Structured deep learning with applications in astrophysics

This work explores structured deep learning algorithms through geometric, temporal, and other inductive biases, as well as their applications in astrophysics. The first part of the thesis first contributes a self-supervised algorithm for time-series particle filter models, effective when data is noisy or underlying dynamics are unknown. This method performs exact inference while allowing integration of expert scientific knowledge. Next, geometric algebra-based neural networks are introduced for modeling dynamical systems, successfully learning transformation laws in areas like rigid body dynamics and fluid mechanics simulations. Third, Clifford Group-Equivariant Neural Networks are proposed for group-equivariant representation learning. Their general framework is applicable to problems in various dimensions and symmetry groups, including the Lorentz group used in relativistic astrophysics. Finally, Rolling Diffusion Models are presented for learning generative models of time-series data, such as video or scientific simulations, showing improved performance with complex temporal dynamics.
In the second part, we introduce a deep learning-backed algorithm for hunting transient radio sources autonomously. It processes imaged radio interferometric data from LOFAR's AARTFAAC system to produce catalogs of candidate transients. This addresses a methodological gap for low-frequency, high-noise, and high-dimensionality data. Finally, normalizing flows are used to infer gravitational wave parameters from LIGO and Virgo detector data.