PhD Position (Fully Funded)

Title: Coverage Measures for Machine Learning Enabled Cyber-Physical Systems

Supervisors: Thao Dang, CNRS, Verimag. Alexandre Donzé, Decyphir SAS.

Location: Université Grenoble Alpes (UGA), Verimag Laboratory, Saint Martin d’Hères and Decyphir SAS, Moirans.


Cyber Physical Systems (CPS) are systems mixing software and hardware (cyber) components in interaction with their (physical) environment. Typical examples include (semi-)autonomous cars, robots, medical devices. Mathematically, they are modelled with so-called hybrid systems, which are dynamical systems with multiple modes, which can be continuous or discrete in nature. Since the modelisation includes the physical/biological environment, the models can be of arbitrary complexity, from trivial (not all models need be complex to be useful) to untractable for nowadays computational resources due to the infiniteness of input and state spaces of these systems. Hence new methods and tools are always needed to manage and handle the type of heterogeneous computations and data generated by the analysis and design of hybrid systems.

In this thesis, we want to tackle this issue from the angle of coverage measures. Given a CPS problem and some data and/or models (e.g., a hybrid system) associated to it, the question is: what is the mathematical domain that can represent all possible data that can be observed, and can we measure how well the given data represent this domain? This question is of primordial theoretical and practical interest in many contexts. One popular contemporaneous instance is that of machine learning (ML). It is well-known that ML-based algorithms, which are more and more used for CPS design, are only as good as the data used to train them. However it is much less well understood how to formally define the “goodness” of the data at our disposal. Hence there is a need for meaningful measures that can be computed and used not only to quantify the quality of a set, but also to fix it by, e.g., shrinking or augmenting it to better represent a domain to learn.

The questions of coverage, sampling, data augmentation, ML, CPS, etc are not new and topics that have attracted a lot of interest recently. The originality of this thesis will be to tackle these problems from the perspective of hybrid systems and formal methods, which are two research directions in which Verimag and Decyphir are specialized into and internationally recognized for. The intrinsic hybrid nature of data and systems considered in machine learning for CPS is often overlooked and we believed there is a need to study it in a more systematic and explicit way. Formal methods makes it possible to derive more rigorous guarantees and the hope is also that through the use of specification languages such as, e.g., Signal Temporal Logics (STL), they can help in the development of “explainable” measures, i.e., measures that are directly related to precisely formulated requirements as opposed to some hard to interpret mean squared error quantity as is the most frequent practice.



The thesis is fully funded for three years by a grant from region Auvergne-Rhône-Alpes starting in 2022. We are looking for candidates with a master degree in computer science or control engineering interested in CPS, artificial intelligence and machine learning. The thesis is expected to feature a strong experimental and development component but opportunities to developping theoretical contributions will also be likely. As a consequence, candidates with both theoretical and practical inclinations are welcome to apply.

Send applications (resume and motivation letter) to thao dot dang at univ-grenoble-alpes dot fr and alex at decyphir dot com