University of Jyväskylä receives ERC Advanced Grant worth millions of euros − research project aims to uncover hidden structures using mathematics

Inverse problems constitute a field of mathematical research seeking to determine an object’s internal structure or properties from external measurements.

The research project is focused on the Calderón problem, which is one of the most famous and important research questions in the mathematical theory of inverse problems. It serves as a mathematical model for imaging methods based on scattering or electrical and optical measurements.

“A typical aim is to determine an object’s internal properties by measuring information attained from its surface so that you don’t need to open or break up the object,” Salo explains.

In recent years, this field has advanced rapidly, particularly in wave-based imaging. Interesting research directions of mathematical theory include the contribution of geometry to inverse problems, non-linear and non-local partial differential equations, and settings with a very limited set of measurements available. The research project will examine these questions and develop new mathematical methods for their solution.

Practical applications in imaging, material research and geophysics

The project seeks to solve new variations of the Calderón problem in curved space-time settings as well as in geometrically demanding environments. In addition, the research team investigates how precisely imaging problems can be solved by methods based on machine learning and neural networks.

While this research will generate new fundamental knowledge in mathematics, it can also have long-term influence on practical applications. The methods of inverse problems are applied, for example, in electrical impedance tomography, which has medical applications, including lung imaging, as well as in soil and bedrock research, structural damage detection, and various telemetric techniques.

Domestic and international recognition

Mikko Salo has worked as Professor of Mathematics at the University of Jyväskylä since 2013. He has received several awards in recognition of his contributions to the field of mathematics.

Salo has previously been awarded highly prestigious funding from the European Research Council: an ERC Starting Grant for 2012−2017 and a Consolidator Grant for 2018−2023.

Salo was also involved in the Centre of Excellence for Inverse Modelling and Imaging funded by the Research Council of Finland from 2018 to 2025.

At present, Salo is working for the Research Council of Finland Flagship programme Advanced Mathematics for Sensing, Imaging and Modelling (FAME), a multidisciplinary research consortium developing methods of applied mathematics and physics for the needs of society. Research in the Jyväskylä-based team is focused on mathematical models for imaging, and the team also coordinates education of the Flagship’s research areas at the national level.

ERC Advanced Grants support leading European researchers striving for new scientific breakthroughs.