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In an earlier paper, we proved the validity of large deviations theory for the particle approximation of quite general chemical reaction networks (CRNs). In this paper, we extend its scope and present a more geometric insight into the…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
We summarize our recent efforts to develop the Density Matrix Renormalization Group (DMRG) method into a practical truncation strategy for large-scale nuclear shell model calculations. Following an overview of the essential features of the…
Machine-learning generative methods for material design are constructed by representing a given chemical structure, either a solid or a molecule, over appropriate atomic features, generally called structural descriptors. These must be fully…
Contemporary graph learning algorithms are not well-defined for large molecules since they do not consider the hierarchical interactions among the atoms, which are essential to determine the molecular properties of macromolecules. In this…
Restricted Boltzmann Machines (RBM) are simple statistical models defined on a bipartite graph which have been successfully used in studying more complicated many-body systems, both classical and quantum. In this work, we exploit the…
In this work we apply methods for describing 3D images to the problem of encoding atomic environments in a way that is invariant to rotations, translations, and permutations of the atoms and, crucially, can be decoded back into the original…
Radon transform is a type of transform which is used in image processing to transfer the image into intercept-slope coordinate. Its diagonal properties made it appropriate for some applications which need processes in different degrees.…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
We introduce mapping-variable ring polymer molecular dynamics (MV-RPMD), a model dynamics for the direct simulation of multi-electron processes. An extension of the RPMD idea, this method is based on an exact, imaginary time path-integral…
Finding complex reaction and transformation pathways, involving many intermediate states, is in general not possible on the DFT level with existing simulation methods due to the very large number of required energy and force evaluations.…
Coverage path planning in a generic known environment is shown to be NP-hard. When the environment is unknown, it becomes more challenging as the robot is required to rely on its online map information built during coverage for planning its…
Robot path planning is difficult to solve due to the contradiction between optimality of results and complexity of algorithms, even in 2D environments. To find an optimal path, the algorithm needs to search all the state space, which costs…
We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…
Molecule property prediction is a fundamental problem for computer-aided drug discovery and materials science. Quantum-chemical simulations such as density functional theory (DFT) have been widely used for calculating the molecule…
Radio Environment Maps (REMs) have the potential to serve as an important enabler for intelligent modeling and control in emerging AI-native 6G networks. Despite significant progress, most REM construction methods remain passive, relying on…
Modern theories of phase transitions and scale-invariance are rooted in path integral formulation and renormalization group (RG). Despite the applicability of these approaches on simple systems with only pairwise interactions, they are less…
Modeling molecules as undirected graphs and chemical reactions as graph rewriting operations is a natural and convenient approach tom odeling chemistry. Graph grammar rules are most naturally employed to model elementary reactions like…
Nowaday, in study of effective interactions, more attention is devoted to single-particle properties of near-magic nuclei and bulk properties of deformed ones but quasiparticle states of the latter are rarely used so far because of…
The restricted Boltzmann machine (RBM) has been successfully applied to solve the many-electron Schr$\ddot{\text{o}}$dinger equation. In this work we propose a single-layer fully connected neural network adapted from RBM and apply it to…