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While recent work towards the development of tight-binding and ab-initio algorithms has focused on molecular dynamics, Monte Carlo methods can often lead to better results with relatively little effort. We present here a multi-step Monte…
Theory can provide important support at all the stages of spectroscopic experiments, from planning the measurements to the interpretation of the results. Such support is particularly valuable for the challenging experiments on heavy,…
We present an extension of constrained-path auxiliary-field quantum Monte Carlo (CP-AFQMC) for the treatment of correlated electronic systems coupled to phonons. The algorithm follows the standard CP-AFQMC approach for description of the…
Electronic nearsightedness is one of the fundamental principles governing the behavior of condensed matter and supporting its description in terms of local entities such as chemical bonds. Locality also underlies the tremendous success of…
Recently, a class of efficient spectral Monte-Carlo methods was developed in \cite{Feng2025ExponentiallyAS} for solving fractional Poisson equations. These methods fully consider the low regularity of the solution near boundaries and…
This work investigates Kolmogorov-Arnold network-based wavefunction ansatz as viable representations for quantum Monte Carlo simulations. Through systematic analysis of one-dimensional model systems, we evaluate their computational…
With the recently emerging global interest in building a next generation of circular electron-positron colliders to study the properties of the Higgs boson, and other important topics in particle physics at ultra-high beam energies, it is…
Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant developments in the past decades and become one of the go-to methods when accurate ground state energy of molecules and materials is needed. The remaining…
Recent advancements in equivariant deep models have shown promise in accurately predicting atomic potentials and force fields in molecular dynamics simulations. Using spherical harmonics (SH) and tensor products (TP), these equivariant…
A one-electron Schroedinger equation based on special one-electron potentials for atoms is shown to exist that produces orbitals for an arbitrary molecule that are sufficiently accurate to be used without modification to construct single-…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…
Estimating the trace of the inverse of a large matrix is an important problem in lattice quantum chromodynamics. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials for the levels. The…
The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of conditional…
The auxiliary-field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time-independent Schroedinger equation in atoms, molecules, solids, and a variety of model systems. AFQMC has recently witnessed…
We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a…
We introduce a constrained energy functional to describe dielectric response. We demonstrate that the local functional is a generalization of the long ranged Marcus energy. Our re-formulation is used to implement a cluster Monte Carlo…
Machine-learned interatomic potentials enable large systems to be simulated for long time scales at near ab-initio accuracy. This accuracy is achieved by fitting extremely flexible model architectures to high quality reference data. In…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…
We derive many-body single- and multi-reference wave functions for quantum Monte Carlo of periodic systems with an anti-symmetric portion that explicitly integrates over the Brillouin zone of one-particle Bloch states. The wave functions…