Co-simulation, state-of-the-art by Claudio Gomes

A few days ago, we had a seminar given by Claudio Gomes (University of Antwerp, Belgium). He recently produced a research report (turned into a paper) on Co-simulation: State of the Art with C. Thule, D. Broman, P. G. Larsen and H. Vangheluwe (arxiv). This work is an impressive body of work on tools enabling experts in different disciplines to collaborate more efficiently in the development of ever more complex systems. It overviews "co-simulation approaches, research challenges, and research opportunities" and "summarizes, bridges, and enhances future research in  this multidisciplinary area".

The attendant slides  nicely summarize in  a didactic way the main issues pertaining to coupled systems, via the composition of sub-system simulations. They deal with Terminology, Simulation units, Input extrapolation techniques, Orchestration algorithms, Algebraic loops, Convergence and Stability.

Abstract:

It is essential to find new ways of enabling experts in different disciplines to collaborate more efficient in the development of ever more complex systems, under increasing market pressures. One possible solution for this challenge is to use a heterogeneous model-based approach where different teams can produce their conventional models and carry out their usual mono-disciplinary analysis, but in addition, the different models can be coupled for simulation (co-simulation), allowing the study of the global behavior of the system. Due to its potential, co-simulation is being studied in many different disciplines but with limited sharing of findings. Our aim with this work is to summarize, bridge, and enhance future research in this multidisciplinary area. We provide an overview of co-simulation approaches, research challenges, and research opportunities, together with a detailed taxonomy with different aspects of the state of the art of co-simulation and classification for the past five years. The main research needs identified are: finding generic approaches for modular, stable and accurate coupling of simulation units; and expressing the adaptations required to ensure that the coupling is correct.

This opportunity was initiated though a very open discussion around extrapolation for co-simulation in cyber-physical systems in CHOPtrey: contextual online polynomial extrapolation for enhanced multi-core co-simulation of complex systems.

CHOPtrey: contextual online polynomial extrapolation for enhanced multi-core co-simulation of complex systems

XKCD. My hobby: extrapolating

CHOPtrey. A long, extrapolated and progressive scientific story. Ace, deuce, trey... ready?

It all started with Cyril Faure, then a PhD student  with Nicolas Pernet in real-time computing. He used to stop by my office. We had coffee, discussed books (from Descartes to Sci-Fi) and music (mostly Loudblast, Slayer, Pink Floyd, Manowar, Bolt Thrower). We exchanged ideas and concerns. One day, he told me about a worry in his thesis. Caveat: I am very bad at computer science, advanced programming, and had little hints about partitioned/slacked real-time co-simulation systems.

So this was not about programming, but simulation and co-simulation. Big physical systems (engines, aircrafts, boats) are complicated to simulate. Protocols and methods include FMI standard (Functional Mockup Interface) and FMU (Functional Mockup Unit). Partitioning them into subsystems may help the simulation, but split discrete subsystems should communicate. Fast enough to be precise, slow enough for speed-ups.

Hoher, 2011, A contribution to the real-time simulation...

So when simulated subsystems communicate at regular communication times, and one want interpolated data at a fractional time interval, one generally uses the last known value. This is called zeroth-order hold (ZOH). 

So I wondered: "this sound a little bit like aliasing, in a causal setting, let's interpolate, say, with a line or a parabola". No so easy. In this cosimulation domain, interpolation is "known" to be unstable. Even with FOH (first-order hold) or SOH (second-order hold).

A few implementations (Matlab prototypes, C++ and a final embedding in the XMOD software) and some tuning later, we produced a hierarchical scheme (with Abir, Cyril, Daniel and Mongi), based on morphological contexts, like in lossless image compression (PNG for instance). It proved very cheap, quite robust, and apparently stable. We called it CHOPtrey, from the old French words "ace, deuce, trey" (1, 2, 3 referring to sides of dice). In reference to a chop tray (or cutting board). Because it allows to chop (or cut) a big simulated system into several smaller ones. Because it is composed of three parts or chops:

• CHOPred: a Computationally Hasty Online Prediction system (improving the trade-off between integration speed-ups, needing large communication steps, and simulation precision)
• CHOPoly: Causal Hopping Oblivious Polynomials, with smoothed adaptive forward prediction improves co-simulation accuracy. They are similar to Savitzky-Golay filters or LOESS or LOWESS regression methods)
• CHOPatt: a Contextual & Hierarchical Ontology of Patterns, where data behavior is segmented  into different classes to handle the discontinuities of the exchanged signals

During this work, I learned a lot about co-simulation, parallel computing, multi-core, etc. But also a lot about least-squares parabolic regression, which I thought I knew for decades. I did not. Not the deepest theory ever, but one of my nicest experience of cross-domain collaboration (along with bioinformatics and our BRANE work on gene regulatory networks), some genuine computer engineering, with a final packaged product (implemented in xMod). Here it is:

CHOPtrey: contextual online polynomial extrapolation for enhanced multi-core co-simulation of complex systems 

Abstract : The growing complexity of Cyber-Physical Systems (CPS), together with increasingly available parallelism provided by multi-core chips, fosters the parallelization of simulation. Simulation speed-ups are expected from co-simulation and parallelization based on model splitting into weak-coupled sub-models, as for instance in the framework of Functional Mockup Interface (FMI). However, slackened synchronization between sub-models and their associated solvers running in parallel introduces integration errors, which must be kept inside acceptable bounds. CHOPtrey denotes a forecasting framework enhancing the performance of complex system co-simulation, with a trivalent articulation. First, we consider the framework of a Computationally Hasty Online Prediction system (CHOPred). It allows to improve the trade-off between integration speed-ups, needing large communication steps, and simulation precision, needing frequent updates for model inputs. Second, smoothed adaptive forward prediction improves co-simulation accuracy. It is obtained by past-weighted extrapolation based on Causal Hopping Oblivious Polynomials (CHOPoly). And third, signal behavior is segmented to handle the discontinuities of the exchanged signals: the segmentation is performed in a Contextual & Hierarchical Ontology of Patterns (CHOPatt). Implementation strategies and simulation results demonstrate the framework ability to adaptively relax data communication constraints beyond synchronization points which sensibly accelerate simulation. The CHOPtrey framework extends the range of applications of standard Lagrange-type methods, often deemed unstable. The embedding of predictions in lag-dependent smoothing and discontinuity handling demonstrates its practical efficiency.

Keywords: parallel simulation; Functional Mockup Interface (FMI); smoothed online prediction; causal polynomial extrapolation; context-based decision; internal combustion engine

Links:

• published: CHOPtrey (January 2017): SIMULATION: Transactions of The Society for Modeling and Simulation International
• arxiv: CHOPtrey: contextual online polynomial extrapolation for enhanced multi-core co-simulation of complex systems
• HAL: CHOPtrey: contextual online polynomial extrapolation for enhanced multi-core co-simulation of complex systems
• A novel CHOPtrey companion page
• Pêcheurs de perles, une parabole
• Ace, Deuce, Trey: The virtual linguist

The full set of numbers for the six sides of a die are ace, deuce, trey, cater, cinque, sice. They are from Old French (cf un, deux, trois, quatre, cinq, six of modern French). Ace is originally from the Latin for 'unit'.