Interoperability with automatic differentiation libraries through NumPy interface to FEniCS

Partial differential equations (PDEs) are used to describe a variety of physical phenomena. Computing derivative information of the solution to PDE with respect to the input parameters is important in many tasks in scientific computing. A high-level interface for evaluating derivatives of FEniCS models is developed. It is intended to be used as the backend for extending Automatic Differentiation libraries to support FEniCS solvers. High-level symbolic representation of PDEs allows bypassing differentiating through low-level possibly many iterations of the underlying nonlinear solvers. Automatic tangent linear and adjoint solvers for FEniCS problems are derived with dolfin-adjoint/pyadjoint. These solvers make it possible to use forward and reverse modes Automatic Differentiation with FEniCS. This package is used for building bridges between FEniCS and JAX, PyMC3 (Theano), PyTorch, Julia's ChainRule.jl, Zygote.jl. This enables the efficient composition of finite element solvers with arbitrary differentiable programs.