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ModelingToolkit: A Composable Graph Transformation System For Equation-Based Modeling
arXiv - CS - Mathematical Software Pub Date : 2021-03-09 , DOI: arxiv-2103.05244 Yingbo Ma, Shashi Gowda, Ranjan Anantharaman, Chris Laughman, Viral Shah, Chris Rackauckas
arXiv - CS - Mathematical Software Pub Date : 2021-03-09 , DOI: arxiv-2103.05244 Yingbo Ma, Shashi Gowda, Ranjan Anantharaman, Chris Laughman, Viral Shah, Chris Rackauckas
Getting good performance out of numerical equation solvers requires that the
user has provided stable and efficient functions representing their model.
However, users should not be trusted to write good code. In this manuscript we
describe ModelingToolkit (MTK), a symbolic equation-based modeling system which
allows for composable transformations to generate stable, efficient, and
parallelized model implementations. MTK blurs the lines of traditional symbolic
computing by acting directly on a user's numerical code. We show the ability to
apply graph algorithms for automatically parallelizing and performing index
reduction on code written for differential-algebraic equation (DAE) solvers,
"fixing" the performance and stability of the model without requiring any
changes to on the user's part. We demonstrate how composable model
transformations can be combined with automated data-driven surrogate generation
techniques, allowing machine learning methods to generate accelerated
approximate models within an acausal modeling framework. These reduced models
are shown to outperform the Dymola Modelica compiler on an HVAC model by 590x
at 3\% accuracy. Together, this demonstrates MTK as a system for bringing the
latest research in graph transformations directly to modeling applications.
中文翻译:
ModelingToolkit:用于基于方程的建模的可组合图形转换系统
要从数值方程求解器中获得良好的性能,需要用户提供代表其模型的稳定且有效的函数。但是,不应信任用户编写好的代码。在本手稿中,我们描述了ModelingToolkit(MTK),这是一个基于符号方程式的建模系统,该系统允许可组合的转换以生成稳定,高效和并行化的模型实现。MTK通过直接作用于用户的数字代码来模糊传统符号计算的界限。我们展示了可以应用图算法在为微分代数方程(DAE)求解器编写的代码上自动并行化和执行索引减少,无需用户进行任何更改即可“固定”模型的性能和稳定性。我们演示了可组合模型转换如何与自动数据驱动的替代物生成技术结合使用,从而允许机器学习方法在非因果建模框架内生成加速的近似模型。这些简化的模型在HVAC模型上的表现优于Dymola Modelica编译器,精度达到590x,精度为3%。总之,这证明了MTK作为将图形转换的最新研究直接带到建模应用程序的系统。
更新日期:2021-03-10
中文翻译:
ModelingToolkit:用于基于方程的建模的可组合图形转换系统
要从数值方程求解器中获得良好的性能,需要用户提供代表其模型的稳定且有效的函数。但是,不应信任用户编写好的代码。在本手稿中,我们描述了ModelingToolkit(MTK),这是一个基于符号方程式的建模系统,该系统允许可组合的转换以生成稳定,高效和并行化的模型实现。MTK通过直接作用于用户的数字代码来模糊传统符号计算的界限。我们展示了可以应用图算法在为微分代数方程(DAE)求解器编写的代码上自动并行化和执行索引减少,无需用户进行任何更改即可“固定”模型的性能和稳定性。我们演示了可组合模型转换如何与自动数据驱动的替代物生成技术结合使用,从而允许机器学习方法在非因果建模框架内生成加速的近似模型。这些简化的模型在HVAC模型上的表现优于Dymola Modelica编译器,精度达到590x,精度为3%。总之,这证明了MTK作为将图形转换的最新研究直接带到建模应用程序的系统。