PhD Position F/M: Investigating Multilevel Distributed Strategies for Physics-Based Deep Learning Models

il y a 4 semaines


Technopole de Sophia Antipolis, France INRIA Temps plein
Job Description

Context and Key Objectives

The development of cost-effective surrogate models is crucial for numerical simulations of electromagnetic wave propagation problems. These simulations rely on space discretization of Maxwell's equations using methods such as finite differences or finite elements. However, for complex and realistic three-dimensional situations, this process can be computationally prohibitive, especially when the end goal consists in many-query analyses.

Recent years have seen the emergence of approaches based on neural networks (NNs) and Deep Learning (DL) for building surrogate models in a non-intrusive way. Model-based neural networks, as opposed to purely data-driven neural networks, are currently the subject of intense research for devising high-performance surrogate models of parametric partial differential equations (PDEs).

Research Objectives

  • Study the development of multilevel distributed strategies for fast training of physics-based DNNs for modeling electromagnetic wave propagation in the frequency domain.
  • Investigate strategies that can accurately and efficiently deal with the simulation of electromagnetic wave interaction with heterogeneous media and geometrically complex scattering structures.
  • Develop high-performance parametric NN surrogates that will be used as the forward model in inverse design studies.

Key Responsibilities

  • Conduct a bibliographical study for a review of physics-based DNNs for wave propagation type models and strategies for designing multilevel and distributed physics-based DNNs.
  • Study in 2D case by considering wave propagation modeled by a Helmholtz-type PDE.
  • Study in the 3D case for dealing with the system of frequency-domain Maxwell equations.
  • Software development activities.
  • Numerical assessment of the proposed NN-based physics-based multilevel surrogate models.
  • Publications.

Requirements

  • Sound knowledge of numerical analysis for PDEs.
  • Sound knowledge of Machine Learning / Deep Learning with Artificial Neural Networks.
  • Basic knowledge of physics of electromagnetic wave propagation.
  • Software development skills: Python programming, TensorFlow, PyTorch.
  • Relational skills: team worker (verbal communication, active listening, motivation and commitment).
  • Good level of spoken and written English.


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