From the seabed to neural networks: BCAM to take part in two european Marie Skłodowska-Curie Actions Staff Exchanges projects showing the cross-cutting strength of mathematics

• The Basque centre for applied mathematics will, from 2027, take part in two international Marie Skłodowska-Curie networks — MOST-PINN and EMERGENCE — dedicated to monitoring marine renewable energy infrastructure and developing new mathematical tools for analysing complex data, respectively.
• Vincenzo Nava (Politecnico di Torino and BCAM External Scientific Member) is the coordinator of the MOST-PINN project, which monitors the health of marine structures for renewable energy, and includes the collaboration of Ana Fernández-Navamuel, a Juan de la Cierva postdoctoral researcher at BCAM, as leader of a work package.
• EMERGENCE is coordinated by Elena Cordero (University of Turin), with Luz Roncal leading a work package within the project, which reinvents mathematical analysis to make sense of data that no longer fits within classical tools.

What do a mooring line on a floating offshore wind turbine and the invisible structure of a data network have in common? At first glance, nothing. But for the Basque Center for Applied Mathematics (BCAM), both are the same question asked in two different ways: how can mathematics help us understand — and trust — complex systems?

From January 2027, the Bilbao-based research centre will coordinate two new international projects funded by the European Commission under the Marie Skłodowska-Curie Actions – Staff Exchanges (MSCA-SE) programme, one of Horizon Europe's flagship instruments for researcher mobility and training.

The two projects — MOST-PINN, coordinated by researcher Vincenzo Nava (Politecnico di Torino and BCAM External Scientific Member), and EMERGENCE, coordinated by researcher Elena Cordero (University of Turin) — start out from very different challenges: one monitors the health of marine structures for renewable energy, while the other reinvents mathematical analysis to make sense of data that no longer fits within classical tools. Together, however, they tell the same story: that of an applied mathematics capable of crossing disciplines, sectors and even oceans.

Both projects have two women researchers from BCAM coordinating a work package each: postdoctoral researcher Ana Fernández-Navamuel in MOST-PINN, and, in EMERGENCE, Ikerbasque and BCAM Associate Professor Luz Roncal. The work is carried out under the Staff Exchanges action of the Marie Skłodowska-Curie Actions, the European Union programme dedicated to excellence in research training and mobility. Its aim is to fund international, cross-sector exchanges of research, technical and administrative staff between universities, research centres, companies and SMEs from different countries, both within and outside the European Union. Consortia must bring together a minimum of three organisations from three different countries and combine academic and non-academic bodies, with one condition that neatly sums up the programme's philosophy: everyone taking part in an exchange always returns to their home institution once the placement ends, so that the knowledge gained feeds directly back into it.

The fact that BCAM is coordinating two projects within this same call confirms the growing standing of the Basque centre as a leading hub in European applied mathematics.

MOST-PINN (Monitoring Offshore Structures using Physics-Informed Neural Networks) brings together researchers in engineering, marine renewable energy, computer science and applied mathematics, alongside industry specialists, around a single tool: physics-informed neural networks — artificial intelligence models that learn by incorporating the physical laws of the problem they are trying to solve, rather than starting from scratch. In short, mathematics for keeping watch over the sea.

Ana Fernández-Navamuel is a Juan de la Cierva postdoctoral researcher at BCAM, specialising in structural health monitoring, integrating computational mechanics and deep learning to identify structural damage in structures such as bridges and offshore wind energy systems. She coordinates a work package in MOST-PINN, the project focuses on two very specific fronts: developing adaptive control strategies for wave energy converters that make it possible to produce more energy while reducing the loads that wear down equipment; and advancing preventive maintenance for floating offshore wind turbines through structural health monitoring of their mooring lines, detecting damage before it turns into costly — or dangerous — failures.

In line with the European Research Area's strategic agenda on the green and digital transition, MOST-PINN contributes directly to the United Nations Sustainable Development Goals on affordable and clean energy and on climate action: every improvement in the reliability and cost of these structures brings floating offshore wind and wave energy closer to being fully competitive.

The second project, EMERGENCE (Emerging Methods in Fourier Analysis, PDEs, Graphs and Machine Learning), tackles a challenge that seems worlds away from the first, yet is just as pressing: how can we analyse, with the same rigour that classical mathematics applies to signals or partial differential equations, complex, high-dimensional data with non-Euclidean structures — such as the graphs that describe social networks, biological systems or artificial intelligence models themselves?

Luz Roncal, an Ikerbasque researcher at BCAM specialising in harmonic analysis and partial differential equations, coordinates a work package within EMERGENCE, a project developing new Fourier analysis techniques for graphs and networks, spectral and microlocal methods for evolution partial differential equations, and Fourier-based interpretations of machine learning models themselves, with particular attention to their stability, representational capacity and generalisation. In short: a common mathematical language capable of bringing together the most classical harmonic analysis with the very latest tools in data science.

Although one looks down to the depths of the ocean and the other to the abstraction of a graph, MOST-PINN and EMERGENCE share the same starting point: the conviction that applied mathematics does not belong to a single sector or a single discipline. It puts itself at the service of engineering, energy, computing or industry, wherever a complex problem needs to be turned into a rigorous, useful model.

That cross-cutting reach is precisely the added value BCAM brings to the Basque and European scientific and industrial ecosystem. Since its founding in 2008 as a Basque Excellence Research Centre (BERC), and having already been awarded the "Severo Ochoa Excellence" seal on three consecutive occasions — the highest distinction granted by the Spanish State to its research centres and units — BCAM has made the application of mathematics to fields as diverse as health, energy, biosciences and advanced industry its hallmark, and has also become a centre of real character and international standing.

For the researchers taking part, both projects represent an opportunity for high-level training, international collaboration and professional development — precisely the goals the Marie Skłodowska-Curie programme has pursued since its creation. For BCAM, every European project is also another tool for attracting and retaining talent: one more reason for researchers from anywhere in the world to choose to settle in Bilbao and contribute, from here, to the science of the future. The centre's own motto sums it up better than any other fact: Matematika mugaz bestalde — mathematics beyond borders.

In figures

• MOST-PINN · Monitoring Offshore Structures using Physics-Informed Neural Networks · Principal Investigator at BCAM: Ana Fernández-Navamuel · Programme: MSCA Staff Exchanges (Horizon Europe) · Duration: 2027–2030
• EMERGENCE · Emerging Methods in Fourier Analysis, PDEs, Graphs and Machine Learning · Principal Investigator at BCAM: Luz Roncal · Programme: MSCA Staff Exchanges (Horizon Europe) · Duration: 2027–2030