My research focuses on two complementary approaches to tackle the fundamental open problems of the Standard Model of particle physics. First, I develop models beyond the Standard Model to explain the mysteries of the small neutrino masses and the strong CP problem. For this, I combine and transfer knowledge on non-perturbative topological phenomena between QCD, gravity, and neutrino physics, with substantial implications for late-time cosmology. Second, I explore numerical lattice techniques based on lattice QCD, tensor networks, deep learning, and quantum computing. While most of these techniques currently focus on lower-dimensional theories, my long-term goal is to apply them to study non-perturbative phenomena in the 3+1 dimensional Standard Model and beyond.