Model-based autotuning of discretization methods in numerical simulations of partial differential equations.

Research output: Contribution to journalResearch articleContributedpeer-review



We present an autotuning approach for compile-time optimization of numerical discretization methods in simulations of partial differential equations. Our approach is based on data-driven regression of performance models for numerical methods. We use these models at compile time to automatically determine the parameters (e.g., resolution, time step size, etc.) of numerical simulations of continuum spatio-temporal models in order to optimize the tradeoff between simulation accuracy and runtime. The resulting autotuner is developed for the compiler of a Domain-Specific Language (DSL) for numerical simulations. The abstractions in the DSL enable the compiler to automatically determine the performance models and know which discretization parameters to tune. We demonstrate that this high-level approach can explore a large space of possible simulations, with simulation runtimes spanning multiple orders of magnitude. We evaluate our approach in two test cases: the linear diffusion equation and the nonlinear Gray-Scott reaction–diffusion equation. The results show that our model-based autotuner consistently finds configurations that outperform those found by state-of-the-art general-purpose autotuners. Specifically, our autotuner yields simulations that are on average 4.2x faster than those found by the best generic exploration algorithms, while using 16x less tuning time. Compared to manual tuning by a group of researchers with varying levels of expertise, the autotuner was slower than the best users by not more than a factor of 2, whereas it was able to significantly outperform half of them.


Original languageEnglish
Article number101489
JournalJournal of Computational Science
Issue number57
Publication statusPublished - 1 Jan 2022

External IDs

Mendeley bfa513a1-37e2-3779-aebe-5103cf62c409
dblp journals/jocs/KhouzamiMICS22
WOS 000798249300001
unpaywall 10.1016/j.jocs.2021.101489


Research priority areas of TU Dresden


  • Autotuning, Compilers, Discretization methods, Domain-specific languages, Numerical simulations, Performance models