Young Mathematicians Lead Innovation in Computational Methods and Neural Network Applications

International Recognition for Neural Network Research

Dr. Carlos Uriarte has brought international acclaim to Spanish mathematics by winning the ECCOMAS Awards for the Two Best PhD Theses in 2024. His thesis, "Solving Partial Differential Equations using Artificial Neural Networks," defended at the University of the Basque Country under the supervision of Professors David Pardo and Elisabete Alberdi, received the highest honors with an "outstanding cum laude" rating and international doctoral mention. Uriarte's work addresses a critical challenge in computational mathematics: solving high-dimensional partial differential equations where traditional methods face limitations. His thesis introduces three innovative approaches:

• Deep Finite Element Method (Deep FEM): Neural network architectures that mimic refined mesh connectivity for parametric problems
• Deep Double Ritz Method (D2RM): A dual neural network approach for enhanced numerical stability
• Memory-Based Monte Carlo Integration: Improved integration accuracy without significant computational overhead

This research establishes new mathematical foundations for the intersection of neural networks and scientific computing, positioning Spain at the forefront of computational innovation.

SeMA Antonio Valle Award Recognizes Diverse Mathematical Talent

The 2025 SeMA Antonio Valle Young Researcher Award recognized two outstanding scientists whose work spans multiple mathematical disciplines:

Matteo Croci (BCAM, Bilbao) brings international expertise as a Ramón y Cajal Research Professor. His interdisciplinary approach encompasses computational stochastics, uncertainty quantification, and industrial mathematics, with particular strength in multilevel methods and Monte Carlo techniques. Previously recognized with the Leslie Fox Prize in Numerical Analysis and the Charles Broyden Prize, Croci's research extends into biomedical computation and brain modeling.

Jesús David Poyato Sánchez (University of Granada) demonstrates excellence in mathematical analysis of nonlinear partial differential equations with singular terms. His work bridges physics, biology, ecology, and fluid mechanics, addressing complex challenges in collective dynamics and biological propagation phenomena. With publications in top-tier journals including Communications of Pure and Applied Mathematics and Nature Communications, Poyato represents the new generation of mathematicians tackling interdisciplinary challenges.

Both award recipients presented their research at the EHF2025 conference in Ciudad Real (July 7-11, 2025), sharing their insights with the international mathematical community.

These achievements underscore the vitality of Spanish applied mathematics and the promising future of computational and analytical mathematical research.

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