Publications

A deep geological repository for radioactive waste, such as Andra’s Cigéo project, requires long-term (persistent) monitoring. To achieve this goal, data from a network of sensors are acquired. This network is subject to deterioration over time due to environmental effects (radioactivity, mechanical deterioration of the cell, etc.), and it is paramount to assess each sensor’s integrity and ensure data consistency to enable the precise monitoring of the facilities. Graph neural networks (GNNs) are suitable for detecting faulty sensors in complex networks because they accurately depict physical phenomena that occur in a system and take the sensor network’s local structure into consideration in the predictions. In this work, we leveraged the availability of the experimental data acquired in Andra’s Underground Research Laboratory (URL) to train a graph neural network for the assessment of data integrity. The experiment considered in this work emulated the thermal loading of a high-level waste (HLW) demonstrator cell (i.e., the heating of the containment cell by nuclear waste). Using real experiment data acquired in Andra’s URL in a deep geological layer was one of the novelties of this work. The used model was a GNN that inputted the temperature field from the sensors (at the current and past steps) and returned the state of each individual sensor, i.e., faulty or not. The other novelty of this work lay in the application of the GraphSAGE model which was modified with elements of the Graph Net framework to detect faulty sensors, with up to half of the sensors in the network being faulty at once. This proportion of faulty sensors was explained by the use of distributed sensors (optic fiber) and the environmental effects on the cell. The GNNs trained on the experimental data were ultimately compared against other standard classification methods (thresholding, artificial neural networks, etc.), which demonstrated their effectiveness in the assessment of data integrity.

Resolving Partial Differential Equations (PDEs) through numerical discretization methods like the Finite Element Method presents persistent challenges associated with computational complexity, despite achieving a satisfactory solution approximation. To surmount these computational hurdles, interpolation techniques are employed to precompute models offline, facilitating rapid online solutions within a metamodel. Probability distribution frameworks play a crucial role in data modeling across various fields such as physics, statistics, and machine learning. Optimal Transport (OT) has emerged as a robust approach for probability distribution interpolation due to its ability to account for spatial dependencies and continuity. However, interpolating in high-dimensional spaces encounters challenges stemming from the curse of dimensionality. The article offers insights into the application of OT, addressing associated challenges and proposing a novel methodology. This approach utilizes the distinctive arrangement of an ANOVA-based sampling to interpolate between more than two distributions using a step-by-step matching algorithm. Subsequently, the ANOVA-PGD method is employed to construct the metamodel, providing a comprehensive solution to address the complexities inherent in distribution interpolation.

The human brain is arguably the most complex “machine” to ever exist. Its detailed functioning is yet to be fully understood, let alone modelled. Neurological processes have logical signal-processing and biophysical aspects, and both affect the brain’s structure, functioning and adaptation. Mathematical approaches based on both information and graph theory have been extensively used in an attempt to approximate its biological functioning, along with Artificial Intelligence frameworks inspired by its logical functioning. In this article, an approach to model some aspects of the brain learning and signal processing is presented, mimicking the metastability and backpropagation found in the real brain while also accounting for neuroplasticity. Several simulations are carried out with this model to demonstrate how dynamic neuroplasticity, neural inhibition and neuron migration can reshape the brain’s logical connectivity to synchronise signal processing and obtain certain target latencies. This work showcases the importance of dynamic logical and biophysical remodelling in brain plasticity. Combining mathematical (agents, graph theory, topology and backpropagation) and biomedical ingredients (metastability, neuroplasticity and migration), these preliminary results prove complex brain phenomena can be reproduced—under pertinent simplifications—via affordable computations, which can be construed as a starting point for more ambitiously accurate simulations.

Machine learning approaches are currently used to understand or model complex physical systems. In general, a substantial number of samples must be collected to create a model with reliable results. However, collecting numerous data is often relatively time-consuming or expensive. Moreover, the problems of industrial interest tend to be more and more complex, and depend on a high number of parameters. High-dimensional problems intrinsically involve the need for large amounts of data through the curse of dimensionality. That is why new approaches based on smart sampling techniques have been investigated to minimize the number of samples to be given to train the model, such as active learning methods. Here, we propose a technique based on a combination of the Fisher information matrix and sparse proper generalized decomposition that enables the definition of a new active learning informativeness criterion in high dimensions. We provide examples proving the performances of this technique on a theoretical 5D polynomial function and on an industrial crash simulation application. The results prove that the proposed strategy outperforms the usual ones.

The aim of this article is to extend Moulinec and Suquet (1998)’s FFT-based method for heterogeneous elasticity to non-periodic Dirichlet/Neumann boundary conditions. The method is based on a decomposition of the displacement into a known term verifying the boundary conditions and a fluctuation term, with no contribution on the boundary, and described by appropriate sine–cosine series. A modified auxiliary problem involving a polarization tensor is solved within a Galerkin-based method, using an approximation space spanned by sine–cosine series. The elementary integrals emerging from the weak formulation of the equilibrium are approximated by discrete sine–cosine transforms, which makes the method relying on the numerical complexity of Fourier transforms. The method is finally assessed in several problems including kinematic uniform, static uniform and arbitrary Dirichlet/Neumann boundary conditions.

Trajectory optimization is a complex process that includes an infinite number of possibilities and combinations. This work focuses on a particular aspect of the trajectory optimization, related to the optimization of a velocity along a predefined path, with the aim of minimizing power consumption. To tackle the problem, a functional formulation and minimization strategy is developed, by means of the Euler-Lagrange equation. The minimization is later performed using a neural network approach. The strategy is deemed Lagrange-Net, as it is based on the minimization of the energy functional, by the means of Lagrange's equation and neural network approximations.

In this paper, we present a general methodology that we call spectral neural network (SNN) which enables to generate automatically knowing a few datapoints (eight at most), a sound and plausible yield surface for any variations of a given anisotropic material, e.g. batches of the same material or same type of material produced by a different supplier. It relies on the use of a reliable parametrization of a performant analytic orthotropic yield function for the generation of a large database of yield surface shapes and the singular value decomposition method to create a reduced basis. For a specific material, a surrogate model for the reduced basis coordinates is further constructed using few additional datapoints. The dense neural network is built such as to ensure that the invariance requirements dictated by the material symmetry as well as the convexity of the yield surface are automatically enforced. The capabilities of this new methodology are demonstrated for hexagonal closed packed materials titanium materials, which are known to be particularly challenging to model due to their anisotropy and tension–compression asymmetry. Furthermore, we show that the SNN methodology can be extended such as to include variations of multiple materials of vastly different plastic behavior and yield surface shapes. The in-depth analysis presented reveals the benefits and limits of the hybrid data-driven models for description of anisotropic plasticity.

This study presents a comparative analysis of different kinetic models applied to the thermochemical pyrolysis of palm empty fruit bunch (PEFB). The kinetic parameters, particularly the activation energy, are determined through thermogravimetric analysis (TGA) of samples that underwent heating rates ranging from 10 to 50 ◦C/min. Image analysis of PEFB in a hot-stage microscope reveals an intriguing correlation between the observed shrinkage and the conversion rate (α) and indicates that significant physical and chemical transformations occurred within α between 0.2 and 0.8. The experimental data from TGA demonstrates good alignment with four distinct kinetic models. The Coast-Redfern model gives activation energies ranging from 60 to 134 kJ/mol for α between 0.2 and 0.8. In contrast, the Kissinger model and the isoconversion models, Kissinger-Akahira-Sunose and Ozawa-Flyn-Wall, show higher activation energy of 151, 156, and 157 kJ/mol, respectively. The findings underscore the significant impact of the selected kinetic model on determining kinetic parameters.

Carbon–carbon (C–C) composites are highly sought-after in aviation, automotive, and defense sectors due to their outstanding thermal and thermo-mechanical properties. These composites are highly valued for their exceptional thermal and thermo-mechanical properties, including remarkably low density and coefficient of thermal expansion, which are expected to surpass those of many alloys and other composites in the production of high-grade components. However, the current manufacturing methods for C–C composites are unable to meet market demands due to their high cost, low production speed, and labor-intensive processes, limiting their broader applications. This study presents an innovative approach by introducing a new extrusion-based 3D printing method using multiphase direct ink writing (MDIW) for C–C composite fabrication. The primary matrix utilized is a phenol-formaldehyde thermosetting resin, reinforced with silicon carbide (SiC) and graphite nanopowder (Gnp), focusing on achieving simple, scalable, and environmentally sustainable production of green parts with enhanced polymer matrix. This is followed by an inert carbonization process to obtain the final C–C composites. The research emphasizes the careful optimization of curing and rheological properties, including the use of suitable viscosity modifiers like carbon black (CB). Furthermore, the MDIW process demonstrates its capability to pattern dual nanoparticles within the composite structure in a well-ordered manner, leading to improved overall performance. Thermo-mechanical and thermo-electrical properties were thoroughly tested, showcasing the multifunctionality of the composite for diverse applications, from high-value industries like aerospace to broader uses such as heatsinks and electronic packaging.

Coal, a crucial natural resource traditionally employed for generating carbonrich materials and powering global industries, has faced escalating scrutiny due to its adverse environmental impacts outweighing its utility in the contemporary world. In response to the worldwide shift toward sustainability, the United States alone has witnessed an approximate 50% reduction in coal consumption. Nevertheless, the ample availability of coal has spurredinterest in identifying alternative sustainable applications. This research delves into the feasibility of utilizing coal as a nonconventional carbon-rich reinforcement in direct ink writing (DIW)-based 3D printing techniques. Our investigation here involves a thermosetting resin serving as a matrix, incorporating pulverized coal (250 μm in size) and carbon black as the reinforcement and a viscosity modifier, respectively. The ink formulation is meticulously designed to exhibit shear-thinning behavior essential for DIW 3D printing, ensuring uniform and continuous printing. Mechanical properties are assessed through the 3D printing of ASTM standard specimens to validate the reinforcing impact. Remarkably, the study reveals that a 2 wt % coal concentration in the ink leads to a substantial improvement in both tensile and flexural properties, resulting in enhancements of 35 and 12.5%, respectively. Additionally, the research demonstrates the printability of various geometries with coal as reinforcement, opening up new possibilities for coal utilization while pursuing more sustainable manufacturing and applications.