  We develop a tool that enables domain experts to quickly generate numerical
solvers for emerging multi-physics phenomena starting from a high-level
description based on ordinary/partial differential equations and their initial
and boundary conditions over a symbolic spacetime domain. This "multi-physics"
compiler aims to bridge the gap between problem formulation and computation,
which historically has spanned years or even decades. Specialized numerical
solvers in areas such as computational fluid dynamics (CFD) often present a
barrier to novice end users not well-versed in the intricacies of their
underlying schemes, and requiring surgical modifications when coupling with
additional physical components initially not accounted for by the solver.
Through the use of an intermediate language that is neutral between classical
and exterior calculus, the compiler generates correct-by-construction numerical
source code that offers guarantees of immutable physical principles like
conservation laws at the discrete level. We present a proof of concept for the
multi-physics compiler through some examples involving compilation to OpenFOAM
[1]. A specific use case that the compiler is well-suited for involves equation
modification approaches, where the aim is to use simple numerical schemes such
as central differencing through the additional of artificial terms to the
original governing equations of the multi-physics problem [2, 3, 4].
