Alan Muriithi

My research lies at the interface of inverse problems, optimisation, operator learning, and scientific machine learning. I develop mathematical foundations for learning-based methods in inverse problems and dynamical systems, with a particular focus on operator learning under imperfect forward models and model uncertainty.

My work studies how analytic structure from approximate physical models can be incorporated into learned operators and reconstruction algorithms to improve identifiability, stability, robustness, and generalisation. I am particularly interested in structural conditions that combine classical regularisation principles with modern learning-based approaches, ensuring that learned corrections remain consistent with the observable and stable components of the underlying inverse problem.

More broadly, I work on the mathematical analysis of optimisation algorithms, stochastic methods, and neural operators, with applications in computational imaging and scientific machine learning. My aim is to establish principled connections between inverse problems, optimisation theory, and modern machine learning, enabling reliable and mathematically grounded learning algorithms for scientific applications.