CB Geo: Differentiable Programming in MPM

CB Geo-Material Point Method is used to simulate particulate and fluid systems. In this method, particles are mapped to a background mesh, and calculations done on the mesh points are transformed into the original particles. In this project, we would implement 1-D and 2-D MPM code in python using the JAX library. We will abstract the code into classes to apply automatic differentiation and use just-in-time compilation. We will also implement 1D MPM code in C++ and apply auto diff. Currently, the MPM code does not have an inverse problem solver; hence in this project, we will implement an inverse problem solver using automatic differentiation and gradient-based optimizations to minimize the loss function.