continuum models of phase separation from molecular dynamics simulation data. I will also talk about applications of these continuum models in biological systems.