Group on Applied Mathematical Modeling, Statistics, and Optimization
MATHMODE is recognized as a Research Group of Excellence (A+) by the Basque Government.
The key objectives of the Group on Applied Mathematical Modeling, Statistics, and Optimization (MATHMODE) are:
1) Develop knowledge on the numerical simulation of ordinary and partial differential equations, as well as on optimization problems and statistics.
2) Transfer this mathematical knowledge to the industry.
3) Train new researchers in the area.
AREAS OF KNOWLEDGE
The Group on Applied Mathematical Modeling, Statistics, and Optimization (MATHMODE) works on four areas of knowledge:
1) Mathematics, used to develop advanced numerical and statistical methods.
2) Scientific Computing, used to implement efficiently those numerical methods.
3) Artificial Intelligence, used to perform rapid inversions of experimental measurements in Computational Mechanics.
4) Engineering, used to understand and solve real-world industry problems.
MAIN RESEARCH DIRECTIONS
Within the group on Applied Mathematical Modeling, Statistics, and Optimization (MATHMODE), we distinguish between three research areas and their applications, although in practice, the interactions between investigators and investigation areas are intertwined, yielding a multidisciplinary and collaborative group.
In offshore wind energy applications, we combine advanced finite element methods with artificial intelligence techniques to generate a multidisciplinary tool able to detect and prevent failures in the offshore platforms and their components, based on experimental measurements.
1) We exploit deep learning concepts to design innovative efficient and robust algorithms able to solve inverse problems arising in geophysics, structural health monitoring and offshore wind energy.
2) We employ statistics to validate and efficiently analyze real data. We promote the transfer of the research in statistics to biomedical and experimental fields through reliable and user-friendly algorithms based on statistical models.
3) We develop and analyze mathematically highly accurate and robust numerical methods for the solution and inversion, via computer simulations, of challenging multiphysics applications. This is also crucial for the generation of sufficiently big and significant datasets for the training of artificial intelligence algorithms.
4) We contribute to the advances in real-world industry and healthcare, by solving the arising mathematical problems with the proposed methods.
5) Advanced numerical methods for time integration of differential equations. This line of research seeks to analyze, design, and implement numerical integration methods for time evolution problems governed by differential equations whose solution cannot be obtained using conventional packages based on multistep methods nor Runge-Kutta schemes.
6) Applied optimization problems. The main objective is to carry out projects with companies, making technology transfer in the fields of optimization, simulation, operational research, and statistics.