Dr. Nat Trask research focuses on integrating physical and mathematical structure into machine learning architectures, providing mathematically rigorous pathways for developing AI-driven tools. The techniques primarily draw from concepts in exterior calculus and geometric/variational mechanics, offering a means to extract models applicable in extreme physics settings where deriving solutions from first-principles models is intractable. He has a particular interest in the relationship between graph neural networks and traditional finite element discretizations of continuum models. Using these techniques, he constructs probabilistic digital twins and performs autonomous scientific discovery, with applications spanning combustion, energy storage, climate simulation, fusion power, multiphase flows, fracture, and soft matter.