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.

Advanced Monte Carlo methods for high-performance uncertainty quantification. We develop state-of-the-art, scalable Monte Carlo methods for quantifying the uncertainty within computational models and estimate risks associated with incorrect predictions. The list of methods developed includes: multilevel Monte Carlo, quasi Monte Carlo, and importance sampling methods.

Biomedical computing and brain fluid simulation. We investigate the mechanisms behind brain solute clearance and neurodegenerative disease progression by simulating the brain fluid and solute dynamics and characterizing brain fluid velocities via Bayesian inference methods.

 

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: Left: Optimized motions. On the propeller geometry (left), we show three optimized motions of the toroidal tool along the same contact path. The optimized tilt functions correspond to optimized accuracy (w = 0), balanced accuracy and tool-wear (w = 0.8), and minimized tool wear (w=1), respectively. All three paths are by construction physically feasible, i.e., globally collision-free.

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. Fig. 3 shows results of modeling and manufacturing of a lightweight blisk; its blade is filled by an interior microstructure and manufactured using hybrid manufacturing.

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 to the right.

Fig. 3: Left: A blisk is a typical aeronautical workpiece. The whole blisk, including curved, free-form blades is usually solid which makes it a heavy component of an aero-engine. Middle: A microstructured alternative of one blade (before optimization) that sustains the prescribed stress limits, yet requires considerably less material (26% material reduction). Bottom: final microstructured blade manufactured using hybrid manufacturing (laser powder bed fusion + 5-axis CNC machining).

Continuous monitoring applications. This line of research focuses on the design of energy‑efficient algorithms for the continuous monitoring of sensor data in both health and industrial settings. Building on techniques such as predictive sensing, event‑based sampling, self‑supervised learning or hyperdimensional computing, we develop models that can run on low‑power embedded and wearable devices while preserving or even improving detection accuracy. In healthcare, these methods are used for long‑term monitoring of biosignals to characterize cardiovascular, respiratory, musculoskeletal and neurological conditions. In parallel, we transfer the same methodological principles to industrial applications, for example to large‑scale sensor networks for early detection and localization of hydrogen leaks, where minimizing latency, communication and energy consumption is critical for safety and reliability.

Evolution-based tool path and motion planning optimization for 5-axis CNC machining of free-form surfaces

Echevarrieta Ibarra, J.; Pérez, A.; Barton, M.; Zaragoza, J.; Bizzarri, M. (2026-01-01)

Manufacturing of free-form geometries using 5-axis Computer Numerically Controlled (CNC) machining brings challenges in path- and motion-planning as one typically wants to minimize the manufacturing time of the object under ...

An Adaptive Sampling Algorithm for Level-set Approximation

Croci, M.; Haji-Ali, A-L.; Powell, I. C. J. (2025-09-18)

We propose a new numerical scheme for approximating level-sets of Lipschitz multivariate functions which is robust to stochastic noise. The algorithm's main feature is an adaptive grid-based stochastic approximation strateg...

On tool wear optimized motion planning for 5-axis CNC machining of free-form surfaces using toroidal cutting tools

Kruppa, K.; Zaragoza, J.; Bizzarri, M.; Barton, M. (2025-01-01)

We propose a computational framework for motion planning for 5-axis CNC machining of free-form surfaces. Given a reference surface, a set of contact paths on it, and a shape of a toroidal cutting tool as input, the proposed ...

On design, analysis, and hybrid manufacturing of microstructured blade-like geometries

Antolin, P.; Bonneau, G.-P.; Buffa, A.; Calleja, A.; Elber, G.; Elgeti, S.; Escudero, G.; Gonzalez, A.; Gonzalez, H.; Hahmann, S.; Hirschler, T.; Hong, Q.-Y.; Key, K.; Kim, M.-S.; Kofler, M.; de Lacalle, N.; de la Maza, S.; Barton, M.; Zwar, J.; Rajain, K. (2025-09-01)

With the evolution of new manufacturing technologies such as multi-material 3D printing, one can think of new type of objects that consist of considerably less, yet heterogeneous, material, consequently being porous, lighter...

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