MATHDES

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.

Geometric Modeling:

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).

Manufacturing Applications:

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.

Geophysical applications:

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

Mixed-precision finite element kernels and assembly: Rounding error analysis and hardware acceleration

Croci, M.; Wells, G. N. (2024-10-16)

In this paper we develop the first fine-grained rounding error analysis of finite element (FE) cell kernels and assembly. The theory includes mixed-precision implementations and accounts for hardware-acceleration via matrix ...

Reducing spatial discretization error on coarse CFD simulations using an openFOAM-embedded deep learning framework

Gonzalez-Sieiro, J.; Pardo, D.; Nava, V.; Calo, V.M.; Towara, M. (2024-09-09)

We propose a method for reducing the spatial discretization error of coarse computational fluid dynamics (CFD) problems by enhancing the quality of low-resolution simulations using deep learning. We feed the model with fine-...

On tiling spherical triangles into quadratic subpatches

Vrsek, J.; Bizzarri, M.; Lavicka, M.; Barton, M.; Kosinka, J. (2024-06-01)

Various interpolation and approximation methods arising in several practical applications in geometric modeling deal, at a particular step, with the problem of computing suitable rational patches (of low degree) on the unit ...

Design, motion-planning, and manufacturing of custom-shaped tools for 5-axis super abrasive machining of a turbomachinary blade like component

Martinez, M.; Gomez, G.; Bo, P.; Barton, M.; Gonzalez, H.; Calleja, A.; López de Lacalle, L.N. (2024-05-18)

Free-form surfaces generated by Non-Uniform Rational B-Splines (NURBS) are evolving to face turbomachinery components requirements, such as turbine blades to enhanced efficiency. Super Abrasive Machining (SAM) is presented a...

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