Ellen Lindqvist will present her master thesis with title "Data Assimilation and Physics-Informed Neural Networks for Parameter Estimation in Diffusion Problems"

Abstract:

Partial Differential Equations (PDEs) are frequently used in engineering and science to model physical phenomena. This thesis explores the use of Physics-Informed Neural Networks (PINNs), a deep learning framework that incorporates the underlying PDEs into the training process, enabling the estimation of unknown model parameters. The focus is on solving inverse problems related to diffusion equations, where the goal is to infer spatially or temporally varying parameters from limited and noisy data. The study compares PINNs with traditional methods such as the Kalman filter and investigates their performance under varying data quality, noise levels, and parameter complexity. Results show that PINNs can provide accurate estimates, especially when data is sparse, and offer a flexible alternative to classical data assimilation techniques. The work highlights both strengths and limitations of PINNs and provides insights into their practical applicability in real-world settings.

Examiner:

Mikael Nilsson, Centre for Mathematical Sciences, Lund University

Supervisors:

Alexandros Sopasakis, Centre for Mathematical Sciences, Lund University

Donglin Liu, Centre for Mathematical Sciences, Lund University