Related papers: Structural analysis of a collective subspace in th…
We present the Gaussian process dynamical mixture model (GPDMM) and show its utility in single-example learning of human motion data. The Gaussian process dynamical model (GPDM) is a form of the Gaussian process latent variable model…
With the recent advances in machine learning for quantum chemistry, it is now possible to predict the chemical properties of compounds and to generate novel molecules. Existing generative models mostly use a string- or graph-based…
We investigate the landscape of the negative log-likelihood function of Gaussian Mixture Models (GMMs) with a general number of components in the population limit. As the objective function is non-convex, there can be multiple local minima…
We discuss the ability of the generator coordinate method (GCM) to select collective states in microscopic calculations. The model studied is a single-$j$ shell with hamiltonian containing the quadrupole-quadrupole interaction. Quadrupole…
Data-driven modeling is playing an increasing role in robotics and control, yet standard learning methods typically ignore the geometric structure of nonholonomic systems. As a consequence, the learned dynamics may violate the nonholonomic…
The dynamics of physical systems that require high-dimensional representation can often be captured in a few meaningful degrees of freedom called collective variables (CVs). However, identifying CVs is challenging and constitutes a…
The dynamic complexity of robots and mechatronic systems often pertains to the hybrid nature of dynamics, where governing equations consist of heterogenous equations that are switched depending on the state of the system. Legged robots and…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
In a scenario where the constituent quarks are composite systems, Generalized Parton Distributions (GPDs) are built from wave functions to be evaluated in a Constituent Quark Model (CQM), convoluted with the GPDs of the constituent quarks…
Sequential assembly with geometric primitives has drawn attention in robotics and 3D vision since it yields a practical blueprint to construct a target shape. However, due to its combinatorial property, a greedy method falls short of…
Generating a data set that is representative of the accessible configuration space of a molecular system is crucial for the robustness of machine learned interatomic potentials (MLIP). However, the complexity of molecular systems,…
This article presents a simplified version of the author's previous work. We first construct a causal growth process (CGP). We then form path Hilbert spaces using paths of varying lengths in the CGP. A sequence of positive operators on…
Kinetically constrained models (KCMs) are models of glass formers based on the concept of dynamic facilitation. This concept accounts for many of the characteristics of the glass transition. KCMs usually display a combination of simple…
In this paper we provide a method for constructing joint distributions for an arbitrary set of observables on finite dimensional Hilbert spaces irrespective of whether the observables commute or not. These distributions have a number of…
The Generalized Method of Moments (GMM) is a partition of unity based technique for solving electromagnetic and acoustic boundary integral equations. Past work on the GMM for electromagnetics was confined to geometries modeled by piecewise…
Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…
The design space of discrete-space diffusion or flow generative models are significantly less well-understood than their continuous-space counterparts, with many works focusing only on a simple masked construction. In this work, we aim to…
Multi-reference calculations along the lines of the Generator Coordinate Method or the restoration of broken symmetries within the nuclear Energy Density Functional (EDF) framework are becoming a standard tool in nuclear structure physics.…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
A computational approach via implementation of the Principle Component Analysis (PCA) and Gaussian Mixture (GM) clustering methods from Machine Learning (ML) algorithms to identify domain structures of supercooled liquids is developed. Raw…