Domain-specific abstractions for large-scale geophysical inverse-problems

Seismic inverse problems for subsurface imaging and parameter estimation are a computationally challenging class of inverse problems and involve solving large numbers of wave equations on big computational domains. Furthermore, seismic inverse problems are challenging from the mathematical point of view as well, as they are often non-linear and ill-posed. Software frameworks for seismic inverse problems therefore need to provide both high-level abstractions for facilitating the implementation of optimization algorithms and solvers for partial differential equations (PDEs), but they also need to scale to problem sizes with over one billion unknown parameters. In this talk, we introduce two high-level abstractions that address these issues; Devito is a domain-specific language and compiler for finite differences embedded in Python and designed for symbolic implementations of PDEs on a high abstraction level. During runtime, the Devito compiler automatically translates these high-level expressions into optimized C code, using a range of performance optimization techniques such as vectorization, loop blocking, elimination of common sub-expressions and OpenMP/MPI parallelism. The second half of the talk introduces an abstract linear algebra framework called JUDI, which provides data containers and matrix-free linear operators built around Devito, for symbolic implementations of optimization algorithms for seismic inversion. The talk will give an overview of these two frameworks and demonstrate through a series of examples from seismic imaging and non-linear parameter estimation, how the mathematical and computational complexity of these problems can be addressed through the power of abstractions.