American Geophysical Union Fall Meeting 2020

The session Addressing Challenges for the Next Generation of Earth System Models could be a good fit for some Firedrake talks. In particular the abstract specifically mentions domain-specific languages. The due date is July 29. If you're interested in working on a presentation please put your name down under the topic below, or if you'd like to present on a topic you don't see then feel free to create it.

Extruded meshes are lovely

Firedrake implements a fortuitous combination of extruded meshes, language extensions to UFL for manipulating forms defined on these meshes, tensor product finite elements, and specialized codegen optimizations like sum factorization. We'll describe how these features are invaluable for implementing models across the geophysical sciences, many of which exhibit a layered structure in the vertical dimension. In particular, they are used in the atmospheric model Gusto, the ocean model Thetis, and the ice sheet model Icepack.

People: Daniel Shapero, Tuomas Kärnä

Automating Code Generation for Point Evaluation in Geoscience Models

Firedrake is a code generation system which enables straightforward and scalable model development using finite element methods via high level abstractions of mathematical concepts. Several software packages build on Firedrake for applications in the geophysical sciences: the ice sheet model Icepack, the atmospheric model Gusto, and the ocean model Thetis. In the past, assimilating sparse point data (as opposed to gridded data) into models discretised using the finite element method has been challenging. We present progress towards evaluating, manipulating, assimilating and creating equation systems with large numbers of point measurements in such models. Examples of point data sets include measurements of ice sheet elevation from satellite altimetry and measurements of ocean salinity and temperature from drifting buoys. Our framework is compatible with the automated adjoint system pyadjoint, facilitating automated code generation for inverse problems with point data. This work is part of a broader project aiming to use Domain Specific Languages (DSLs) to automate diagnostics of geoscientific models with very large output data sets.

People: Reuben Hill

External operators

Firedrake is an automated system for the solution of partial differential equations (PDEs). It enables writing down PDE-based problems, like those occurring across the geophysical sciences, in a highly productive way while relying on automatic code generation to achieve high-performance simulations. Many software packages have been built on top of Firedrake, including Thetis, Gusto, and Icepack. One limitation of high level domain-specific languages for describing simulations is that they do not take into account operators that are not directly expressible using vector calculus. This limitation is critical in many applications where PDEs are not enough to accurately describe the physical problem of interest. These applications include nonlinear implicit constitutive laws such as the Glen's flow law for glacier flow, the use of neural networks to include features not represented in the differential equations, or closures for unresolved spatiotemporal scales. Example applications of of neural networks include regularization of inverse problems such as in seismic inversion and subgrid parameterization of atmospheric or oceanographic processes like clouds or turbulence. We present extensions to Firedrake that enable the inclusion of arbitrary external operators. This external operator feature composes seamlessly with the automatic differentiation capabilities of Firedrake.

People: Nacime Bouziani