Autoregressive Transformers for Data-Driven Spatio-Temporal Learning of Turbulent Flows

A convolutional encoder-decoder-based transformer model has been developed to autoregressively train on spatio-temporal data of turbulent flows. It works by predicting future fluid flow fields from the previously predicted fluid flow field to ensure long-term predictions without diverging. The model exhibits significant agreements for \textit{a priori} assessments, and the \textit{a posterior} predictions, after a considerable number of simulation steps, exhibit predicted variances. Autoregressive training and prediction of \textit{a posteriori} states is the primary step towards the development of more complex data-driven turbulence models and simulations

Efficient time‐domain numerical analysis of waveguides with tailored wideband pulses

International audienceA simple procedure for the generation of accurate polychromatic sources in waveguides taking into account mode dispersion is presented. It allows for an efficient use of time‐domain solvers in the analysis of guided modes, and can be used whether the mode dispersion and field distribution are known analytically or numerically. This method is implemented in the Diogenes discontinuous Galerkin time‐domain (DGTD) solver (http://diogenes.inria.fr), and is validated on a waveguide mode converter

Simulation de la propagation d'ondes électromagnétiques en nano-optique par une méthode Galerkine discontinue d'ordre élevé

The goal of this thesis is to develop a discontinuous Galerkin time-domain method to be able to handle realistic nanophotonics computations. During the last decades, the evolution of lithography techniques allowed the creation of geometrical structures at the nanometer scale, thus unveiling a variety of new phenomena arising from light-matter interactions at such levels. These effects usually occur when the device is of comparable size or (much) smaller than the wavelength of the incident field. This work relies on the development and implementation of appropriate models for dispersive materials (mostly metals), as well as on a large panel of classical computational techniques. Two major methodological developments are presented and studied in details: (i) curvilinear elements, and (ii) local order of approximation. This work is complemented with several physical studies of real-life nanophotonics applications.L’objectif de cette thèse est de développer une méthode Galerkine discontinue d’ordre élevé capable de prendre en considération des simulations réalistes liées à la nanophotonique. Au cours des dernières décennies, l’évolution des techniques de lithographie a permis la création de structure géométriques de tailles nanométriques, révélant ainsi une large gamme de phénomènes nouveaux nés de l’interaction lumière-matière à ces échelles. Ces effets apparaissent généralement pour des objets de taille égale ou (très) inférieure à la longueur d’onde du champ incident. Ce travail repose sur le développement et l’implémentation de modèles de dispersion appropriés (principalement pour les métaux), ainsi que sur un large éventail de méthodes computationnelles classiques. Deux développements méthodologiques majeurs sont présentés et étudiés en détails: (i) les éléments courbes, et (ii) l’ordre d’approximation local. Ces études sont accompagnées de plusieurs cas-tests réalistes tirés de la nanophotonique

Efficient time-domain numerical analysis of waveguides with tailored wideband pulses

A simple procedure for the generation of accurate polychromatic sources in waveguides taking into account mode dispersion is presented. It allows for an efficient use of time-domain solvers in the analysis of guided modes, and can be used wether the mode dispersion and field distribution are known analytically or numerically. This method is implemented in the DIOGENES Discontinuous Galerkin Time-Domain (DGTD) solver (http://diogenes.inria.fr), and is validated on a waveguide mode converter

A review on deep reinforcement learning for fluid mechanics: an update

In the past couple of years, the interest of the fluid mechanics community for deep reinforcement learning (DRL) techniques has increased at fast pace, leading to a growing bibliography on the topic. While the capabilities of DRL to solve complex decision-making problems make it a valuable tool for active flow control, recent publications also demonstrated applications to other fields, such as shape optimization or microfluidics. The present work aims at proposing an exhaustive review of the existing literature, and is a follow-up to our previous review on the topic. The contributions are regrouped by field of application, and are compared together regarding algorithmic and technical choices, such as state selection, reward design, time granularity, and more. Based on these comparisons, general conclusions are drawn regarding the current state-of-the-art in the domain, and perspectives for future improvements are sketched

Curvilinear DGTD method for nanophotonics applications

International audienceClassical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element, on domains which physical boundaries are indifferently straight or curved. This approximation represents serious hindrance for high-order methods, since they limit the precision of the spatial discretization to second order. Thus, exploiting an enhanced representation of the physical geometry of a considered problem is in agreement with the natural procedure of high-order methods, such as the discontinuous Galerkin method. In the latter framework, we propose and validate an implementation of a high-order mapping for tetrahedra, and then focus on specific nanophotonics setups to assess the gains of the method in terms of memory and performances

A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects

The interaction of light with metallic nanostructures is of increasing interest for various fields of research. When metallic structures have sub-wavelength sizes and the illuminating frequencies are in the regime of metal's plasma frequency, electron interaction with the exciting fields have to be taken into account. Due to these interactions, plasmonic surface waves can be excited and cause extreme local field enhancements (e.g. surface plasmon polariton electromagnetic waves). Exploiting such field enhancements in applications of interest requires a detailed knowledge about the occurring fields which can generally not be obtained analytically. For the latter mentioned reason, numerical tools as well as a deeper understanding of the underlying physics, are absolutely necessary. For the numerical modeling of light/structure interaction on the nanoscale, the choice of an appropriate material model is a crucial point. Approaches that are adopted in a first instance are based on local (i.e. with no interaction between electrons) dispersive models e.g. Drude or Drude-Lorentz models. From the mathematical point of view, when a time-domain modeling is considered, these models lead to an additional system of ordinary differential equation which is coupled to Maxwell's equations. When it comes to very small structures in a regime of 2~nm to 25~nm, non-local effects due to electron collisions have to be taken into account. Non-locality leads to additional, in general non-linear, system of partial differential equations and is significantly more difficult to treat, though. Nevertheless, dealing with a linear non-local dispersion model is already a setting that opens the route to numerous practical applications of plasmonics. In this work, we present a Discontinuous Galerkin Time-Domain (DGTD) method able to solve the system of Maxwell equations coupled to a linearized non-local dispersion model relevant to plasmonics. While the method is presented in the general 3d case, numerical results are given for 2d simulation settings only

Simulation of near-field plasmonic interactions with a local approximation order discontinuous Galerkin time-domain method

International audienceDuring the last ten years, the discontinuous Galerkin time-domain (DGTD) method has progressively emerged as a viable alternative to well established finite-difference time-domain (FDTD) and finite-element time-domain (FETD) methods for the numerical simulation of electromagnetic wave propagation problems in the time-domain. The method is now actively studied for various application contexts including those requiring to model light/matter interactions on the nanoscale. In this paper we further demonstrate the capabilities of the method for the simulation of near-field plasmonic interactions by considering more particularly the possibility of combining the use of a locally refined conforming tetrahedral mesh with a local adaptation of the approximation order

Analysis of a Generalized Dispersive Model Coupled to a DGTD Method with Application to Nanophotonics

International audienceIn this paper, we are concerned with the numerical modelling of the propagation of electromagnetic waves in dispersive materials for nanophotonics applications. We focus on a generalized model that allows for the description of a wide range of dispersive media. The underlying differential equations are recast into a generic form, and we establish an existence and uniqueness result. We then turn to the numerical treatment and propose an appropriate discontinuous Galerkin time domain framework. We obtain the semidiscrete convergence and prove the stability (and to a larger extent, convergence) of a Runge--Kutta 4 fully discrete scheme via a technique relying on energy principles. Finally, we validate our approach through two significant nanophotonics test cases