arXiv subjects

Régis Cottereau

Publications and source records attributed to Régis Cottereau.

8 recordsLinked to original sources

arXiv2026

Fast 3D Diffusion for Scalable Granular Media Synthesis

Discrete Element Method (DEM) simulations of granular media are computationally intensive, particularly during initialization phases dominated by large displacements and kinetic energy. This paper presents a novel generative pipeline based on 3D diffusion models that directly synthesizes arbitrarily large granular assemblies in mechanically realistic configurations. The approach employs a two-stage pipeline. First, an unconditional diffusion model generates independent 3D voxel grids representing granular media; second, a 3D inpainting model, adapted from 2D techniques using masked inputs and repainting strategies, seamlessly stitches these grids together. The inpainting model uses the outputs of the unconditional diffusion model to learn from the context of adjacent generations and creates new regions that blend smoothly into the context region. Both models are trained on binarized 3D occupancy grids derived from a database of small-scale DEM simulations, scaling linearly with the number of output voxels. Simulations that spanned over days can now run in hours, practically enabling simulations containing more than 200k ballast particles. The pipeline remains fully compatible with existing DEM workflows as it post-processes the diffusion generated voxel grids into DEM compatible particle meshes. Being mechanically consistent on key granulometry metrics with the original DEM simulations, the pipeline is also compatible with many other applications in the field of granular media, with capability of generating both convex and non-convex particles. Showcased on two examples (railway ballast and lunar regolith), the pipeline reimagines the way initialization of granular media simulations is performed, enabling scales of generation previously unattainable with traditional DEM simulations.

cs.LG↗

arXiv2024

Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend

We study the amount of backscattering of Valley Hall modes in a classical topological insulator. In reciprocal systems, the conservation of the valley index has been argued to be at the root of the high-transmission of Valley Hall modes, observed in many experimental realisations. Here, we reconsider this hypothesis by quantitatively analysing the canonical scattering problem of interface Valley Hall modes impinging on sharp bends which may or may not conserve the valley index. We consider a tight binding model of graphene ribbons with an interface and compute the reflection and transmission coefficients using a transfer matrix formalism. We find that, in all configurations considered, the transmission of Valley Hall modes is close to being maximal, even in cases where the valley index is not conserved. Hence there appears to be no correlation between valley conservation and good transmission. Our results serve as a reference case for the design of Valley Hall type metamaterial.

cond-mat.mes-hall↗

arXiv2023

Multi-level Neural Networks for Accurate Solutions of Boundary-Value Problems

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy, classical discretization methods such as the finite element methods, remains a significant challenge. Deep learning methods usually struggle to reliably decrease the error in their approximate solution. A new methodology to better control the error for deep learning methods is presented here. The main idea consists in computing an initial approximation to the problem using a simple neural network and in estimating, in an iterative manner, a correction by solving the problem for the residual error with a new network of increasing complexity. This sequential reduction of the residual of the partial differential equation allows one to decrease the solution error, which, in some cases, can be reduced to machine precision. The underlying explanation is that the method is able to capture at each level smaller scales of the solution using a new network. Numerical examples in 1D and 2D are presented to demonstrate the effectiveness of the proposed approach. This approach applies not only to physics informed neural networks but to other neural network solvers based on weak or strong formulations of the residual.

math.NA↗

arXiv2023

Weak localization in radiative transfer of acoustic waves in a randomly-fluctuating slab

This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating slab (between two parallel planes) in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the Wigner transform of the wave solution. These radiative transfer equations allow to model the transport of wave energy density, taking into account the scattering by random heterogeneities. The approach builds on the method of images, where the slab is extended to a full-space, with a periodic map of mechanical properties and a series of sources located along a periodic pattern. Two types of boundary effects, both on the (small) scale of the wavelength, are observed: one at the boundaries of the slab, and one inside the domain. The former impact the entire energy density (coherent as well as incoherent) and is also observed in half-spaces. The latter, more specific to slabs, corresponds to the constructive interference of waves that have reflected at least twice on the boundaries of the slab and only impacts the coherent part of the energy density.

math.AP↗

arXiv2023

Operator approximation of the wave equation based on deep learning of Green's function

Deep operator networks (DeepONets) have demonstrated their capability of approximating nonlinear operators for initial- and boundary-value problems. One attractive feature of DeepONets is their versatility since they do not rely on prior knowledge about the solution structure of a problem and can thus be directly applied to a large class of problems. However, convergence in identifying the parameters of the networks may sometimes be slow. In order to improve on DeepONets for approximating the wave equation, we introduce the Green operator networks (GreenONets), which use the representation of the exact solution to the homogeneous wave equation in term of the Green's function. The performance of GreenONets and DeepONets is compared on a series of numerical experiments for homogeneous and heterogeneous media in one and two dimensions.

math.NA↗

arXiv2022

Crossover Between Quantum and Classical Waves and High Frequency Localization Landscapes

Anderson localization is a universal interference phenomenon occurring when a wave evolves through a random medium and it has been observed in a great variety of physical systems, either quantum or classical. The recently developed localization landscape theory offers a computationally affordable way to obtain useful information on the localized modes, such as their location or size. Here we examine this theory in the context of classical waves exhibiting high frequency localization and for which the original localization landscape approach is no longer informative. Using a Webster's transformation, we convert a classical wave equation into a Schrödinger equation with the same localization properties. We then compute an adapted localization landscape to retrieve information on the original classical system. This work offers an affordable way to access key information on high-frequency mode localization.

cond-mat.dis-nn↗

arXiv2015

On damping created by heterogeneous yielding in the numerical analysis of nonlinear reinforced concrete frame elements

In the dynamic analysis of structural engineering systems, it is common practice to introduce damping models to reproduce experimentally observed features. These models, for instance Rayleigh damping, account for the damping sources in the system altogether and often lack physical basis. We report on an alternative path for reproducing damping coming from material nonlinear response through the consideration of the heterogeneous character of material mechanical properties. The parameterization of that heterogeneity is performed through a stochastic model. It is shown that such a variability creates the patterns in the concrete cyclic response that are classically regarded as source of damping.

cs.CE↗

arXiv2014

Kinetic modeling of multiple scattering of elastic waves in heterogeneous anisotropic media

In this paper we develop a multiple scattering model for elastic waves in random anisotropic media. It relies on a kinetic approach of wave propagation phenomena pertaining to the situation whereby the wavelength is comparable to the correlation length of the weak random inhomogeneities--the so-called weak coupling limit. The waves are described in terms of their associated energy densities in the phase space position x wave vector. They satisfy radiative transfer equations in this scaling, characterized by collision operators depending on the correlation structure of the heterogeneities. The derivation is based on a multi-scale asymptotic analysis using spatio-temporal Wigner transforms and their interpretation in terms of semiclassical operators, along the same lines as Bal [Wave Motion 43, 132-157 (2005)]. The model accounts for all possible polarizations of waves in anisotropic elastic media and their interactions, as well as for the degeneracy directions of propagation when two phase speeds possibly coincide. Thus it embodies isotropic elasticity which was considered in several previous publications. Some particular anisotropic cases of engineering interest are derived in detail.

math-ph↗