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Domain-specific high-productivity environments are playing an increasingly important role in scientific computing due to the levels of abstraction and automation they provide. In this paper we introduce Devito, an open-source domain-specific framework for solving partial differential equations from symbolic problem definitions by the finite difference method. We highlight the generation and automated execution of highly optimized stencil code from only a few lines of high-level symbolic Python for a set of scientific equations, before exploring the use of Devito operators in seismic inversion problems.
Domain specific languages (DSL) have been used in a variety of fields to express complex scientific problems in a concise manner and provide automated performance optimization for a range of computational architectures. As such DSLs provide a powerfu
In addition to hardware wall-time restrictions commonly seen in high-performance computing systems, it is likely that future systems will also be constrained by energy budgets. In the present work, finite difference algorithms of varying computationa
Exascale computing will feature novel and potentially disruptive hardware architectures. Exploiting these to their full potential is non-trivial. Numerical modelling frameworks involving finite difference methods are currently limited by the static n
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions in their ow
Discovering the underlying behavior of complex systems is an important topic in many science and engineering disciplines. In this paper, we propose a novel neural network framework, finite difference neural networks (FDNet), to learn partial differen