arXiv subjects

Stéphane P. A. Bordas

Publications and source records attributed to Stéphane P. A. Bordas.

At least 19 recordsLinked to original sources

arXiv2026

A structure-preserving discretisation of SO(3)-rotation fields for finite Cosserat micropolar elasticity

We introduce a new method, dubbed Geometric Structure-Preserving Interpolation ($Γ$-SPIN) to preserve physics-constraints inherent in the material parameter limits of the finite-strain Cosserat micropolar model. The method advocates to interpolate the Cosserat rotation tensor using geodesic elements, which maintain objectivity and correctly represent curvature measures. At the same time, it proposes relaxing the interaction between the rotation tensor and the deformation tensor to alleviate locking effects. This relaxation is achieved in two steps. First, the regularity of the Cosserat rotation tensor is reduced by interpolating it into the Nédélec space. Second, the resulting field is projected back onto the Lie-group of rotations. Together, these steps define a lower-regularity projection-based interpolation. The construction allows the discrete Cosserat rotation tensor to match the polar part of the discrete deformation tensor. This ensures stable behaviour in the asymptotic regime as the Cosserat couple modulus tends to infinity, which constrains the model towards its couple-stress limit. We establish the consistency, stability, and optimality of the proposed method through several benchmark problems. The study culminates in a demonstration of its efficacy on a more intricate curved domain, contrasted with outcomes obtained from conventional interpolation techniques.

math.NA↗

arXiv2026

Cosserat micropolar and couple-stress elasticity models of flexomagnetism at finite deformations

We propose geometrically nonlinear (finite) continuum models of flexomagnetism based on the Cosserat micropolar and its descendent couple-stress theory. These models introduce the magneto-mechanical interaction by coupling the micro-dislocation tensor of the micropolar model with the magnetisation vector using a Lifshitz invariant. In contrast to conventional formulations that couple strain-gradients to the magnetisation using fourth-order tensors, our approach relies on third-order tensor couplings by virtue of the micro-dislocation being a second-order tensor. Consequently, the models permit centrosymmetric materials with a single new flexomagnetic constant, and more generally allow cubic-symmetric materials with two such constants. We postulate the flexomagnetic action-functionals and derive the corresponding governing equations using both scalar and vectorial magnetic potential formulations, and present numerical results for a nano-beam geometry, confirming the physical plausibility and computational feasibility of the models.

cond-mat.mtrl-sci↗

arXiv2026

Structured force reformulation of many-body dispersion: towards effective atom--atom decomposition and surrogate modeling

We present a structured force reformulation of the many-body dispersion (MBD) model that enables a physically consistent decomposition of forces into pairwise components. By introducing a many-body correlation matrix that scales dipole--dipole interactions, we derive unified expressions for the MBD energy, force, and Hessian. This reformulation reveals a natural structure for effective atom--atom force decomposition and provides a promising foundation for interpretable analysis and machine learning surrogate modeling of MBD interactions.

physics.comp-ph↗

arXiv2026

Machine learning surrogate models of many-body dispersion interactions in polymer melts

Accurate prediction of many-body dispersion (MBD) interactions is essential for understanding the van der Waals forces that govern the behavior of many complex molecular systems. However, the high computational cost of MBD calculations limits their direct application in large-scale simulations. In this work, we introduce a machine learning surrogate model specifically designed to predict MBD forces in polymer melts, a system that demands accurate MBD description and offers structural advantages for machine learning approaches. Our model is based on a trimmed SchNet architecture that selectively retains the most relevant atomic connections and incorporates trainable radial basis functions for geometric encoding. We validate our surrogate model on datasets from polyethylene, polypropylene, and polyvinyl chloride melts, demonstrating high predictive accuracy and robust generalization across diverse polymer systems. In addition, the model captures key physical features, such as the characteristic decay behavior of MBD interactions, providing valuable insights for optimizing cutoff strategies. Characterized by high computational efficiency, our surrogate model enables practical incorporation of MBD effects into large-scale molecular simulations.

cs.LG↗

arXiv2025

Data-driven inverse uncertainty quantification: application to the Chemical Vapor Deposition Reactor Modeling

This study presents a Bayesian framework for (inverse) uncertainty quantification and parameter estimation in a two-step Chemical Vapor Deposition coating process using production data. We develop an XGBoost surrogate model that maps reactor setup parameters to coating thickness measurements, enabling efficient Bayesian analysis while reducing sampling costs. The methodology handles a mixture of data including continuous, discrete integer, binary, and encoded categorical variables. We establish parameter prior distributions through Bayesian Model Selection and perform Inverse Uncertainty Quantification via weighted Approximate Bayesian Computation with summary statistics, providing robust parameter credible intervals while filtering measurement noise across multiple reactor locations. Furthermore, we employ clustering methods guided by geometry embeddings to focus analysis within homogeneous production groups. This integrated approach provides a validated tool for improving industrial process control under uncertainty.

stat.OT↗

arXiv2025

Implementing NLPs in industrial process modeling: Addressing Categorical Variables

Important variables of processes are often categorical, i.e. names or labels representing, e.g. categories of inputs, or types of reactors or a sequence of steps. In this work, we use Natural Language Processing Models to derive embeddings of such inputs that represent their actual meaning, or reflect the "distances" between categories, i.e. how similar or dissimilar they are. This is a marked difference from the current standard practice of using binary, or one-hot encoding to replace categorical variables with sequences of ones and zeros. Combined with dimensionality reduction techniques, either linear such as Principal Component Analysis, or nonlinear such as Uniform Manifold Approximation and Projection, the proposed approach leads to a meaningful, low-dimensional feature space. The significance of obtaining meaningful embeddings is illustrated in the context of an industrial coating process for cutting tools that includes both numerical and categorical inputs. In this industrial process, subject matter expertise suggests that the categorical inputs are critical for determining the final outcome but this cannot be taken into account with the current state-of-the-art. The proposed approach enables feature importance which is a marked improvement compared to the current state-of-the-art in the encoding of categorical variables. The proposed approach is not limited to the case-study presented here and is suitable for applications with similar mix of categorical and numerical critical inputs.

cs.LG↗

arXiv2025

Hierarchical poromechanical approach to investigate the impact of mechanical loading on human skin micro-circulation

Research on human skin anatomy reveals its complex multi-scale, multi-phase nature, with up to 70% of its composition being bounded and free water. Fluid movement plays a key role in the skin's mechanical and biological responses, influencing its time-dependent behavior and nutrient transport. Poroelastic modeling is a promising approach for studying skin dynamics across scales by integrating multi-physics processes. This paper introduces a hierarchical two-compartment model capturing fluid distribution in the interstitium and micro-circulation. A theoretical framework is developed with a biphasic interstitium -- distinguishing interstitial fluid and non-structural cells -- and analyzed through a one-dimensional consolidation test of a column. This biphasic approach allows separate modeling of cell and fluid motion, considering their differing characteristic times. An appendix discusses extending the model to include biological exchanges like oxygen transport. Preliminary results indicate that cell viscosity introduces a second characteristic time, and at high viscosity and short time scales, cells behave similarly to solids. A simplified model was used to replicate an experimental campaign on short time scales. Local pressure (up to 31 kPa) was applied to dorsal finger skin using a laser Doppler probe PF801 (Perimed Sweden), following a setup described in Fromy Brain Res (1998). The model qualitatively captured ischemia and post-occlusive reactive hyperemia, aligning with experimental data. All numerical simulations used the open-source software FEniCSx v0.9.0. To ensure transparency and reproducibility, anonymized experimental data and finite element codes are publicly available on GitHub.

q-bio.TO↗

arXiv2025

Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids

Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-investigated problem, especially when input-output relationships are non-linear. To handle this problem, the present work introduces an innovative approach that combines autoencoder deep neural networks with the probabilistic regression capabilities of Gaussian processes. The autoencoder provides a low-dimensional representation of the solution space, while the Gaussian process is a Bayesian method that provides a probabilistic mapping between the low-dimensional inputs and outputs. We validate the proposed framework for its application to surrogate modeling of non-linear finite element simulations. Our findings highlight that the proposed framework is computationally efficient as well as accurate in predicting non-linear deformations of solid bodies subjected to external forces, all the while providing insightful uncertainty assessments.

cs.CE↗

arXiv2024

Poromechanical modelling of the time-dependent response of in vivo human skin during extension

This paper proposes a proof of concept application of a biphasic constitutive model to identify the mechanical properties of in vivo human skin under extension. Although poromechanics theory has been extensively used to model other soft biological tissues, only a few studies have been published for skin, and most have been limited to ex vivo or in silico conditions. However, in vivo procedures are crucial to determine the subject-specific properties at different body sites. This study focuses on cyclic uni-axial extension of the upper arm skin, using unpublished data collected by Chambert et al. Our analysis shows that a two-layer finite element model allows representing all relevant features of the observed mechanical response to the imposed external loading, which was composed, in this contribution, of four loading-sustaining-unloading cycles. The Root Mean Square Error (RMSE) between the calibrated model and the measured Force-time response was 8.84e-3 N. Our biphasic model represents a preliminary step toward investigating the mechanical conditions responsible for the onset of injury. It allows for the analysis of changes in Interstitial Fluid (IF) pressure, flow, and osmotic pressure, in addition to the mechanical fields. Future work will focus on the interaction of multiple biochemical factors and the complex network of regulatory signals.

q-bio.TO↗

arXiv2024

Design of thermal meta-structures made of functionally graded materials using isogeometric density-based topology optimization

The thermal conductivity of Functionally Graded Materials (FGMs) can be efficiently designed through topology optimization to obtain thermal meta-structures that actively steer the heat flow. Compared to conventional analytical design methods, topology optimization allows handling arbitrary geometries, boundary conditions and design requirements; and producing alternate designs for non-unique problems. Additionally, as far as the design of meta-structures is concerned, topology optimization does not need intuition-based coordinate transformation or the form invariance of governing equations, as in the case of transformation thermotics. We explore isogeometric density-based topology optimization in the continuous setting, which perfectly aligns with FGMs. In this formulation, the density field, geometry and solution of the governing equations are parameterized using non-uniform rational basis spline entities. Accordingly, the heat conduction problem is solved using Isogeometric Analysis. We design various 2D & 3D thermal meta-structures under different design scenarios to showcase the effectiveness and versatility of our approach. We also design thermal meta-structures based on architected cellular materials, a special class of FGMs, using their empirical material laws calculated via numerical homogenization.

cs.CE↗

arXiv2024

Intrinsic mixed-dimensional beam-shell-solid couplings in linear Cosserat continua via tangential differential calculus

We present an approach to the coupling of mixed-dimensional continua by employing the mathematically enriched linear Cosserat micropolar model. The kinematical reduction of the model to lower dimensional domains leaves its fundamental degrees of freedom intact. Consequently, the degrees of freedom intrinsically agree even at the interface with a domain of a different dimensionality. Thus, this approach circumvents the need for intermediate finite elements or mortar methods. We introduce the derivations of all models of various dimensions using tangential differential calculus. The coupling itself is then achieved by defining a mixed-dimensional action functional with consistent Sobolev trace operators. Finally, we present numerical examples involving a three-dimensional silicone-rubber block reinforced with a curved graphite shell on its lower surface, a three-dimensional silver block reinforced with a graphite plate and beams, and lastly, intersecting silver shells reinforced with graphite beams.

math.NA↗

arXiv2024

A short perspective on a posteriori error control and adaptive discretizations

Error control by means of a posteriori error estimators or indica-tors and adaptive discretizations, such as adaptive mesh refinement, have emerged in the late seventies. Since then, numerous theoretical developments and improvements have been made, as well as the first attempts to introduce them into real-life industrial applications. The present introductory chapter provides an overview of the subject, highlights some of the achievements to date and discusses possible perspectives.

math.NA↗

arXiv2024

Graph Representation Learning Strategies for Omics Data: A Case Study on Parkinson's Disease

Omics data analysis is crucial for studying complex diseases, but its high dimensionality and heterogeneity challenge classical statistical and machine learning methods. Graph neural networks have emerged as promising alternatives, yet the optimal strategies for their design and optimization in real-world biomedical challenges remain unclear. This study evaluates various graph representation learning models for case-control classification using high-throughput biological data from Parkinson's disease and control samples. We compare topologies derived from sample similarity networks and molecular interaction networks, including protein-protein and metabolite-metabolite interactions (PPI, MMI). Graph Convolutional Network (GCNs), Chebyshev spectral graph convolution (ChebyNet), and Graph Attention Network (GAT), are evaluated alongside advanced architectures like graph transformers, the graph U-net, and simpler models like multilayer perceptron (MLP). These models are systematically applied to transcriptomics and metabolomics data independently. Our comparative analysis highlights the benefits and limitations of various architectures in extracting patterns from omics data, paving the way for more accurate and interpretable models in biomedical research.

cs.LG↗

arXiv2024

Discovering deposition process regimes: leveraging unsupervised learning for process insights, surrogate modeling, and sensitivity analysis

This work introduces a comprehensive approach utilizing data-driven methods to elucidate the deposition process regimes in Chemical Vapor Deposition (CVD) reactors and the interplay of physical mechanism that dominate in each one of them. Through this work, we address three key objectives. Firstly, our methodology relies on process outcomes, derived by a detailed CFD model, to identify clusters of "outcomes" corresponding to distinct process regimes, wherein the relative influence of input variables undergoes notable shifts. This phenomenon is experimentally validated through Arrhenius plot analysis, affirming the efficacy of our approach. Secondly, we demonstrate the development of an efficient surrogate model, based on Polynomial Chaos Expansion (PCE), that maintains accuracy, facilitating streamlined computational analyses. Finally, as a result of PCE, sensitivity analysis is made possible by means of Sobol' indices, that quantify the impact of process inputs across identified regimes. The insights gained from our analysis contribute to the formulation of hypotheses regarding phenomena occurring beyond the transition regime. Notably, the significance of temperature even in the diffusion-limited regime, as evidenced by the Arrhenius plot, suggests activation of gas phase reactions at elevated temperatures. Importantly, our proposed methods yield insights that align with experimental observations and theoretical principles, aiding decision-making in process design and optimization. By circumventing the need for costly and time-consuming experiments, our approach offers a pragmatic pathway towards enhanced process efficiency. Moreover, this study underscores the potential of data-driven computational methods for innovating reactor design paradigms.

physics.chem-ph↗

arXiv2024

Integrating supervised and unsupervised learning approaches to unveil critical process inputs

This study introduces a machine learning framework tailored to large-scale industrial processes characterized by a plethora of numerical and categorical inputs. The framework aims to (i) discern critical parameters influencing the output and (ii) generate accurate out-of-sample qualitative and quantitative predictions of production outcomes. Specifically, we address the pivotal question of the significance of each input in shaping the process outcome, using an industrial Chemical Vapor Deposition (CVD) process as an example. The initial objective involves merging subject matter expertise and clustering techniques exclusively on the process output, here, coating thickness measurements at various positions in the reactor. This approach identifies groups of production runs that share similar qualitative characteristics, such as film mean thickness and standard deviation. In particular, the differences of the outcomes represented by the different clusters can be attributed to differences in specific inputs, indicating that these inputs are critical for the production outcome. Leveraging this insight, we subsequently implement supervised classification and regression methods using the identified critical process inputs. The proposed methodology proves to be valuable in scenarios with a multitude of inputs and insufficient data for the direct application of deep learning techniques, providing meaningful insights into the underlying processes.

cs.LG↗

arXiv2024

Quantum-informed simulations for mechanics of materials: DFTB+MBD framework

The macroscopic behaviors of materials are determined by interactions that occur at multiple lengths and time scales. Depending on the application, describing, predicting, and understanding these behaviors require models that rely on insights from electronic and atomic scales. In such cases, classical simplified approximations at those scales are insufficient, and quantum-based modeling is required. In this paper, we study how quantum effects can modify the mechanical properties of systems relevant to materials engineering. We base our study on a high-fidelity modeling framework that combines two computationally efficient models rooted in quantum first principles: Density Functional Tight Binding (DFTB) and many-body dispersion (MBD). The MBD model is applied to accurately describe non-covalent van der Waals interactions. Through various benchmark applications, we demonstrate the capabilities of this framework and the limitations of simplified modeling. We provide an open-source repository containing all codes, datasets, and examples presented in this work. This repository serves as a practical toolkit that we hope will support the development of future research in effective large-scale and multiscale modeling with quantum-mechanical fidelity.

cs.CE↗

arXiv2024

MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations

In many cutting-edge applications, high-fidelity computational models prove to be too slow for practical use and are therefore replaced by much faster surrogate models. Recently, deep learning techniques have increasingly been utilized to accelerate such predictions. To enable learning on large-dimensional and complex data, specific neural network architectures have been developed, including convolutional and graph neural networks. In this work, we present a novel encoder-decoder geometric deep learning framework called MAgNET, which extends the well-known convolutional neural networks to accommodate arbitrary graph-structured data. MAgNET consists of innovative Multichannel Aggregation (MAg) layers and graph pooling/unpooling layers, forming a graph U-Net architecture that is analogous to convolutional U-Nets. We demonstrate the predictive capabilities of MAgNET in surrogate modeling for non-linear finite element simulations in the mechanics of solids.

cs.LG↗

arXiv2023

A graph-based probabilistic geometric deep learning framework with online enforcement of physical constraints to predict the criticality of defects in porous materials

Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as surrogates to approximate and extrapolate the solution of such multiscale simulations. These methodologies are usually limited to 2D problems due to the high computational cost of 3D voxel based CNNs. We propose a novel geometric learning approach based on a Graph Neural Network (GNN) that efficiently deals with three-dimensional problems by performing convolutions over 2D surfaces only. Following our previous developments using pixel-based CNN, we train the GNN to automatically add local fine-scale stress corrections to an inexpensively computed coarse stress prediction in the porous structure of interest. Our method is Bayesian and generates densities of stress fields, from which credible intervals may be extracted. As a second scientific contribution, we propose to improve the extrapolation ability of our network by deploying a strategy of online physics-based corrections. Specifically, we condition the posterior predictions of our probabilistic predictions to satisfy partial equilibrium at the microscale, at the inference stage. This is done using an Ensemble Kalman algorithm, to ensure tractability of the Bayesian conditioning operation. We show that this innovative methodology allows us to alleviate the effect of undesirable biases observed in the outputs of the uncorrected GNN, and improves the accuracy of the predictions in general.

cs.CE↗