Molecular simulations serve as fundamental tools for understanding and predicting the system of interest at atomic level. It is significant for applications like drug and material discovery, but often cannot scale to real-world problems due to the computational bottleneck. In this seminar, I will briefly introduce this area and recent machine learning algorithms that have shown great promise in accelerating the molecular simulations. I will also introduce some of my recent research in this direction. First work is about structure prediction of metal-organic frameworks using geometric flow matching (or neural ODE on SO(3) manifolds) and (2) simulating chemical reactions / transition paths through RL-like training of diffusion models (or log-divergence minimization between path measures).
The concept of p-th variation of a real-valued continuous function along a general class of refining sequence of partitions is presented. We show that the finiteness of the p-th variation of a given function is closely related to the finiteness of ℓp-norm of the coefficients along a Schauder basis, similar to the fact that Hölder coefficient of the function is connected to ℓ∞-norm of the Schauder coefficients. This result provides an isomorphism between the space of α-Hölder continuous functions with finite (generalized) p-th variation along a given partition sequence and a subclass of infinite-dimensional matrices equipped with an appropriate norm, in the spirit of Ciesielski.
