arXiv subjects

Sebastian Rodriguez

Publications and source records attributed to Sebastian Rodriguez.

At least 19 recordsLinked to original sources

arXiv2026

A plausible Parametrization of Modal Basis for Dynamical Systems Analysis

In the field of solid dynamics, knowing the corresponding modal basis of the system is capital, in order to improve design with respect to a desired dynamical behavior, such as avoiding natural frequencies at specific values or designing mechanical systems that can account for desired frequency spectrum. However, the determination of the modal basis involve the resolution of an eigenvalue problem, which can be expensive to perform for large systems, especially when dealing with a optimization of a parametric system design. In the present work, we propose to determine the parametrization of modal basis by considering an advanced Deep Learning technique based on the Rank Reduction AutoEncoder (RRAE). The RRAE is based on an autoencoder whose latent space is constrained through a truncated Singular Value Decomposition (SVD) approximation. This formulation enables the latent space to capture the dominant features of the data efficiently. As a result, the autoencoder is guided toward learning the underlying physical behavior represented across the dataset, mitigating overfitting and spurious predictions. The main idea consists of identifying a reduced parameter space using the RRAE for the first eigenvector, while the remaining modes are subsequently reconstructed through neural networks that take the same reduced parameter space as input, thereby coupling all modes in a nonlinear parametric framework. The proposed architecture is validated through the parametrization of the modal basis in 1D and 2D problems.

cs.CE↗

arXiv2026

Physics-Informed Single Atom Convolutional Matching Pursuit: Guided-Waves Wavenumbers and Propagation Distance Estimation for Damage Localization in Structural Health Monitoring

Structural Health Monitoring (SHM) aims at the real-time monitoring of the integrity of engineering structures, with Guided-waves (GWs) providing high sensitivity to damage presence and to ageing effects for thin-walled components. In conventional GW-based SHM, a bonded piezoelectric transducer (PZT) emits a short tone burst that produces an Initial Wave Packet (IWP) propagating through the structure. As this packet interacts with boundaries and potential damages, additional scattered wave packets are produced. A major limitation of such approaches lies in the simultaneous excitation of multiple dispersive GW modes by a single PZT, which significantly complicates signal interpretation and damage monitoring. In this context, this work proposes the Physics-Informed Single Atom Convolutional Matching Pursuit (PISACMP) method, a signal decomposition method grounded in the physical principles governing wave propagation. In contrast with purely data-driven or numerically intensive techniques, the proposed approach embeds strong physical constraints into a low-dimensional and computationally efficient signal representation. This formulation enables the direct identification of key physically meaningful features, including modal wavenumber functions and propagation distances between actuator, damage and sensors. These extracted features, especially source-damage-sensor distances, allows to subsequently perform damage location using well established Elliptical Localization techniques. The principal novelty of this study lies in integrating wave propagation physics into a compact signal decomposition framework and developing an interpretable damage localization methodology for GW-SHM applications.

cs.CE↗

arXiv2026

CRADIPOR: Crash Dispersion Predictor

We present CRADIPOR, a numerical dispersion prediction tool for automotive crash simulations. Finite Element (FE) crash models are widely used throughout vehicle development, but their predictions are not strictly repeatable because of parallel computation and model complexity. As a result, performance criteria evaluated during post-processing may exhibit significant numerical dispersion, which complicates engineering decision-making. Although dispersion can be estimated by repeating the same simulation, this approach is generally impractical because of its high computational cost. This work therefore investigates a prediction tool that can be applied during routine crash-simulation post-processing without repeating the computation. The proposed approach relies on a Rank Reduction Autoencoder (RRAE) combined with supervised classification in order to identify regions sensitive to numerical dispersion. The comparative analysis suggests that the RRAE-based framework is more effective than the Random Forest baseline on the studied dataset. Among the tested signal representations, wavelet-based and slope-based inputs appear to be the most promising, with slope variations providing the best classification performance. These results support the use of structured latent representations for improving numerical-dispersion detection in automotive crash post-processing.

cs.LG↗

arXiv2026

Data-driven discovery of roughness descriptors for surface characterization and intimate contact modeling of unidirectional composite tapes

Unidirectional tapes surface roughness determines the evolution of the degree of intimate contact required for ensuring the thermoplastic molecular diffusion and the associated inter-tapes consolidation during manufacturing of composite structures. However, usual characterization of rough surfaces relies on statistical descriptors that even if they are able to represent the surface topology, they are not necessarily connected with the physics occurring at the interface during inter-tape consolidation. Thus, a key research question could be formulated as follows: Which roughness descriptors simultaneously enable tape classification-crucial for process control-and consolidation modeling via the inference of the evolution of the degree of intimate contact, itself governed by the process parameters?. For providing a valuable response, we propose a novel strategy based on the use of Rank Reduction Autoencoders (RRAEs), autoencoders with a linear latent vector space enforced by applying a truncated Singular Value Decomposition (SVD) to the latent matrix during the encoder-decoder training. In this work, we extract useful roughness descriptors by enforcing the latent SVD modes to (i) accurately represent the roughness after decoding, and (ii) allow the extraction of existing a priori knowledge such as classification or modelling properties.

cs.LG↗

arXiv2026

ADIOSS Automatic Diagnostic Of System Simulations

Automotive engineering makes extensive use of numerical simulation throughout the design process. The development of numerical models, their validation against experimental tests, and their updating during vehicle and engine projects constitute a core engineering activity. However, this activity must continuously evolve to reduce costs and lead times. In this context, we propose a method for detecting faulty modules within a system-level simulation workflow, represented as a graph of 0D models, following model updates. The proposed method requires a very limited number of system simulations and can therefore be easily integrated into existing engineering processes. It is designed as a toolbox based on well established and widely validated techniques, including Dynamic Mode Decomposition commonly used for 3D model reduction, linear programming, and autoencoders.

cs.CE↗

arXiv2026

Stress-constrained Topology Optimization for Metamaterial Microstructure Design

Although stress-constrained topology optimization has been extensively studied in structural design, the development of optimization frameworks to enable the creation of metamaterials with optimal mechanical performance is still an open problem. This study incorporates local stress constraints into the topology optimization framework for metamaterial microstructure design, aiming to avoid the stress concentration in the optimized microstructure. For the efficient solution of multi-constraint topology optimization problems, the Augmented Lagrangian formulation is extended to address local minimization problems subjected to the combined action of local and global constraints. Additionally, as an extension of static load conditions, this study further investigates the design of metamaterial microstructures under cyclic loading. Finally, the effectiveness of the proposed approach is demonstrated through a series of two-dimensional and three-dimensional benchmark problems.

cs.CE↗

arXiv2026

M-Tensor Formalism: A Non-iterative High Dimensional Least Squares Regression for Nonlinear Models with Scarce Data

We present a multilinear regression framework based on tensor algebra tailored to high-dimensional contexts where data is scarce. We exploit algebraic properties of a partial tensor product, namely the m-tensor product, to leverage structured equations with separated variables. The proposed method combines kernel properties along with tensor algebra to prevent explicit construction of the exponentially large feature space and tackle approximations up to hundreds of parameters while avoiding the fixed-point strategy. This is achieved by only ever employing the regression operator in a factorized form. We present this formalism along with different regularization techniques suited for low amount of data with a high number of parameters while preserving well-known matrix-based properties. We demonstrate complexity scaling on a general benchmark to show robustness for engineering problems and ease of implementation.

cs.CE↗

arXiv2026

Rank Reduction AutoEncoders for Mechanical Design: Advancing Novel and Efficient Data-Driven Topology Optimization

This work presents a data-driven framework for fast forward and inverse analysis in topology optimization (TO) by combining Rank Reduction Autoencoders (RRAEs) with neural latent-space mappings. The methodology targets the efficient approximation of the relationship between optimized geometries and their corresponding mechanical responses or Quantity of Interest (QoI), with a particular focus on compliance-minimized linear elastic structures. High-dimensional TO results are first compressed using RRAEs, which encode the data into a low-rank approximation via Singular Value Decomposition (SVD), obtained in this sense the most important features that approximate the data. Separate RRAE models are trained for geometry and for different types of QoIs, including scalar metrics, one-dimensional stress fields, and full two-dimensional von Mises stress distributions. The resulting low-dimensional latent coefficients of the latent space are then related through multilayer perceptrons to address both direct problems -- predicting structural responses from geometry -- and inverse problems -- recovering geometries from prescribed performance targets. The proposed approach is demonstrated on a benchmark TO problem based on a half MBB beam, using datasets generated via density-based Solid Isotropic Material with Penalization (SIMP) optimization. Numerical results show that the framework enables accurate and computationally efficient surrogate models, with increasing robustness and fidelity as richer QoIs are considered. The methodology also provides a foundation for generative mechanical design by enabling the synthesis of new geometries and responses through latent-space exploration.

math.NA↗

arXiv2025

Generative Parametric Design (GPD): A framework for real-time geometry generation and on-the-fly multiparametric approximation

This paper presents a novel paradigm in simulation-based engineering sciences by introducing a new framework called Generative Parametric Design (GPD). The GPD framework enables the generation of new designs along with their corresponding parametric solutions given as a reduced basis. To achieve this, two Rank Reduction Autoencoders (RRAEs) are employed, one for encoding and generating the design or geometry, and the other for encoding the sparse Proper Generalized Decomposition (sPGD) mode solutions. These models are linked in the latent space using regression techniques, allowing efficient transitions between design and their associated sPGD modes. By empowering design exploration and optimization, this framework also advances digital and hybrid twin development, enhancing predictive modeling and real-time decision-making in engineering applications. The developed framework is demonstrated on two-phase microstructures, in which the multiparametric solutions account for variations in two key material parameters.

cs.CE↗

arXiv2025

RRAEDy: Adaptive Latent Linearization of Nonlinear Dynamical Systems

Most existing latent-space models for dynamical systems require fixing the latent dimension in advance, they rely on complex loss balancing to approximate linear dynamics, and they don't regularize the latent variables. We introduce RRAEDy, a model that removes these limitations by discovering the appropriate latent dimension, while enforcing both regularized and linearized dynamics in the latent space. Built upon Rank-Reduction Autoencoders (RRAEs), RRAEDy automatically rank and prune latent variables through their singular values while learning a latent Dynamic Mode Decomposition (DMD) operator that governs their temporal progression. This structure-free yet linearly constrained formulation enables the model to learn stable and low-dimensional dynamics without auxiliary losses or manual tuning. We provide theoretical analysis demonstrating the stability of the learned operator and showcase the generality of our model by proposing an extension that handles parametric ODEs. Experiments on canonical benchmarks, including the Van der Pol oscillator, Burgers' equation, 2D Navier-Stokes, and Rotating Gaussians, show that RRAEDy achieves accurate and robust predictions. Our code is open-source and available at https://github.com/JadM133/RRAEDy. We also provide a video summarizing the main results at https://youtu.be/ox70mSSMGrM.

cs.LG↗

arXiv2025

Application of Reduced-Order Models for Temporal Multiscale Representations in the Prediction of Dynamical Systems

Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods that fail to capture high frequency behaviours. To overcome these difficulties, we propose three approaches for multiscale learning. The first leverages the Partition of Unity (PU) method, integrated with neural networks, to decompose the dynamics into local components and directly predict both macro- and micro-scale behaviors. The second applies the Singular Value Decomposition (SVD) to extract dominant modes that explicitly separate macro- and micro-scale dynamics. Since full access to the data matrix is rarely available in practice, we further employ a Sparse High-Order SVD to reconstruct multiscale dynamics from limited measurements. Together, these approaches ensure that both coarse and fine dynamics are accurately captured, making the framework effective for real-world applications involving complex, multi-scale phenomena and adaptable to higher-dimensional systems with incomplete observations, by providing an approximation and interpretation in all time scales present in the phenomena under study.

cs.LG↗

arXiv2025

A Scoresheet for Explainable AI

Explainability is important for the transparency of autonomous and intelligent systems and for helping to support the development of appropriate levels of trust. There has been considerable work on developing approaches for explaining systems and there are standards that specify requirements for transparency. However, there is a gap: the standards are too high-level and do not adequately specify requirements for explainability. This paper develops a scoresheet that can be used to specify explainability requirements or to assess the explainability aspects provided for particular applications. The scoresheet is developed by considering the requirements of a range of stakeholders and is applicable to Multiagent Systems as well as other AI technologies. We also provide guidance for how to use the scoresheet and illustrate its generality and usefulness by applying it to a range of applications.

cs.AI↗

arXiv2024

Quantum Potato Chips

We examine qubit states under symmetric informationally-complete measurements, representing state vectors as probability 4-vectors within a 3-simplex in $bb(R)^4$. Using geometric transformations, this 3-simplex is mapped to a tetrahedron in $bb(R)^3$. A specific surface within this tetrahedron allows for the separation of probability vectors into two disjoint 1-simplices. The intersection of this surface with the insphere identifies a "quantum potato chip" region, where probability 4-vectors reduce to two binary classical variables. States within this region can be fully reconstructed using only two given projective measurements, a feature not found elsewhere in the state space.

quant-ph↗

arXiv2024

Single Atom Convolutional Matching Pursuit: Theoretical Framework and Application to Lamb Waves based Structural Health Monitoring

Structural Health Monitoring (SHM) aims to monitor in real time the health state of engineering structures. For thin structures, Lamb Waves (LW) are very efficient for SHM purposes. A bonded piezoelectric transducer (PZT) emits LW in the structure in the form of a short tone burst. This initial wave packet (IWP) propagates in the structure and interacts with its boundaries and discontinuities and with eventual damages generating additional wave packets. The main issues with LW based SHM are that at least two LW modes are simultaneously excited and that those modes are dispersive. Matching Pursuit Method (MPM), which consists of approximating a signal as a sum of different delayed and scaled atoms taken from an a priori known learning dictionary, seems very appealing in such a context, however is limited to nondispersive signals and relies on a priori known dictionary. An improved version of MPM called the Single Atom Convolutional Matching Pursuit method (SACMPM), which addresses the dispersion phenomena by decomposing a measured signal as delayed and dispersed atoms and limits the learning dictionary to only one atom, is proposed here. Its performances are illustrated when dealing with numerical and experimental signals as well as its usage for damage detection. Although the signal approximation method proposed in this paper finds an original application in the context of SHM, this method remains completely general and can be easily applied to any signal processing problem.

cs.CE↗

arXiv2024

The LATIN-PGD methodology to nonlinear dynamics and quasi-brittle materials for future earthquake engineering applications

This paper presents a first implementation of the LArge Time INcrement (LATIN) method along with the model reduction technique called Proper Generalized Decomposition (PGD) for solving nonlinear low-frequency dynamics problems when dealing with a quasi-brittle isotropic damage constitutive relations. The present paper uses the Time-Discontinuous Galerkin Method (TDGM) for computing the temporal contributions of the space-time separate-variables solution of the LATIN-PGD approach, which offers several advantages when considering a high number of DOFs in time. The efficiency of the method is tested for the case of a 3D bending beam, where results and benchmarks comparing LATIN-PGD to classical time-incremental Newmark/Quasi-Newton nonlinear solver are presented. This work represents a first step towards taking into account uncertainties and carrying out more complex parametric studies imposed by seismic risk assessment.

cs.CE↗

arXiv2024

A reduced simulation applied to viscoelastic fatigue of polymers using a time multi-scale approach based on Partition of Unity method

The simulation of viscoelastic time-evolution problems described by a large number of internal variables and with a large spectrum of relaxation times requires high computational resources for their resolution. Furthermore, the internal variables evolution is described by a set of linear differential equations which involves many time scales. In this context, the use of a space-time PGD approximation is proposed here to boost their resolution, where the temporal functions are constructed following a multi-scale strategy along with the Partition of Unity method, in order to catch each dynamic efficiently. The feasibility and the robustness of the method are discussed in the case of a polymer in a non-equilibrium state under cyclic loading.

cs.CE↗

arXiv2024

Predicting Individual Depression Symptoms from Acoustic Features During Speech

Current automatic depression detection systems provide predictions directly without relying on the individual symptoms/items of depression as denoted in the clinical depression rating scales. In contrast, clinicians assess each item in the depression rating scale in a clinical setting, thus implicitly providing a more detailed rationale for a depression diagnosis. In this work, we make a first step towards using the acoustic features of speech to predict individual items of the depression rating scale before obtaining the final depression prediction. For this, we use convolutional (CNN) and recurrent (long short-term memory (LSTM)) neural networks. We consider different approaches to learning the temporal context of speech. Further, we analyze two variants of voting schemes for individual item prediction and depression detection. We also include an animated visualization that shows an example of item prediction over time as the speech progresses.

cs.SD↗

arXiv2024

Rank Reduction Autoencoders

The choice of an appropriate bottleneck dimension and the application of effective regularization are both essential for Autoencoders to learn meaningful representations from unlabeled data. In this paper, we introduce a new class of deterministic autoencoders, Rank Reduction Autoencoders (RRAEs), which regularize their latent spaces by employing a truncated singular value decomposition (SVD) during training. In RRAEs, the bottleneck is defined by the rank of the latent matrix, thereby alleviating the dependence of the encoder/decoder architecture on the bottleneck size. This approach enabled us to propose an adaptive algorithm (aRRAEs) that efficiently determines the optimal bottleneck size during training. We empirically demonstrate that both RRAEs and aRRAEs are stable, scalable, and reliable, as they do not introduce any additional training hyperparameters. We evaluate our proposed architecture on a synthetic data set, as well as on MNIST, Fashion MNIST, and CelebA. Our results show that RRAEs offer several advantages over Vanilla AEs with both large and small latent spaces, and outperform other regularizing AE architectures.

cs.LG↗