*06/12/2023*

Behind the idea of the *MODELISCALE* Challenge is an observation: hybrid system modeling languages in general, and in particular the Modelica language, commonly used in industry (aeronautics, energy, etc.), suffer from **a certain number of imperfections**. The semantics, i.e. the mathematical meaning that can be given to a model expressed in these languages, is not clearly defined, making it impossible, for example, to prove the properties of a particular model, and consequently the proper functioning of these systems.

In 2018, this problem has led three Inria teams (Hycomes, Parkas and Tripop), a team from LIX (Cosynus) and two researchers from ENSTA (Goran Frehse) and Centrale-Supelec (Antoine Girard) to collaborate on the **modeling, simulation and verification of cyberphysical systems**, i.e., anything dominated by physics (nuclear power plants, mechanical systems such as robotics, heat networks, electricity distribution networks, etc.), but which have the particularity of being able to operate in the same way as other systems. ) but which have the particularity of having a computerized control.

**Modeling, simulation and verification: what is the difference?**

**Modeling** allows us to build mathematical models of objects, while **simulation** allows us to execute them and make them evolve before our eyes. **Verification**, on the other hand, allows us to prove, in a mathematical sense, properties of these systems (in particular safety properties that allow us to avoid possible catastrophes).

## Modeliscale, a Challenge to advance modeling technologies

Called MODELISCALE, the Challenge has one main objective: **to advance modelling technologies** (languages, static analyses, simulation techniques) for cyber-physical systems combining physical interactions and software components. *"We set out to answer a number of questions concerning the design of modelling languages and, above all, the good principles that should underpin modelling languages for cyber-physical systems,"* explains Benoît Caillaud, head of the Hycomes project team.

According to the team behind this challenge, mastering cyber-physical systems comprising thousands or millions of components requires **radical paradigm shifts**. For example, modelling techniques need to be reviewed, especially when physics is involved. Modelling languages must be improved to cope with larger models. This can only be done by combining new compilation techniques (to control the structural complexity of the models) with new mathematical tools (new numerical methods, in particular).

*"We therefore decided to bring together a number of researchers who we felt could provide an interesting perspective on this issue,"* says Benoît Caillaud. The Inria Parkas project-team, for example, is already behind the hybrid language Zélus. The Hycomes team has been interested for many years in the design of languages based on algebraic-differential equations, which are notably at the heart of the Modelica language. The Cosynus team and Goran Frehse from ENSTA are specialised in the verification of hybrid systems. Antoine Girard, from Centrale Supelec, brings a competence in symbolic control of hybrid systems, to answer certain problems in automation.

## A continuation of the Challenge in research... and industry

Four years later, the Challenge has ended and the results are there. In research, first of all, with convincing results on the structural analysis of systems of multimode algebraic-differential equations, which is an analysis done statically (i.e., not at the time of the simulation, but at the time of the compilation of these models). These results are essential to detect errors in the models (e.g., too many equations, or not enough, in certain modes), but also to generate efficient simulation code that can scale to systems of the order of 300,000 equations. *"That led to the development of a software prototype called IsamDAE. There is also a Technological Development Action that has been financed by Inria to push the consolidation and maturation of the software,"* says Benoît Caillaud.

Some of the Challenge's work has also been developed in the framework of a **collaborative project with an industrial focus** (the FUI MODELISCALE), which involved several industrial partners, and which helped to push some of the MODELISCALE Challenge results to a higher level of maturation. Among the partners in question: Dassault Systèmes, vendor of the Dymola modeling and simulation tool, as well as EDF and Engie, which worked in particular on modeling urban energy networks. *"Within the framework of the FUI MODELISCALE, an experimental coupling between the Dymola tool and our structural analysis tool IsamDAE was created,"* says Benoît Caillaud.

Finally, and despite the end of the MODELISCALE Challenge, discussions and collaborations have continued between Inria teams, notably on two subjects: the design of modeling languages for hybrid systems, between Parkas and Hycomes, and the exploration of links between complementarity systems and multimode AED systems, between Tripop and Hycomes.