Pierre-Nicholas Roy, Department of Chemistry, University of Waterloo - February 11th 2021
3:30 p.m. talk
Quantum Molecular Dynamics
Molecular assemblies are often described using classical concepts and simulated using Newtonian dynamics or Classical Monte Carlo methods. At low temperatures, this classical description fails to capture the nature of the dynamics of molecules, and a quantum description is required in order to explain and predict the outcome of experiments. We will present mathematical formalisms and simulation algorithms for the study of nano-confined systems. For instance, the Feynman path integral formulation of quantum statistical mechanics is a very powerful tool that is amenable to large-scale simulations . We will show how path integral simulations can be used to predict the properties of molecular rotors trapped in superfluid helium and hydrogen clusters . We will demonstrate that microscopic Andronikashvili experiments can be viewed as a measurement of superfluidity in a quantum mechanical frame of reference . Issues such as quantization in curved spaces will be addressed. The estimation of entanglement measures in Quantum Monte Carlo simulations will be discussed  and applied to confined molecular rotors . Such systems can be realized using molecules confined in endohedral fullerene materials such as H2O@C60 and HF@C60 in peapods assemblies. These systems will be used as a platform to assess the relative merits of many- body wavefunction representations based on path integrals , truncated product bases , matrix product states , and other possibilities such as Restricted Boltzmann Machines .
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 T. Sahoo and D. Iouchtchenko and C. Herdman and P.-N. Roy, J. Chem. Phys. 152 184113 (2020)  I. J. De Vlugt and D. Iouchtchenko and E. Merali and P.-N. Roy and R. G. Melko, Phys. Rev. B 102 035108 (2020)
Samuel Wong - University of Waterloo - January 14th 2021
3:30 p.m. talk
Inference of Dynamic Systems from Noisy and Sparse Data via Manifold-constrained Gaussian Processes
Ordinary differential equations are a ubiquitous tool for modeling behaviors in science, such as gene regulation, epidemics and ecology. An important problem is to infer and characterize the uncertainty of parameters that govern the equations. In this talk I will present an accurate and fast inference method using manifold-constrained Gaussian processes, such that the derivatives of the Gaussian process must satisfy the dynamics of the differential equations. Our method completely avoids the use of numerical integration and is thus fast to compute. Our construction is embedded in a principled statistical framework and is demonstrated to yield fast and reliable inference in a variety of practical problems, including when a system component is unobserved.
This is joint work with Shihao Yang (Georgia Tech) and Samuel Kou (Harvard).
Kimon Fountoulakis - Cheriton School of Computer Science - December 10th 2021
3:30 p.m. talk
Advanced Diffusion Methods on Large Graphs
Diffusion is defined as the generic process of spreading mass among vertices by sending mass along edges of a graph. A plethora of real-world applications require the utilization of diffusion methods, e.g., online search, recommendation systems and fraud detection to name a few. Due to the increased size and complexity of real graphs, fast and accurate diffusion algorithms are in need. The new algorithms should have strongly-local running time, i.e., their running time depends on the size of the output instead of the size of the graph, they should be expansive, i.e., they should only require a single seed node as input. In this talk, we will discuss state-of-the-art local spectral-, flow-based and p-norm diffusion methods that are specialized in finding small-scale clusters in large graphs without accessing the whole graph. We will discuss worst- and average-case theoretical results and we will demonstrate their empirical performance