Automated adjoints of coupled PDE-ODE systems
For researchers in biology, medicine, and chemistry who need to solve coupled PDE-ODE models, this work provides an automated tool that reduces manual implementation effort.
The paper extends FEniCS finite element software to automatically generate efficient parallel solvers and adjoint/tangent linearizations for coupled PDE-ODE systems, demonstrated on cardiac electrophysiology and mitochondrial swelling examples.
Mathematical models that couple partial differential equations (PDEs) and spatially distributed ordinary differential equations (ODEs) arise in biology, medicine, chemistry and many other fields. In this paper we discuss an extension to the FEniCS finite element software for expressing and efficiently solving such coupled systems. Given an ODE described using an augmentation of the Unified Form Language (UFL) and a discretisation described by an arbitrary Butcher tableau, efficient code is automatically generated for the parallel solution of the ODE. The high-level description of the solution algorithm also facilitates the automatic derivation of the adjoint and tangent linearization of coupled PDE-ODE solvers. We demonstrate the capabilities of the approach on examples from cardiac electrophysiology and mitochondrial swelling.