ATLANTIS is a joint project-team between Inria, CNRS and Université Côte d'Azur thanks to its association with the J.A. Dieudonné Mathematics Laboratory (UMR 7351). Our research activities aim at the design, analysis, development and application of advanced computational techniques for systems of partial differential equations (PDEs) modeling nanoscale light-matter interaction problems. The corresponding science, referred to as nanophotonics, aims at exploiting nanoscale light-matter interactions to achieve an unprecedented level of control on light. Nanophotonics encompasses a wide variety of topics including metamaterials, plasmonics, high resolution imaging, quantum nanophotonics and functional photonic materials. We study concrete questions and applications that are linked to specific physical fields that we consider in close collaboration with physicists. From the numerical modeling point of view, the underlying physical processes raise a number of challenges: they exhibit multiple space and time scales; they are highly sensitive to exquisite geometrical features of nanostructures and matter nanostructuring; they impose dealing with unconventional material models; they may require to leave the comfortable setting of linear differential models; some of them are inherently multiphysics processes. In order to address these challenges, our research agenda is organized around topics in relation with the numerical treatment of the considered PDE systems: (1) high-fidelity numerical modeling with various formulations of the Discontinuous Galerkin (DG) method; (2) reduced-order modeling with reduced basis methods or neural networks or a combination of them; (3) inverse design strategies with statistical learning-based global optimization methods; (3) data-driven or model-driven modeling with neural networks; (4) In some cases, the associated methodological contributions are implemented in the DIOGENeS software suite, which is dedicated to computational nanophotonics. DIOGENeS is at the heart of our contributions to most of our collaborative projects with physicists from academic labs or research engineers from companies or industrial groups.
