Composing Modeling and Simulation with Machine Learning in Julia

Abstract

In this paper we introduce JuliaSim, a high-performance programming environment designed to blend traditional modeling and simulation with machine learning. JuliaSim can build accelerated surrogates from component-based models, such as those conforming to the FMI standard, using continuous-time echo state networks (CTESN). The foundation of this environment, ModelingToolkit.jl, is an acausal modeling language which can compose the trained surrogates as components within its staged compilation process. As a complementary factor we present the Ju-liaSim model library, a standard library with differentialalgebraic equations and pre-trained surrogates, which can be composed using the modeling system for design, optimization, and control. We demonstrate the effectiveness of the surrogate-accelerated modeling and simulation approach on HVAC dynamics by showing that the CTESN surrogates accurately capture the dynamics of a HVAC cycle at less than 4% error while accelerating its simulation by 340x. We illustrate the use of surrogate acceleration in the design process via global optimization of simulation parameters using the embedded surrogate, yielding a speedup of two orders of magnitude to find the optimum. We showcase the surrogate deployed in a co-simulation loop, as a drop-in replacement for one of the coupled FMUs, allowing engineers to effectively explore the design space of a coupled system. Together this demonstrates a workflow for automating the integration of machine learning techniques into traditional modeling and simulation processes.

A Modular, Extensible, and Modelica-Standard-Compliant OpenModelica Compiler Framework in Julia Supporting Structural Variability

“…Furthermore, since the MTK environment supports more solvers compared to OMC, we can also leverage this difference and achieve better performance than OMC. The feasibility of the MTK framework has also been discussed in other literature, such as [13], where MTK outperformed the commercial Dymola compiler in a specific case. However, due to the high memory requirements of Julia and MTK, we were currently unable to go further than 25,600 equations in this benchmark.…”

“…Similarly, to model reduction, the accuracy of the numerical simulation is reduced in order to simulate systems or parts of systems faster. A contemporary example of this technique in the context of equation-based languages is [13]. Bruder and Mikelsons [12] have also demonstrated the benefits of this technique.…”

“…Model reduction [8][9][10], which can speed up simulations by switching between a more or less complex model depending on some conditions. • Grey-box modeling [11][12][13], where surrogate models are trained and employed before or during runtime to speed up simulation.…”

“…The results regarding automatic surrogatization of algebraic loops are described in [6]. (Surrogatization means replacing a concrete model or in this case parts of model with a surrogate generated by a machine-learning algorithm [13]).…”

Towards an Open Platform for Democratized Model-Based Design and Engineering of Cyber-Physical Systems

“…We have already tested different analysis toolkits using our HPC CI environment, to include UncertainPy (Tennøe, Halnes, and Einevoll 2018) and Dakota (Adams et al 2020). We are working to provide seamless support for surrogate-assisted methods to accelerate computationally expensive analyses using methods such as pre-trained surrogate models for accelerated simulation, as done by JuliaSim (Rackauckas et al 2021), and dynamically generated surrogates, as done by GreyOpt (Nachawati and Brodsky 2021), for enhanced optimization.…”