CRIKit

This project earned me much Python and automatic differentiation experience.

CRIKit (2019-2023)

• Developed a software framework to enable training and testing complex CRs (constitutive relations) in material science.
• Integrated automatic differentiation frameworks with Pyadjoint, thus allowing seamless use of diverse CR implementations.
• Investigated CR parametrizations that respect physical symmetries and invariants, thus increasing generalizability.

Code here

Forward problem

Adjoint problem

Figure 1: When computing the loss, information flows from parameters \(p\) to loss \(J\), with intermediate computations of the PDE output \(u\) and the observable quantity \(d\). For computing the parameter gradient, information flows backward from \(J\) to \(p\). Even though the matrix \(\frac{du}{dp}\) grows quadratically with the problem size, applying its adjoint to \(\frac{dJ}{du}\) is cheap. This allows scalable gradient-based optimization of the parameters \(p\) when \(p\) is high-dimensional compared to the loss \(J\).

Boundary conditions for the damage \(\phi\)

Boundary conditions for the velocity \(u\)

Figure 2: Boundary conditions for a 2D vertical slice of a large mound of ice.

Figure 3: Solution from solving PDE with “ground-truth” damage model.

Figure 4: Error in learned damage model for 3 levels of noise (0%, 1%, and 5%) and 3 types of measurements.