A new adaptive local polynomial density estimation procedure on complicated domains

This paper presents a novel approach for pointwise estimation of multivariate density functions on known domains of arbitrary dimensions using nonparametric local polynomial estimators. Our method is highly flexible, as it applies to both simple domains, such as open connected sets, and more complicated domains that are not star-shaped around the point of estimation. This enables us to handle domains with sharp concavities, holes, and local pinches, such as polynomial sectors. Additionally, we introduce a data-driven selection rule based on the general ideas of Goldenshluger and Lepski. Our results demonstrate that the local polynomial estimators are minimax under a $L^2$ risk across a wide range of H\"older-type functional classes. In the adaptive case, we provide oracle inequalities and explicitly determine the convergence rate of our statistical procedure. Simulations on polynomial sectors show that our oracle estimates outperform those of the most popular alternative method, found in the sparr package for the R software. Our statistical procedure is implemented in an online R package which is readily accessible.Comment: 35 pages, 4 figure

Microscopic theory for the rheology of jammed soft suspensions

We develop a constitutive model allowing for the description of the rheology of two-dimensional soft dense suspensions above jamming. Starting from a statistical description of the particle dynamics, we derive, using a set of approximations, a non-linear tensorial evolution equation linking the deviatoric part of the stress tensor to the strain-rate and vorticity tensors. The coefficients appearing in this equation can be expressed in terms of the packing fraction and of particle-level parameters. This constitutive equation rooted in the microscopic dynamic qualitatively reproduces a number of salient features of the rheology of jammed soft suspensions, including the presence of yield stresses for the shear component of the stress and for the normal stress difference. More complex protocols like the relaxation after a preshear are also considered, showing a smaller stress after relaxation for a stronger preshear.Comment: 5 pages, 1 figur

Learning dislocation dynamics mobility laws from large-scale MD simulations

The computational method of discrete dislocation dynamics (DDD), used as a coarse-grained model of true atomistic dynamics of lattice dislocations, has become of powerful tool to study metal plasticity arising from the collective behavior of dislocations. As a mesoscale approach, motion of dislocations in the DDD model is prescribed via the mobility law; a function which specifies how dislocation lines should respond to the driving force. However, the development of traditional hand-crafted mobility laws can be a cumbersome task and may involve detrimental simplifications. Here we introduce a machine-learning (ML) framework to streamline the development of data-driven mobility laws which are modeled as graph neural networks (GNN) trained on large-scale Molecular Dynamics (MD) simulations of crystal plasticity. We illustrate our approach on BCC tungsten and demonstrate that our GNN mobility implemented in large-scale DDD simulations accurately reproduces the challenging tension/compression asymmetry observed in ground-truth MD simulations while correctly predicting the flow stress at lower straining rate conditions unseen during training, thereby demonstrating the ability of our method to learn relevant dislocation physics. Our DDD+ML approach opens new promising avenues to improve fidelity of the DDD model and to incorporate more complex dislocation motion behaviors in an automated way, providing a faithful proxy for dislocation dynamics several orders of magnitude faster than ground-truth MD simulations

Minimax properties of Dirichlet kernel density estimators

This paper is concerned with the asymptotic behavior in $\beta$-H\"older spaces and under $L^p$ losses of a Dirichlet kernel density estimator proposed by Aitchison & Lauder (1985) for the analysis of compositional data. In recent work, Ouimet & Tolosana-Delgado (2022) established the uniform strong consistency and asymptotic normality of this nonparametric estimator. As a complement, it is shown here that for $p \in [1, 3)$ and $\beta \in (0, 2]$, the Aitchison--Lauder estimator can achieve the minimax rate asymptotically for a suitable choice of bandwidth, but that this estimator cannot be minimax when either $p \in [4, \infty)$ or $\beta \in (2, \infty)$. These results extend to the multivariate case, and also rectify in a minor way, earlier findings of Bertin & Klutchnikoff (2011) concerning the minimax properties of Beta kernel estimators.Comment: 15 pages, 1 figur

Prediction of optical communication link availability: real-time observation of cloud patterns using a ground-based thermal infrared camera

The growing demand for high-speed broadband communications with low orbital or geostationary satellites is a major challenge. Using an optical link at 1.55 μm is an advantageous solution which potentially can increase the satellite throughput by a factor 10. Nevertheless, cloud cover is an obstacle for this optical frequency. Such communication requires an innovative management system to optimize the optical link availability between a satellite and several Optical Ground Stations (OGS). The Saint-Exupery Technological Research Institute (France) leads the project ALBS (French acronym for BroadBand Satellite Access). This initiative involving small and medium enterprises, industrial groups and research institutions specialized in aeronautics and space industries, is currently developing various solutions to increase the telecommunication satellite bandwidth. This paper presents the development of a preliminary prediction system preventing the cloud blockage of an optical link between a satellite and a given OGS. An infrared thermal camera continuously observes (night and day) the sky vault. Cloud patterns are observed and classified several times a minute. The impact of the detected clouds on the optical beam (obstruction or not) is determined by the retrieval of the cloud optical depth at the wavelength of communication. This retrieval is based on realistic cloud-modelling on libRadtran. Then, using subsequent images, cloud speed and trajectory are estimated. Cloud blockage over an OGS can then be forecast up to 30 minutes ahead. With this information, the preparation of the new link between the satellite and another OGS under a clear sky can be prepared before the link breaks due to cloud blockage

Mapping and Describing Geospatial Data to Generalize Complex Models: The Case of LittoSIM-GEN

For some scientific questions, empirical data are essential to develop reliable simulation models. These data usually come from different sources with diverse and heterogeneous formats. The design of complex data-driven models is often shaped by the structure of the data available in research projects. Hence, applying such models to other case studies requires either to get similar data or to transform new data to fit the model inputs. It is the case of agent-based models (ABMs) that use advanced data structures such as Geographic Information Systems data. We faced this problem in the LittoSIM-GEN project when generalizing our participatory flooding model (LittoSIM) to new territories. From this experience, we provide a mapping approach to structure, describe, and automatize the integration of geospatial data into ABMs