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Reference : UMR9015-LIOMAT-001
Workplace : ST AUBIN
Date of publication : Tuesday, September 28, 2021
Scientific Responsible name : Lionel Mathelin
Type of Contract : PhD Student contract / Thesis offer
Contract Period : 36 months
Start date of the thesis : 1 November 2021
Proportion of work : Full time
Remuneration : 2 135,00 € gross monthly
Description of the thesis topic
This thesis is part of a trans-disciplinary research project toward inference and prediction of complex physical systems. Such systems are often ineffectively described by first principles models and should be modeled via a data-driven approach. However, difficulties arise from the high dimensional and multi-scale nature of these systems. Further, only limited and poorly informative observations are typically available.
The thesis will revisit every aspect of deep learning, in view of the additional information stemming from expertise knowledge upon the physical system at hand. For instance, this information can take the form of constraints, usually derived from Physics first principles (invariant quantities, symmetries, bounds, asymptotic behavior, stability, etc).
The aim of this research effort is to infer models more robust and less data hungry thanks to Physics-based constraints, inspect the behavior of the resulting models, provide prediction guarantees, and relate Physics and computational regularities in order to improve the model understanding and assessment.
The thesis will more specifically focus on an active approach to deep learning a model for a Physics-driven system. Two crucial aspects of the learning procedure will be particularly addressed:
- a carefully designed dataset, tailored to the particular objective at hand, since it has a dramatic impact upon the quality of the resulting model it allows to derive. The student will hence be involved in assessing the potential of information theory criteria to qualify the relevance of the training set, and to develop an adaptive Design of Experiment strategy (aDoE) to improve the quantity of information one can extract from the system for a given budget of observations.
- an optimal model structure. Indeed, adapting the dataset should go together with finding a good structure for the model. The PhD student will focus on deriving refinement criteria of the structure based on the functional gradients and will leverage on an adjoint-based a posteriori refinement framework.
The PhD candidate will be hosted at LISN (Laboratoire Interdisciplinaire des Sciences du Numérique). He/She will be advised by members of the Decipher team, together with advisors from the Tau INRIA team. He/She will also benefit from interactions with other PhD students in the group.
If allowed by sanitary conditions, conferences and visits to research teams abroad are planned.
Main advisors: G. Charpiat (INRIA Saclay), L. Mathelin (LISN-CNRS), O. Semeraro (LISN-CNRS)
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