Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers

Gardner, David J.; Reynolds, Daniel R.; Woodward, Carol S.; Balos, Cody J.

doi:10.1145/3539801

Cited by 43 publications

(32 citation statements)

References 67 publications

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“…Our implementation uses the AMReX (Zhang et al 2019(Zhang et al , 2020) adaptive mesh refinement library and its predecessor package, BoxLib (Zhang et al 2016) for spatial discretizations and the SUNDIALS library (Hindmarsh et al 2005;Gardner et al 2022;Reynolds et al 2022) for temporal discretizations. Interfacing SUNDIALS with BoxLib allowed for an easier, direct comparison to previously developed code, and interfacing SUNDIALS with AMReX demonstrates the interoperability of the two libraries.…”

Section: Methodsmentioning

confidence: 99%

“…The MRI methods evaluated in this work are provided by the SUNDIALS suite of time integrators and nonlinear solvers (Hindmarsh et al 2005;Gardner et al 2022). The suite is comprised of the ARKODE package of onestep methods for ODEs, the multistep integrators CVODE and IDA for ODEs and DAEs, respectively, the forward and adjoint sensitivity analysis enabled variants, CVODES and IDAS, and the nonlinear algebraic equation solver KINSOL.…”

Section: Time Integratorsmentioning

confidence: 99%

“…There have been few performance studies for multirate integration on complex application problems. Here we compare several MRI schemes supported by the ARKODE package (Reynolds et al 2022) in the SUNDIALS library (Hindmarsh et al 2005;Gardner et al 2022) of time integrators and nonlinear solvers to an existing SDC implementation for a combustion problem containing detailed kinetics and transport using the BoxLib block-structured AMR framework (Zhang et al 2016). Additionally, we look at the performance of newly developed explicit and implicit-explicit (IMEX) multirate methods on a similar problem implemented with the AMReX block-structured AMR framework (Zhang et al 2019(Zhang et al , 2020.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks

Loffeld¹,

Nonaka²,

Reynolds³

et al. 2022

Preprint

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Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges, since these systems enable ever increasing size and complexity. In recent years, there has been renewed interest in developing multirate methods as a means to handle the large range of time scales, as these methods may afford greater accuracy and efficiency than more traditional approaches of using IMEX and low-order operator splitting schemes. However, to date there have been few performance studies that compare different classes of multirate integrators on complex application problems. In this work, we study the performance of several newly developed multirate infinitesimal (MRI) methods, implemented in the SUNDIALS solver package, on two reacting flow model problems built on structured mesh frameworks. The first model revisits the work of Emmett et al. ( 2014) on a compressible reacting flow problem with complex chemistry that is implemented using BoxLib but where we now include comparisons between a new explicit MRI scheme with the multirate spectral deferred correction (SDC) methods in the original paper. The second problem uses the same complex chemistry as the first problem, combined with a simplified flow model, but run at a large spatial scale where explicit methods become infeasible due to stability constraints. Two recently developed implicit-explicit (IMEX) MRI multirate methods are tested. These methods rely on advanced features of the AMReX framework on which the model is built, such as multilevel grids and multilevel preconditioners. The results from these two problems show that MRI multirate methods can offer significant performance benefits on complex multiphysics application problems and that these methods may be combined with advanced spatial discretization to compound the advantages of both.

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Section: Methodsmentioning

confidence: 99%

Section: Time Integratorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks

Loffeld¹,

Nonaka²,

Reynolds³

et al. 2022

Preprint

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“…The ODE models were solved with scikit-odes, a Python wrapper for the sundials suite of solvers 50 . In all cases, the initial concentrations of heterologous pathway enzymes were assumed to be zero.…”

Section: B Model Pathwaysmentioning

confidence: 99%

Bayesian optimization for design of multiscale biological circuits

Merzbacher

Aodha

Oyarzún

2023

Preprint

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Recent advances in synthetic biology have enabled the construction of molecular circuits that operate across multiple scales of cellular organization, for example by interfacing gene regulation with signalling or metabolic pathways. Computational methods can effectively aid and accelerate the design process, but current methods are generally unsuited for systems with multiple temporal or concentration scales, as these are challenging to simulate due to their numerical stiffness. Here, we present a machine learning method for the efficient optimization of biological circuits across scales. We employ a Bayesian optimization approach and nonparametric statistical models to learn the shape of a performance landscape and iteratively navigate the design space towards an optimal design. This strategy allows the joint optimization of both circuit architecture and parameters, and hence provides a feasible approach to solve a highly non-convex optimization problem in a mixed-integer input space. We illustrate the applicability of the method on gene circuits designed to control biosynthetic pathways, as these display strong nonlinearities and have molecular components that evolve in different timescales and different scales of molecular concentrations. We test the method on various models of dynamic production pathways previously built in the literature, and highlight its ability to optimize large multiscale models with more than 20 species and circuit architectures, as well as large parametric sweeps that are useful for assessing the robustness of optimal designs to perturbations. The method can serve as an efficient \textit{in silico} screening method for circuit architectures prior to experimental testing.

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“…Despite the limited uptake of ForTrilinos, the SWIG-Fortran product has been integrated into numerous libraries both inside and outside ECP. It is currently in use by SUNDIALS [16], STRUMPACK [17], TASMANIAN [18], and DTK [19], either as a supplement to their C/C++-only library or replacing previous handwritten code, lowering the maintenance burden on library developers. SWIG-Fortran is also being used by the SCALE project [5], which shares code with the ExaSMR ECP application, to help transition away from Fortran development by integrating new C++ code into older Fortran code.…”

Section: Swig-fortranmentioning

confidence: 99%

Five years of ForTrilinos ECP

Johnson¹,

Prokopenko²

2022

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The ForTrilinos subproject of the Exascale Computing Project (ECP) [1] was initiated to bring the capabilities and scalability of the Trilinos numerical solver collection [2] to Fortran scientific application codes. A novel Fortran extension to the Simplified Wrapper and Interface Generator (SWIG) tool, which automatically generates Fortran bindings from existing C/C++ library code, has been applied to key Trilinos solver libraries to generate the new ForTrilinos libraries. SWIG-Fortran has additionally been used to generate new Fortran compatibility layers for additional scientific libraries and applications. This report summarizes the products and impact of the ForTrilinos subproject.

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Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers

Cited by 43 publications

References 67 publications

Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks

Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks

Bayesian optimization for design of multiscale biological circuits

Five years of ForTrilinos ECP

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