# George Baravdish

Senior Associate Professor, Head of Unit

## Presentation

Senior associate professor of applied mathematics at the Unit of Physics, Electronics and Mathematics (FEM) at the Department of Science and Technology (ITN), Linköping University.

## Publications

### 2024

*p*-Laplace operator Nonlinear Analysis, Vol. 244, Article 113553 (Article in journal) Continue to DOI

### 2023

### 2020

## My research

My research deals with ill-posed and inverse problems that took off at the turn of the century when well-posed problems were defined, i.e. problems that have a unique solution and depend continuously on the input data. This means that ill-posed problems are difficult to solve because even though they describe physical situations with a unique solution, they are numerically unstable. Many inverse problems are also ill-posed. Inverse problems are when the output is given but the model or input is unknown. As computers have become more powerful in recent decades, research on these problems has also taken off. Ill-posed and inverse problems in mathematics can be found in complex analysis, functional analysis, differential equations, and linear algebra.

In application areas, they can be found in machine learning, signal processing, computer vision, control engineering, meteorology, geophysics, optics, and nuclear physics. Some of the classic questions that have been studied intensively are to reconstruct an initial temperature for a heat conduction equation given the temperature at a later time. Another well-known problem is the analytic continuation of harmonic solutions, i.e. solving the Cauchy problem for the Laplace equation.

### Ongoing projects

Right now I am working on these projects and have various collaborations:

### Websites for ongoing projects

#### Mathematics for Machine Learning

Mathematics for Machine Learning (MML) is an interdisciplinary group, developing state-of-the-art methods for parameter identification in neural differential equations with applications in science-informed neural networks and inverse problems.

#### Mathematical Oncology

Mathematical Oncology is an interdisciplinary collaboration to develop direct and inverse mathematical models for brain cancer growth, making use of AI for applications in healthcare.

### Additional research

In addition to the projects that can be read more about via the links above, my research has the following focus:

#### Image processing

I have collaborated with several different researchers for a long time to study mathematical models in image processing and computer vision where we have proposed (a) Various optimization models for image enhancement (b) Generalization of the p-Laplace operator for noise reduction.

#### Telecommunications

Here I have studied the problem of reconstructing 3D objects using Wi-Fi signals, AI, and Compressed Sensing.

#### Inverse and Ill-Posed Problems: Theory and Algorithms

This project constitutes the mathematical core of my research areas that I have continued to develop and generalize both theory and methods applied to ODE and PDE, which are the mathematical models in the research areas listed above.

### Research in Mathematics at ITN

Mathematical research is conducted in several areas such as inverse problems with applications in machine learning, medicine, and image processing. As well as computational science, harmonic analysis, integrable systems, and potential theory.

## Organisation

### Physics, Electronics and Mathematics

We conduct research and research education in communication electronics, mathematics, engineering didactics, physical electronics and nanotechnology.

### Department of Science and Technology (ITN)

We research and teach in several technical and scientific disciplines in which our main areas are organic electronics, media, communications and logistics.