Master's Thesis, 30-45 HP: Scientific Machine Learning for Physics-Informed Inverse Problems in SAR imaging

Scientific machine learning (SciML) is an emerging discipline that integrates learned algorithms with physical laws and domain knowledge, enabled through multiple core areas within scientific computing. SciML tackles several well-known issues in ML related to, e.g., model accuracy, efficiency, and interpretability. SciML is fundamentally connected to inverse problems that naturally arise in synthetic aperture radar (SAR) imaging, where many key challenges are related to the notion of ill-posedness. SAR systems generate high-resolution imagery, by emitting microwave pulses by processing the returned echoes. To reconstruct an image from observed raw data (complex phase histories) is a highly ill-posed inverse problem. In this project, you will develop high-performance computing (HPC) simulation tools from SciML, in the context of electromagnetic wave scattering problems that arise in SAR imaging. Radar wave imaging is of critical importance to, e.g., situational awareness and threat detection. It amounts to solving an inverse problem, where, given some output observations (e.g., raw sensor data), one tries to uncover the latent (hidden) signals (e.g., image) that produced that data. The corresponding forward model is a simulation method, typically based on a mathematical representation (e.g., partial differential equation) that, given a set of inputs, produces or predicts observations. Inverse problems are typically ill-posed, i.e., their solutions are highly unstable with respect to small changes in the observed data. Addressing ill-posedness is key for the development of robust inverse reconstruction methods that form the backbone in many applications, such as SAR imaging. The main challenge is to develop reconstruction methods that have significantly better performance while being computationally feasible, bearing in mind the time-critical nature of common radar applications.