Mathematical Design, Modeling, and Simulations (MATHDES) group works on the design, analysis, implementation, and optimization of numerical schemes for mathematical models arising from real-life applications.
Michael Barton and David Pardo
Our research spans areas of Deep Learning, Inverse Problems, Finite Elements, Massive Computations, Numerical Analysis, Geometric Modeling, Computer Aided Design, and Modeling of Manufacturing Processes. We work in close interaction with industrial partners and institutions to promote transfer of knowledge and obtain feedback from real-life applications.
We currently work on three European Projects:
(a) a FET-OPEN project on Analysis, Design, and Manufacturing using Microstructures ADAM^2, which aims at revolutionizing the design-analysis-manufacturing pipeline, coordinated by Michael Barton; (b) a Marie Curie RISE Action MATHROCKS, intended to improve and exchange interdisciplinary knowledge on applied mathematics, high performance computing, and geophysics, coordinated by David Pardo; and (c) the European NextGenerationEU project IA4TES, funded by the Spanish Ministry for Economic Affairs and Digital Transition and led by Iberdrola, for structural health monitoring and assessment of remaining useful life of offshore wind platforms.
We collaborate with multiple prestigious institutions and industrial partners, including The University of Texas at Austin (USA), Stratasys LTD (Israel), INRIA (France), Hutchinson S.A. (France), Seoul National University (South Korea), Technion - Israel Institute of Technology (Israel), MacQuaire University (Australia), Ecole Polytechnique Federale de Lausanne (Switzerland), Curtin University (Australia), Technical University of Wein (Austria), King Abdullah University of Science and Technology (Saudi Arabia), Software Competence Center Hagenberg (Austria), Pontifical Catholic University of Valparaíso (Chile), Pontifical Catholic University of Chile, National University of Colombia, Central University of Venezuela, University of Buenos Aires (Argentina), Barcelona Supercomputing Center (Spain), Polytechnic University of Catalunya (Spain), University of Barcelona (Spain), University Charles III of Madrid (Spain), Tecnalia (Spain), Trimek S.A. (Spain), and University of the Basque Country (UPV/EHU).
This BCAM group has strong collaboration ties with the sister UPV/EHU Group MATHMODE.
In particular, we are currently involved in the following research projects:
Deep Learning Algorithms for Inverse Problems:
We study and develop Deep Learning methods to interpret (invert) in real-time elasto-acoustic and electromagnetic measurements. To achieve this objective, we design and implement proper Deep Neural Network architectures, loss functions, and error control algorithms enabling us to efficiently approximate physically meaningful inverse solutions.
Massive Finite Element Simulations:
We develop a set of numerical Galerkin-based methods for producing massive synthetic datasets for training Deep Neural Networks. Some examples include variants of Isogeometric Analysis, Dimensionality Reduction Algorithms, Reduced Order Models, Proper Generalized Decompositions, and hp-Adaptivity.
We model manufacturing processes such as 5-axis Computer Numerically Controlled (CNC) machining, see Fig.1, hot-wire cutting, or hybrid (additive and subtractive) manufacturing.
Fig. 1: 5-axis flank machinability of a reference surface (dark) using various machining tools (green). The tool-paths that meet fine machining tolerances are shown as ruled surface (motions of the tool axis, yellow).
In collaboration with the High Performance Manufacturing Group (UPV/EHU), we design path-planning algorithms for multi-axis CNC machining. An example of a simulation of 5-axis flank milling with a custom-shaped tool is shown in Fig. 2. The tool and its motion are both unknowns in our optimization-based framework. Manufactured result (blisk) machined with our algorithm using a conical tool is shown in Fig. 3.
Fig. 2: Simulation of path-planning for 5-axis double-flank CNC machining of a spiral bevel gear using a custom-shaped milling tool, (left). The 3D-printed prototype of the designed tool is shown in right.
Fig. 3: Finishing of the blisk blade using the state-of-the-art software (Siemens NX, left) and our algorithm (right). Additionally, to higher accuracy (not visible), observe the smooth light reflection in our result, that is due to negligible distance error between the neighboring milling paths.
We employ advanced numerical simulation and inversion methods to characterize the Earth´s subsurface, see Fig. 4. This is critical in several applications, such as (a) the prospecting of water, precious minerals, and hydrocarbons, (b) earthquake prediction and seismic hazard estimation, (c) seismic monitoring, (d) mine detection, (e) geothermal energy production, and (f) management of CO2 sequestration at the industrial scale that is needed to abate the global climate change problem.
Fig. 4: Controlled Source Electromagnetic Measurements for Earth Exploration
Offshore Wind Energy application:
We design Deep Neural Network architectures as a support of the design and operation of emerging technologies for offshore wind energy applications in three areas: (a) for accelerating CFD simulations using OpenFoam for analysing the hydrodynamics of support structures; (b) for structural health monitoring of components (mooring systems, power cables) in offshore floating platforms (see Fig. 5).; (c) real-time control of offshore wind energy farms for Fault Detection and Fault Tolerant Control.
Fig. 5: Autoencoder architecture for Structural Health Monitoring of Floating offshore wind components
Advanced Numerical Methods and Neural Networks for Structural Health Monitoring of Offshore Wind Platforms
Nuevos métodos numéricos y software para la simulación de propagación de ondas electromagnéticas en medios heterogéneos
Numerical simulation of wave propagation is at the core of many applications. For example, radar or sonar detection, medical imaging, seismology and oil field exploitation. It is a phenomenon that unfolds in an infinite (or very large) computational domain relative to the simulated wavelengths.
Reliable computational methods for infinite dimensional problems.
Partial differential equations (PDEs) and functional differential equations (FDEs) are suc- cessful, widely used mathematical models that describe, explain and predict phenomena in areas as broad as physics, chemistry, biology and economics.
A Dimensionally Adapted Method for the Efficient Simulations of Geophysical Electromagnetic Measurements
This Project (EMEARTHSIM) aims at developing more efficient simulation methods of geophysical electromagnetic (EM) measurements for the characterization of the materials composing the Earth’s subsurface.
Adaptive Stabilized Galerkin Methods with Multiphysics Applications
Advanced computer-aided simulation methods are of vital importance for solving many engineering applications.
Electromagnetic Imaging of the Earth's Subsurface using Advanced Galerkin Methods
IMAGEARTH Project is focused on the development of advanced numerical methods for the proper simulation and inversion of geophysical electromagnetic (EM) measurements.
Geophysical Exploration using Advanced GAlerkin Methods
The main objective of this Marie Curie RISE action is to improve and exchange interdisciplinary knowledge on applied mathematics, high performance computing, and geophysics to be able to better simulate and understand the materials composing the Earth's subsurface.
COPTER - Metrología aplicable a geometrías de alta complejidad para transmisiones de ultraprecisión
The COPTER project is presented as a radical solution to the design, manufacture and inspection of components formed by free-form surfaces; more specifically ultra-precision transmissions.
VIVIR - Validación de un método de reducción de Incertidumbre de la VIda Remanente de sistemas de fondeo para turbinas eólicas offshore flotantes
The present project aims at developing, verifying, and validating an artificial intelligence algorithm via data treatment and physical modelling. The objective is to reduce operational costs in offshore wind structures.
ExpertIA: Evolución del modelado y control de proceso industrial: modelos avanzados combinando conocimiento experto con técnicas IA en el diseño y desarrollo
ExpertIA proposes to start from the classical models of resolution or FEM models (finite differences for solving differential equations that describe the behaviour of many physical systems) with AI/ML/DL techniques that allow: 1) to reduce the computation time required by numerical models; 2) to red
MAnufacturing of CuRved Objects via Path-desIgn of cuSTom-shAped toolS
MACROPISTAS aims at questioning of few decades of traditional paradigms in 5-axis flank CNC machining by performing cutting-edge research in geometric modeling, mathematics, and manufacturing.
Real-time Inversion using Deep Learning Methods
DEEPINVERSE project focuses on the numerical real-time inversion of wave propagation problems governed by Partial Differential Equations (PDEs) utilizing Deep Learning (DL) algorithms.
Geometric numerical integrators fr quantum problems, celestial mechanics and Monte Carlo
This subproject constitutes part of the coordianted proposal GEOMETRIC NUMERICAL INTEGRATORS FOR QUANTUM PROBLEMS, CELESTIAL MECHANICS AND MONTE CARLO SIMULATIONS (GNI-QUAMC), devoted to the design, analysis, and implementation of special purpose geometric numerical integration schemes, with particu
Multiscale Inversion of Porous Rock Physics using High-Performance Simulators: Bridging the Gap between Mathematics and Geophysics
The main objective of this Marie Curie RISE Action is to improve and exchange interdisciplinary knowledge on applied mathematics, high performance computing, and geophysics to be able to better simulate and understand the materials composing the Earth's subsurface.
The Intergovernmental Panel on Climate Change (IPCC) has concluded that climate change is now indisputable and is having irreversible consequences.
Pyrenees Imaging eXperience: an InternationaL network
Creating a top-level cross-border network in R&D related to the characterization of subsoil by means of geophysical imaging. The technological application focuses on the field of geothermal energy, thus helping to promote this source of clean energy in the region.
European Network for Alloys Behaviour Law Enhancement
The Energy Union Framework Strategy laid out on 25 February 2015 has embraced a citizens-oriented energy transition based on a low-carbon transformation of the energy system.
IA4TES - Inteligencia Artificial para la Transición Energética Sostenible
The project researches the solutions that can be provided by the different Artificial Intelligence technologies to the electricity sector, thinking about the new paradigm of the electricity system, with a mostly renewable production, a mixture of centralised and distributed; with a digitalised and a
Space-time DPG methods for partial-differential equations with geophysical applications
The main objective of this project is to design stabilized space-time adaptive techniques based on Discontinuous Petrov-Galerkin (DPG) methodology for the simulation of transient Partial Differential Equations (PDEs), with special emphasis on advection-dominated- diffusion and wave propagation probl
Analysis, Design, And Manufacturing using Microstructures
ADAM^2 aims at questioning five decades of traditional paradigms in computer aided design CAD.
Pongó, T.; Fan, B.; Hernández-Delfin, D.; Török, J.; Stannarius, R.; Hidalgo, R. C.; Börzsönyi, T. (2022-10-01)
The time evolution of silo discharge is investigated for different granular materials made of spherical or elongated grains in laboratory experiments and with discrete element model (DEM) calculations. For spherical grains, ...
Piette, J. H.; Moreno, N.; Fried, E.; Giacomin, A. J. (2020-09-01)
Using general rigid bead-rod theory, we explore the effect of twisting a macromolecule on its rheological properties in suspensions. We thus focus on macromolecules having the form of Möbius bands so that the number of twist...
Tribological variable-friction coefficient models for the simulation of dense suspensions of rough polydisperse particles
Ruiz-Lopez, J.A.; Prasanna Kumar, S. S.; Vazquez-Quesada, A.; De Vicente, J.; Ellero, M. (2023-03-01)
The rheology of concentrated suspensions of particles is complex and typically exhibits a shear-thickening behavior in the case of repulsive interactions. Despite the recent interest arisen, the causes of the shear-thickenin...
Non-affine motion and selection of slip coefficient in constitutive modeling of polymeric solutions using a mixed derivative
Nieto, D.; Español, P.; Ellero, M. (2023-01-01)
Constitutive models for the dynamics of polymer solutions traditionally rely on closure relations for the extra stress or related microstructural variables (e.g., conformation tensor) linking them to flow history. In this wo...
Geometry and Tool Motion Planning for Curvature Adapted CNC Machining