Basque Center for Applied Mathematics

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    2063 research outputs found

    Cloud benchmarking and performance analysis of an HPC application in Amazon EC2

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    Cloud computing platforms have been continuously evolving. Features such as the Elastic Fabric Adapter (EFA) in the Amazon Web Services (AWS) platform have brought yet another revolution in the High Performance Computing (HPC) world, further accelerating the convergence of HPC and cloud computing. Other public clouds also support similar features further fueling this change. In this paper, we show how and why the performance of a large-scale computational fluid dynamics (CFD) HPC application on AWS competes very closely with the one on Beskow - a Cray XC40 supercomputer at the PDC Center for High-Performance Computing - in terms of cost-efficiency with strong scaling up to 2304 processes. We perform an extensive set of micro and macro bench- marks in both environments and conduct a comparative analysis. Until as recently as 2020 these benchmarks have notoriously yielded unsatisfactory results for the cloud platforms compared with on-premise infrastructures. Our aim is to access the HPC capabilities of the cloud, and in general to demonstrate how researchers can scale and evaluate the performance of their application in the cloud.ENABL

    Computational Mesoscale Framework for Biological Clustering and Fractal Aggregation

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    Hierarchical clustering due to diffusion and reaction is a widespread occurrence in natural phenomena, displaying fractal behavior with non-integer size scaling. The study of this phenomenon has garnered interest in both biological systems such as morphogenesis and blood clotting, and synthetic systems such as colloids and polymers. The modeling of biological clustering can be difficult, as it can occur on a variety of scales and involve multiple mechanisms, necessitating the use of various methods to capture its behavior. Here, we propose a novel framework, the generalized-mesoscale-clustering (GMC), for the study of complex hierarchical clustering phenomena in biological systems. The GMC framework incorporates the effects of hydrodynamic interactions, bonding, and surface tension, and allows for the analysis of both static and dynamic states of cluster development. The framework is applied to a range of biological clustering mechanisms, with a focus on blood-related clustering from fibrin network formation to platelet aggregation. Our study highlights the importance of a comprehensive characterization of the structural properties of the cluster, including fractal dimension, pore-scale diffusion, initiation time, and consolidation time, in fully understanding the behavior of biological clustering systems. The GMC framework also provides the potential to investigate the temporal evolution and mechanical properties of the clusters by tracking bond density and including hydrodynamic interactions

    On C0 and C1 continuity of envelopes of rotational solids and its application to 5-axis CNC machining

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    We study the smoothness of envelopes generated by motions of rotational rigid bodies in the context of 5-axis Computer Numerically Controlled (CNC) machining. A moving cutting tool, conceptualized as a rotational solid, forms a surface, called envelope, that delimits a part of 3D space where the tool engages the material block. The smoothness of the resulting envelope depends both on the smoothness of the motion and smoothness of the tool. While the motions of the tool are typically required to be at least C2, the tools are frequently only C0 continuous, which results in discontinuous envelopes. In this work, we classify a family of instantaneous motions that, in spite of only C0 continuous shape of the tool, result in C0 continuous envelopes. We show that such motions are flexible enough to follow a free-form surface, preserving tangential contact between the tool and surface along two points, therefore having applications in shape slot milling or in a semi-finishing stage of 5-axis flank machining. We also show that C1 tools and motions still can generate smooth envelopes.Juan de la Cierva - Formation [grant number FJC2019-039804-I] Ram\รณn y Cajal fellowship RYC-2017-22649

    A kernel-enriched order-dependent nonparametric spatio-temporal process

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    Spatio-temporal processes are necessary modeling tools for various environmental, biological, and geographical problems. The underlying model is commonly considered to be parametric and to be a Gaussian process. Additionally, the covariance function is expected to be stationary and separable. This structure need not always be realistic. Moreover, attempts have been made to construct nonparametric processes of neither stationary nor separable covariance functions. Nevertheless, as we elucidate, some desirable and necessary spatio-temporal properties are not guaranteed by the existing approaches, thus, calling for further innovative ideas. In this article, using kernel convolution of order-based dependent Dirichlet process, we construct a novel spatio-temporal model. We show that this satisfies desirable properties and includes the stationary, separable, parametric processes as special cases. Our resultant posterior distribution is variable dimensional, which we attack using Transdimensional Transformation based Markov Chain Monte Carlo, which can update all the variables and change dimensions using deterministic transformations of a random variable drawn from some arbitrary density defined on relevant support. We demonstrate our modelโ€™s performance on simulated and real data sets. In all situations, the findings are highly encouraging

    Bridge damage identification under varying environmental and operational conditions combining Deep Learning and numerical simulations

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    This work proposes a novel supervised learning approach to identify damage in operating bridge structures. We propose a method to introduce the effect of environmental and operational conditions into the synthetic damage scenarios employed for training a Deep Neural Network, which is applicable to large-scale complex structures. We apply a clustering technique based on Gaussian Mixtures to effectively select Q representative measurements from a long-term monitoring dataset. We employ these measurements as the target response to solve various Finite Element Model Updating problems before generating different damage scenarios. The synthetic and experimental measurements feed two Deep Neural Networks that assess the structural health condition in terms of damage severity and location. We demonstrate the applicability of the proposed method with a real full-scale case study: the Infante Dom Henrique bridge in Porto. A comparative study reveals that neglecting different environmental and operational conditions during training detracts the damage identification task. By contrast, our method provides successful results during a synthetic validation

    Easy-to-implement hp-adaptivity for non-elliptic goal-oriented problems

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    The FEM has become a foundational numerical technique in computational mechanics and civil engineering since its inception by Courant in 1943 Courant1943. Originating from the Ritz method and variational calculus, the FEM was primarily employed to derive solutions for vibrational systems. A distinctive strength of the FEM is its capability to represent mathematical models through the weak variational formulation of PDE, facilitating computational feasibility even in intricate geometries. However, the search for accuracy often imposes a significant computational task. In the FEM, adaptive methods have emerged to balance the accuracy of solutions with computational costs. The hh-adaptive FEM designs more efficient meshes by reducing the mesh size hh locally while keeping the polynomial order of approximation pp fixed (usually p=1,2p=1,2). An alternative approach to the hh-adaptive FEM is the pp-adaptive FEM, which locally enriches the polynomial space pp while keeping the mesh size hh constant. By dynamically adapting hh and pp, the hphp-adaptive FEM achieves exponential convergence rates. Adaptivity is crucial for obtaining accurate solutions. However, the traditional focus on global norms, such as L2L^2 or H1H^1, might only sometimes serve the requirements of specific applications. In engineering, controlling errors in specific domains related to a particular QoI is often more critical than focusing on the overall solution. That motivated the development of GOA strategies. In this dissertation, we develop automatic GO hphp-adaptive algorithms tailored for non-elliptic problems. These algorithms shine in terms of robustness and simplicity in their implementation, attributes that make them especially suitable for industrial applications. A key advantage of our methodologies is that they do not require computing reference solutions on globally refined grids. Nevertheless, our approach is limited to anisotropic pp and isotropic hh refinements. We conduct multiple tests to validate our algorithms. We probe the convergence behavior of our GO hh- and pp-adaptive algorithms using Helmholtz and convection-diffusion equations in one-dimensional scenarios. We test our GO hphp-adaptive algorithms on Poisson, Helmholtz, and convection-diffusion equations in two dimensions. We use a Helmholtz-like scenario for three-dimensional cases to highlight the adaptability of our GO algorithms. We also create efficient ways to build large databases ideal for training DNN using hphp MAGO FEM. As a result, we efficiently generate large databases, possibly containing hundreds of thousands of synthetic datasets or measurements

    Sharp estimates for Jacobi heat kernels in conic domains

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    We prove genuinely sharp estimates for the Jacobi heat kernels introduced in the context of the multidimensional cone Vd+1\mathbb V^{d+1}and its surface V0d+1\mathbb V^{d+1}_0. To do so, we combine the theory of Jacobi polynomials on the cone explored by Xu with the recent techniques by Nowak, Sjรถgren, and Szarek, developed to find genuinely sharp estimates for the spherical heat kernel.Basque Government (BERC 2022-2025), Spanish State Research Agency (CEX2021-001142-S and RYC2021-031981-I), Foundation for Polish Science (START 032.2022)

    A Novel Mathematical Approach for Analysis of Integrated Cellโ€“Patient Data Uncovers a 6-Gene Signature Linked to Endocrine Therapy Resistance

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    A significant number of breast cancers develop resistance to hormone therapy. This progression, while posing a major clinical challenge, is difficult to predict. Despite important contributions made by cell models and clinical studies to tackle this problem, both present limitations when taken individually. Experiments with cell models are highly reproducible but do not reflect the indubitable heterogeneous landscape of breast cancer. On the other hand, clinical studies account for this complexity but introduce uncontrolled noise due to external factors. Here, we propose a new approach for biomarker discovery that is based on a combined analysis of sequencing data from controlled MCF7 cell experiments and heterogeneous clinical samples that include clinical and sequencing information from The Cancer Genome Atlas. Using data from differential gene expression analysis and a Bayesian logistic regression model coupled with an original simulated annealing-type algorithm, we discovered a novel 6-gene signature for stratifying patient response to hormone therapy. The experimental observations and computational analysis built on independent cohorts indicated the superior predictive performance of this gene set over previously known signatures of similar scope. Together, these findings revealed a new gene signature to identify patients with breast cancer with an increased risk of developing resistance to endocrine therapy

    A Multimodal Dataset for Automatic Edge-AI Cough Detection

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    Counting the number of times a patient coughs per day is an essential biomarker in determining treatment efficacy for novel antitussive therapies and personalizing patient care. Automatic cough counting tools must provide accurate information, while running on a lightweight, portable device that protects the patientโ€™s privacy. Several devices and algorithms have been developed for cough counting, but many use only error-prone audio signals, rely on offline processing that compromises data privacy, or utilize processing and memory-intensive neural networks that require more hardware resources than can fit on a wearable device. Therefore, there is a need for wearable devices that employ multimodal sensors to perform accurate, privacy-preserving, automatic cough counting algorithms directly on the device in an edge Artificial Intelligence (edge-AI) fashion. To advance this research field, we contribute the first publicly accessible cough counting dataset of multimodal biosignals. The database contains nearly 4 hours of biosignal data, with both acoustic and kinematic modalities, covering 4,300 annotated cough events from 15 subjects. Furthermore, a variety of non-cough sounds and motion scenarios mimicking daily life activities are also present, which the research community can use to accelerate machine learning (ML) algorithm development. A technical validation of the dataset reveals that it represents a wide variety of signal-to- noise ratios, which can be expected in a real-life use case, as well as consistency across experimental trials. Finally, to demonstrate the usability of the dataset, we train a simple cough vs non-cough signal classifier that obtains a 91% sensitivity, 92% specificity, and 80% precision on unseen test subject data. Such edge-friendly AI algorithms have the potential to provide continuous ambulatory monitoring of the numerous chronic cough patients.RYC2021-032853-

    Adaptive Estimation of Distribution Algorithms for Low-Thrust Trajectory Optimization

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    A direct adaptive scheme is presented as an alternative approach for minimum-fuel low-thrust trajectory design in non-coplanar orbit transfers, utilizing fitness landscape analysis (FLA). Spacecraft dynamics is modeled with respect to modified equinoctial elements, considering J2 J_2 orbital perturbations. Taking into account the timings of thrust arcs, the discretization nodes for thrust profile, and the solution of multi-impulse orbit transfer, a constrained continuous optimization problem is formed for low-thrust orbital maneuver. An adaptive method within the framework of Estimation of Distribution Algorithms (EDAs) is proposed, which aims at conserving feasibility of the solutions within the search process. Several problem identifiers for low-thrust trajectory optimization are introduced, and the complexity of the solution domain is analyzed by evaluating the landscape feature of the search space via FLA. Two adaptive operators are proposed, which control the search process based on the need for exploration and exploitation of the search domain to achieve optimal transfers. The adaptive operators are implemented in the presented EDA and several perturbed and non-perturbed orbit transfer problems are solved. Results confirm the effectiveness and reliability of the proposed approach in finding optimal low-thrust transfer trajectories.BEAZ Bizkaia, 3/12/DP/2021/00150; SPRI Group, Ekintzaile Program EK-00112-202

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