2063 research outputs found
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Tensorial Implementation for Robust Variational Physics-Informed Neural Networks
Full text linkVariational Physics-Informed Neural Networks (VPINN) train the parameters of neural networks (NN) to solve partial differential equations (PDEs). They perform unsupervised training based on the physical laws described by the weak-form residuals of the PDE over an underlying discretized variational setting; thus defining a loss function in the form of a weighted sum of multiple definite integrals representing a testing scheme. However, this classical VPINN loss function is not robust. To overcome this, we employ Robust Variational Physics-Informed Neural Networks (RVPINN), which modifies the original VPINN loss into a robust counterpart that produces both lower and upper bounds of the true error. The robust loss modifies the original VPINN loss by using the inverse of the Gram matrix computed with the inner product of the energy norm. The drawback of this robust loss is the computational cost related to the need to compute several integrals of residuals, one for each test function, multiplied by the inverse of the proper Gram matrix. In this work, we show how to perform efficient generation of the loss and training of RVPINN method on GPGPU using a sequence of einsum tensor operations. As a result, we can solve our 2D model problem within 350 s on A100 GPGPU card from Google Colab Pro. We advocate using the RVPINN with proper tensor operations to solve PDEs efficiently and robustly. Our tensorial implementation allows for 18 times speed up in comparison to for-loop type implementation on the A100 GPGPU card
On the modeling of dynamic queue formation and decision-making in pedestrian dynamics simulations
Full text linkThis work presents two distinct and novel approaches to simulating dynamic queue formation
and route decision-making in pedestrian systems. Queue formation is modeled by detecting
pedestrians within a specific cutoff distance from others already in line, altering movement
forces and leading to organized queuing behavior. Two distinct methodologies are introduced
to simulate dense, compressed formations and elongated, thin lines. A parametric analysis
assesses how queue dimensions depend on model parameters. Additionally, we introduce a
simple criterion for route selection based on the identification of queuing agents, prioritizing the
most time-efficient route while accounting for delays caused by queues. Dynamic route changes
are modeled by shifting between multiple pre-calculated velocity maps for each potential exit.
Finally, both queuing and decision-making approaches are combined to study how queues affect
route choice. Our results predict that pedestrian decision is influenced by the type of queue
forming before the gates.BCAM Severo Ochoa excellence accreditation CEX2021-001142-S/MICINAEI/10.13039/501100011033
Basque Government through the ‘‘Mathematical Modeling Applied to Health’’ Project
Provincial Council of Bizkaia as part of the 2023 Technology Transfer Program, Spain (M3OVE Project)
Adapting to Marginal Distribution Shifts in Supervised Learning: A Double-Weighting Approach
Full text linkSupervised classification traditionally assumes that training and testing samples are independently and identically distributed (i.i.d.) from the same underlying distribution. However, practical scenarios are often affected by distribution shifts, such as covariate shift and label shift. In covariate shift, the marginal distribution over the instances (covariates) differs at training and testing while the label conditional distribution remains the same. In label shift, the marginal distribution over the labels differs at training and testing while the instance conditional distribution remains the same. Additionally, in multi-source scenarios, the training data is obtained from multiple sources, each of which has different probability distributions. In scenarios affected by distribution shift, conventional supervised classification methods, like empirical risk minimization, can perform poorly because the empirical risk approximates the training expected risk, rather than the testing expected risk.
Most existing techniques for correcting distribution shifts are based on a reweighted approach that weights training samples, assigning lower relevance to the samples that are unlikely at testing. However, these methods may achieve poor performance under support mismatch or when the weights obtained take large values at certain training samples. In addition, in multi-source cases, existing methods inherit the problems of single-source reweighted methods and do not exploit complementary information among sources, equally combining sources for all instances.
In this dissertation, we establish learning methodologies for supervised learning under marginal distribution shifts. The methodology proposed is based on minimax risk classification and avoids the limitations of existing methods by weighting both training and testing samples. For the multi-source case, the presented methods assign source-dependent weights for training and testing samples, where weights are obtained jointly using information from all sources. In addition, we develop effective techniques that obtain the sets of training and testing weights, generalizing the techniques based on the conventional kernel mean matching. We also present generalization bounds for the proposed methods that show a significant increase in the effective sample size. Empirically, the proposed methods achieve enhanced classification performance in both synthetic and empirical experiments using multiple real datasets.
This dissertation makes theoretical contributions leading to efficient algorithms for multiple supervised learning scenarios under distribution shifts with classification rules that provide confidence in the predictions and enhanced performance in comparison with state-of-the-art techniques.“Early Prognosis of COVID-19 Infections via Machine Learning” funded by the AXA Research Fun
Smoothed Dissipative Particle Dynamics for Mesoscale Advection-Diffusion-Reaction Problems
No full textSmoothed dissipative particle dynamics (SDPD) is a widely used particle-based method for modeling soft matter systems at mesoscopic and macroscopic scales, offering thermodynamic consistency and direct control over the fluid’s
transport properties. Here, we present an SDPD model that incorporates the transport of reactants on scales smaller
than the discretizing particles, including the evolution of compositional fields. The proposed methodology is well-suited
for modeling complex systems governed by advection-diffusion-reaction (ADR) dynamics. Implemented in LAMMPS,
the model is validated using a range of benchmark problems spanning diffusion-dominated, reaction-dominated, and
coupled ADR regimes. Our simulation results demonstrate that the implemented SDPD model effectively captures
complex behaviors, such as Turing pattern formation. The proposed model holds promise for applications across various fields, including biology, chemistry, materials science, and environmental engineering
Variational Autoencoder-Based Alert System for Onshore Wind Turbine: Application to a Real Case Study
No full textStructural Health Monitoring (SHM) of wind turbines is still far from a practical and effective implementation. One of the main limitations is the access to long-term experimental data from operative systems, as well as the access to a computational counterpart (e.g., Finite Element (FE) model) for testing purposes. This work proposes an unsupervised learning approach based on Deep Neural Networks (DNNs) for structural damage detection in a wind turbine operating within an onshore wind farm.
The target system belongs to a wind farm in Portugal, where a long-term acceleration dataset was recorded and postprocessed to estimate the modal properties (eigenfrequencies and eigenmodes). Since the available monitoring data corresponds to what we assume is the healthy state, an unsupervised approach is required to learn from the data. We propose a Variational Autoencoder (VAE) approach to compress the measured features (particularly the eigenfrequencies) into a latent space variable and subsequently expand them into the original data space with minimal loss of information.
This approach can be seen as a single-class classifier, where we learn to represent and reconstruct data from a known class, and any measurement that comes from a different generation process (e.g., damaged system) will be raised as an outlier. Given the stochastic character of the architecture, we explore the damage detection capability during testing by comparing statistical indicators. In order to generate damage scenarios, we employ a simple FE model, from which some damage simulations are resolved. We prevent the modeling error from being transferred to the experimental data by obtaining the relative change between the healthy and the damaged synthetic scenarios. These ratios are free from modeling error and can be applied, assuming the similarity of the domains to the experimental data. The results demonstrate that the VAE successfully detects the presence of damage. For slight damage cases, we find some scenarios where the histogram from the reconstruction error in (i) the healthy and (ii) the damaged scenario are almost overlapped, indicating some limitations. We explore the Receiver Operating Curves (ROC), which represent one of the most extensively employed techniques to measure the capability of single-class classifiers.Juan de la Cierva Postdoctoral Fellowship under the Grant JDC2023-051132-I funded by MICIU/AEI/10.13039/501100011033 and by the FSE+.
The European Union’s Horizon Europe research and innovation programme under Grant Agreement 101162248 -ORE4Citizens
GABAergic neurons can facilitate the propagation of cortical spreading depolarization: experiments in mouse neocortical slices and a novel neural field computational model
Full text linkPID2023-146683OB-10
A Novel Multi-Resolution Heart Rate Variability Analysis for IoT-based Drowsiness Detection: Preserving Temporal Trends in Features Series
No full textHeart rate variability (HRV) analysis provides valuable insights into autonomic nervous system regulation and serves as an effective indicator for drowsiness detection in transportation safety applications. This study presents the so-called Multi-CNM, a novel approach to HRV analysis for drowsiness detection through multi-resolution extraction of HRV features without additional processing to preserve the temporal trends in its series. To determine if our approach effectively captures drowsiness-related patterns in HRV features series, we compare it with two commonly used techniques in signal windowing and feature extraction: 1) the standard single window analysis with overlapping, redefined as CNM, 2) the well-known multi-scale entropy (MSE), used to measure the complexity of the time series and therefore give insights to abnormal events, applied on top of our approach (Multi-CNM-MSE). Experimental evaluations on a public drowsiness detection dataset demonstrate that our proposed Multi-CNM approach shows promising results achieving up to 99% accuracy and F1-score, comparable to the standard CNM and the coarse-grained Multi-CNM-MSE techniques, with up to 93% and 95% respectively. Statistical analysis reveals that the time series of HRV features such as MeanNN, LFHF ratio, and pNN20 exhibit the strongest discriminative power between drowsy and non-drowsy states, significantly underlined by our Multi-CNM. Our findings highlight the importance of preserving multi-resolution temporal structure in HRV analysis for real-time drowsiness detection in resource-constrained IoT implementations. The proposed methodology balances computational efficiency with detection accuracy, making it suitable for deployment in wearable and automotive monitoring systems.RYC2021-032853-I from MCIN/AEI/ 10.13039/501100011033
European Union NextGenerationEU/PRT
Lech-Mumford constant and stability of local rings
No full textThis work systematically develops a theory of the Lech–Mumford constant, an invariant defined as an optimal constant in the classical Lech’s inequality and underlined Mumford’s notion of local semistability. We establish a number of properties of semistable singularities, and, in particular, show that semistable singularities are log canonical under mild assumptions. We also provide new examples of semistable singularities.RYC2020-028976-I
EUR2023-14344
Colength, Multiplicity, and Ideal Closure Operations II
No full textLet be a Noetherian local ring. This paper concerns several extremal invariants arising from the study of the relation between colength and (Hilbert–Samuel or Hilbert–Kunz) multiplicity of an -primary ideal. We introduce versions of these invariants by restricting to various closures and “cross-pollinate” the two multiplicity theories by asking for analog invariants already established in one of the theories.
On the Hilbert–Samuel side, we prove that the analog of the Stückrad–Vogel invariant (the infimum of the ratio between the multiplicity and colength) for integrally closed -primary ideals is often 1 under mild assumptions. We also compute the supremum and infimum of the relative drops of multiplicity for (integrally closed) -primary ideals. On the Hilbert–Kunz side, we study several analogs of the Lech–Mumford and Stückrad–Vogel invariants.RYC2020-028976-I
EUR2023-14344
Human-Centered and Context-Aware Smart ML-based IoT Framework for Online Fatigue Detection: a Real-World Study of Football Training
No full textFatigue is one of the factors that most influences competitive athletes’ performance, leading to injuries and overtraining. To effectively monitor and predict fatigue levels during real-world training, it is necessary to integrate Internet of Things (IoT) technology with machine learning (ML). In this context, the paper presents three main contributions : a) a smart IoT framework that integrates edge and cloud-based modules to collect physiological parameters, monitor fatigue during real-world sessions, and assist coaches in optimizing exercise strategies ; b) a dataset collected through the proposed framework in a real pilot study with eight futsal players over five training sessions, each lasting between 35 and 50 minutes depending on performed exercises, using ECG and PPG-based sensors ; c) an online ML-based fatigue detection module and on-cloud analysis of various ML models, traditional and deep learning, including CNN+GRU, XGBoost, and Transformer architectures, and context-aware feature sets. We evaluated the accuracy of our fatigue detection method using standard metrics, achieving an F1-score of up to 95% with pilot study data. Our framework incorporates a context-aware design, where contextual information (exercise type) and sensing modality (ECG- or PPG-based) are explicitly integrated with physiological features (HRV and HR) in the fatigue prediction model to adapt it to different settings, improving robustness and interpretability. Finally, we evaluated the framework’s efficacy and the value of user and expert input, highlighting the benefits of integrating IoT and ML within a human-centered, context-aware approach to balance sensor accuracy, comfort, and efficiency in competitive sports training.SWEATHEART (HE-101202439)
RYC2021-032853-I from MCIN/AEI/ 10.13039/501100011033
European Union NextGenerationEU/PRT