A large-scale framework for symbolic implementations of seismic inversion algorithms in Julia

Abstract

Writing software packages for seismic inversion is a very challenging task because problems such as full-waveform inversion or least-squares imaging are algorithmically and computationally demanding due to the large number of unknown parameters and the fact that waves are propagated over many wavelengths. Therefore, software frameworks need to combine versatility and performance to provide geophysicists with the means and flexibility to implement complex algorithms that scale to exceedingly large 3D problems. Following these principles, we have developed the Julia Devito Inversion framework, an open-source software package in Julia for large-scale seismic modeling and inversion based on Devito, a domain-specific language compiler for automatic code generation. The framework consists of matrix-free linear operators for implementing seismic inversion algorithms that closely resemble the mathematical notation, a flexible resilient parallelization, and an interface to Devito for generating optimized stencil code to solve the underlying wave equations. In comparison with many manually optimized industry codes written in low-level languages, our software is built on the idea of independent layers of abstractions and user interfaces with symbolic operators. Through a series of numerical examples, we determined that this allows users to implement a series of increasingly complex algorithms for waveform inversion and imaging as simple Julia scripts that scale to large-scale 3D problems. This illustrates that software based on the paradigms of abstract user interfaces and automatic code generation and makes it possible to manage the complexity of the algorithms and performance optimizations, thus providing a high-performance research and production framework.

Devito (v3.1.0): an embedded domain-specific language for finite differences and geophysical exploration

“…Devito aims to combine the performance benefits of dedicated stencil frameworks (Bondhugula et al, 2008;Tang et al, 2011;Henretty et al, 2013;Yount, 2015) with the expressiveness of symbolic PDE-solving DSLs (Logg et al, 2012;Rathgeber et al, 2015) through automated code generation and optimization from high-level symbolic expressions of the mathematics. Thus, the primary design objectives of the Devito DSL are to allow users to define explicit finitedifference operators for (time-dependent) PDEs in a concise symbolic manner and provide an API that is flexible enough to fully support realistic scientific use cases.…”

“…1166 M. Louboutin et al: Devito: an embedded domain-specific language for finite differences 2015a; Weiss and Shragge, 2013). When considering how to design a DSL for explicit finite-difference schemes, it is useful to recognize the algorithm as being primarily a subclass of stencil algorithms or polyhedral computation (Henretty et al, 2013;Andreolli et al, 2015;Yount, 2015). However, stencil compilers lack two significant features required to develop a DSL for finite differences: symbolic computational support required to express finite-difference discretizations at a high level, enabling these expressions to be composed and manipulated algorithmically; and support for algorithms that are not stencil-like, such as source and receiver terms that are both sparse and unaligned with the finite-difference grid.…”

“…Two prominent contemporary projects based on the finite-element method (FEM), FEniCS (Logg et al, 2012) and Firedrake (Rathgeber et al, 2015), both implement a common DSL, UFL (Alnaes et al, 2014), that allows for the expression of variational problems in weak form. Multiple DSLs to express stencillike algorithms have also emerged over time (Henretty et al, 2013;Zhang and Mueller, 2012;Christen et al, 2011;Unat et al, 2011;Köster et al, 2014;Membarth et al, 2012;Osuna et al, 2014;Tang et al, 2011;Bondhugula et al, 2008;Yount, 2015). Other stencil DSLs have been developed with the objective of solving PDEs using finite differences (Hawick and Playne, 2013;Arbona et al, 2017;Jacobs et al, 2016).…”

A dual formulation for time-domain wavefield reconstruction inversion

“…The implementation of the method described in this paper leverages on the Devito framework, which allows the automatic generation of highly-optimized finite-difference C code, starting from a symbolic representation of the wave equation Louboutin et al, 2018). In Julia, we interface to Devito through the JUDI package (Witte et al, 2019).…”

Event-driven workflows for large-scale seismic imaging in the cloud

“…Generally, it is possible to add modeling codes of any programming language to a Docker container, but it is important to consider that user interfaces for the cloud (e.g. for writing results to buckets) exist only for high-level languages such as Python, but not for Fortran or C. In our workflow, we use the Julia Devito Inversion framework (JUDI) to compute individual gradients by solving the corresponding forward and adjoint wave-equations Witte et al, 2019). JUDI is implemented in the Julia programming language and consists of symbolic operators and data containers that allow us to express modeling operations and gradients for seismic inversion in terms of linear algebra expression.…”