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DOE OSTI2024

A hybrid Monte Carlo, discontinuous Galerkin method for linear kinetic transport equations

Here we present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise constant solution and the discrete ordinates use bilinear discontinuous finite elements. From the hybridization of the problem, the resulting problem solved by Monte Carlo is scattering free, resulting in a simple, efficient solution procedure. Between time steps, we use a projection approach to “relabel” collided particles as uncollided particles. In conclusion, from a series of standard 2-D Cartesian test problems we observe that our hybrid method has improved accuracy and reduction in computational complexity of approximately an order of magnitude relative to standard discrete ordinates solutions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Interaction-expansion inchworm Monte Carlo solver for lattice and impurity models

Multiorbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications, including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. We generalize the inchworm quantum Monte Carlo method to the interaction expansion, and we explore its application to typical single- and multiorbital problems encountered in investigations of impurity and lattice models. Our implementation generically outperforms bare and bold-line quantum Monte Carlo algorithms in the interaction expansion. For the systems studied here, our implementation remains inferior to the more specialized hybridization expansion and auxiliary field algorithms. So, the problem of convergence to unphysical fixed points, which hampers so-called bold-line methods, is not encountered in inchworm Monte Carlo.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Integrating machine learning interatomic potentials with hybrid reverse Monte Carlo structure refinements in RMCProfile

Structure refinement with reverse Monte Carlo (RMC) is a powerful tool for interpreting experimental diffraction data. To ensure that the under-constrained RMC algorithm yields reasonable results, the hybrid RMC approach applies interatomic potentials to obtain solutions that are both physically sensible and in agreement with experiment. To expand the range of materials that can be studied with hybrid RMC, we have implemented a new interatomic potential constraint in RMCProfile that grants flexibility to apply potentials supported by the Large-scale Atomic/Molecular Massively Parallel Simulator ( LAMMPS ) molecular dynamics code. This includes machine learning interatomic potentials, which provide a pathway to applying hybrid RMC to materials without currently available interatomic potentials. To this end, we present a methodology to use RMC to train machine learning interatomic potentials for hybrid RMC applications.

Cuillier, Paul↗

DOE OSTI2024

SmoQyDQMC.jl: A flexible implementation of determinant quantum Monte Carlo for Hubbard and electron-phonon interactions

We introduce the SmoQyDQMC.jl package, a Julia implementation of the determinant quantum Monte Carlo algorithm. SmoQyDQMC.jl supports generalized tight-binding Hamiltonians with on-site Hubbard and generalized electron-phonon ( e e -ph) interactions, including non-linear e e -ph coupling and anharmonic lattice potentials. Our implementation uses hybrid Monte Carlo methods with exact forces for sampling the phonon fields, enabling efficient simulation of low-energy phonon branches, including acoustic phonons. The SmoQyDQMC.jl package also uses a flexible scripting interface, allowing users to adapt it to different workflows and interface with other software packages in the Julia ecosystem. The code for this package can be downloaded from our GitHub repository at https://github.com/SmoQySuite/SmoQyDQMC.jl or installed using the Julia package manager. The online documentation, including examples, can be obtained from our document page at https://smoqysuite.github.io/SmoQyDQMC.jl/stable/.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Codebase release r0.3 for SmoQyDQMC.jl

Cohen-Stead, Benjamin (ORCID:0000000279156280)↗

DOE OSTI2021

The XFaster Power Spectrum and Likelihood Estimator for the Analysis of Cosmic Microwave Background Maps

We present the XFaster analysis package, XFaster is a fast, iterative angular power spectrum estimator based on a diagonal approximation to the quadratic Fisher matrix estimator. XFaster uses Monte Carlo simulations to compute noise biases and filter transfer functions and is thus a hybrid of both Monte Carlo and quadratic estimator methods. In contrast to conventional pseudo-C ℓ based methods, the algorithm described here requires a minimal number of simulations, and does not require them to be precisely representative of the data to estimate accurate covariance matrices for the bandpowers. The formalism works with polarization-sensitive observations and also data sets with identical, partially overlapping, or independent survey regions. The method was first implemented for the analysis of BOOMERanG data (Netterfield et al. 2002; Jones et al. 2006), and also used as part of the Planck analysis (Rocha et al. 2011). Here, we describe the full, publicly available analysis package, written in Python, as developed for the analysis of data from the 2015 flight of the SPIDER instrument (SPIDER Collaboration 2021). The package includes extensions for self-consistently estimating null spectra and for estimating fits for Galactic foreground contributions. We show results from the extensive validation of XFaster using simulations, and its application to the SPIDER data set.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Optimization Stability in Excited-State-Specific Variational Monte Carlo

Here, we investigate the issue of optimization stability in variance-based state-specific variational Monte Carlo, discussing the roles of the objective function, the complexity of wave function ansatz, the amount of sampling effort, and the choice of minimization algorithm. Using a small cyanine dye molecule as a test case, we systematically perform minimizations using variants of the linear method as both a standalone algorithm and in a hybrid combination with accelerated descent. We demonstrate that adaptive step control is crucial for maintaining the linear method's stability when optimizing complicated wave functions and that the hybrid method enjoys both greater stability and minimization performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Reinforcement learning based hybrid bond-order coarse-grained interatomic potentials for exploring mesoscale aggregation in liquid–liquid mixtures

Exploring mesoscopic physical phenomena has always been a challenge for brute-force all-atom molecular dynamics simulations. Although recent advances in computing hardware have improved the accessible length scales, reaching mesoscopic timescales is still a significant bottleneck. Coarse-graining of all-atom models allows robust investigation of mesoscale physics with a reduced spatial and temporal resolution but preserves desired structural features of molecules, unlike continuum-based methods. Here, we present a hybrid bond-order coarse-grained forcefield (HyCG) for modeling mesoscale aggregation phenomena in liquid–liquid mixtures. The intuitive hybrid functional form of the potential offers interpretability to our model, unlike many machine learning based interatomic potentials. We parameterize the potential with the continuous action Monte Carlo Tree Search (cMCTS) algorithm, a reinforcement learning (RL) based global optimizing scheme, using training data from all-atom simulations. The resulting RL-HyCG correctly describes mesoscale critical fluctuations in binary liquid–liquid extraction systems. cMCTS, the RL algorithm, accurately captures the mean behavior of various geometrical properties of the molecule of interest, which were excluded from the training set. The developed potential model along with the RL-based training workflow could be applied to explore a variety of other mesoscale physical phenomena that are typically inaccessible to all-atom molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Velocity-Space Hybridization of Direct Simulation Monte Carlo and a Quasi-Particle Boltzmann Solver

This paper presents a new method for modeling rarefied gas flows based on hybridization of direct simulation Monte Carlo (DSMC) and discrete velocity method (DVM)-based quasi-particle representations of the velocity distribution function. It is aimed at improving the resolution of the tails of the distribution function (compared with DSMC) and computational efficiency (compared with DVM). Details of the method, such as the collision algorithm and the particle merging scheme, are discussed. The hybrid approach is applied to the study of noise in a Maxwellian distribution, computation of electron-impact ionization rate coefficient, as well as numerical simulation of a supersonic Couette flow. The hybrid-based solver is compared with pure DSMC and DVM approaches in terms of accuracy, computational speed, and memory use. It is shown that such a hybrid approach can provide a lower computational cost than a pure DVM approach, while being able to retain accuracy in modeling high-velocity tails of the distribution function. For problems where trace species have a significant impact on the flow physics, the proposed method is shown to be capable of providing better computational efficiency and accuracy compared with standard fixed-weight DSMC.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Application of Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Transport Problems

Determination of the components of a radioactive source/shield system using the system’s radiation signature is of great importance in homeland security, material safeguards, and waste management. Although significant progress has been made toward solving this inverse transport problem in recent years, work remains to be done to quantify the uncertainty in reconstructed results. In this article we apply two Markov chain Monte Carlo (MCMC) approaches, the delayed rejection adaptive metropolis (DRAM) and differential evolution adaptive metropolis (DREAM) methods, to solve inverse problems and quantify uncertainty. The DRAM method uses delayed rejection combined with global adaptation of the proposal covariance matrix. Furthermore, the DREAM method hybridizes MCMC sampling with the differential evolution (DE) algorithm. In numerical test cases, the DRAM and DREAM methods are shown to be superior to a first-order inverse Hessian approach for problems with noisy data and multiple unknown quantities, with DREAM converging to the posterior distribution more quickly than DRAM. The DREAM and DRAM results indicate that a full posterior distribution is required to quantify uncertainty in many inverse transport problems.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2021

Accelerated impurity solver for DMFT and its diagrammatic extensions

Here, we present ComCTQMC, a GPU accelerated quantum impurity solver. It uses the continuous-time quantum Monte Carlo (CTQMC) algorithm wherein the partition function is expanded in terms of the hybridisation function (CT-HYB). ComCTQMC supports both partition and worm-space measurements, and it uses improved estimators and the reduced density matrix to improve observable measurements whenever possible. ComCTQMC efficiently measures all one and two-particle Green's functions, all static observables which commute with the local Hamiltonian, and the occupation of each impurity orbital. ComCTQMC can solve complex-valued impurities with crystal fields that are hybridized to both fermionic and bosonic baths. Most importantly, ComCTQMC utilizes graphical processing units (GPUs), if available, to dramatically accelerate the CTQMC algorithm when the Hilbert space is sufficiently large. We demonstrate acceleration by a factor of over 600 (100) in a simulation of δ-Pu at 600 K with (without) crystal fields. In easier problems, the GPU offers less impressive acceleration or even decelerates the CTQMC. Here we describe the theory, algorithms, and structure used by ComCTQMC in order to achieve this set of features and level of acceleration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Bidding Curve Design for Hybrid Power Plants with Uncertain Solar Forecast: Preprint

This paper presents a novel bidding curve design algorithm tailored for hybrid power plants (HPPs) to participate in the wholesale electricity market. Utilizing forecasts for photovoltaic (PV) generation and available battery power, our algorithm strategically computes the bidding curve to maximize HPP profit while adeptly managing the inherent uncertainty associated with PV power generation. In addition, the introduction of the penalty cost in HPP bidding curves provides the system operator a tool to effectively manage the system-level uncertainty that caused by HPPs. Numerical analysis through Monte Carlo simulations confirms that our bidding curve methodology outperforms the benchmark across various scenarios.

bidding curve↗

DOE OSTI2025

Bidding Curve Design for Hybrid Power Plants with Uncertain Solar Forecast

bidding curve↗

DOE OSTI2022

Charge singlets and orbital-selective charge density wave transitions

The possibility of “orbitally selective Mott transitions” within a multiband Hubbard model, in which one orbital with large on-site electron-electron repulsion U 1 is insulating and another orbital, to which it is hybridized, with small U –1 , is metallic, is a problem of long-standing debate and investigation. In this paper we study an analogous phenomenon, the coexistence of metallic and insulating bands in a system of orbitals with different electron-phonon coupling. To this end, we examine two variants of the bilayer Holstein model: a uniform bilayer and a “Holstein-metal interface” where the electron-phonon coupling, λ, is zero in the “metallic” layer. In the uniform bilayer Holstein model, charge density wave (CDW) order dominates at small interlayer hybridization t 3 , but decreases and eventually vanishes as t 3 grows, providing a charge analog of singlet (spin liquid) physics. In the interface case, we show that CDW order penetrates into the metal layer and forms long-range CDW order at an intermediate ratio of inter- to intralayer hopping strengths, 1.4 ≲ t 3 /t ≲ 3.4. Furthermore, this is consistent with the occurrence of an “orbitally selective CDW” regime at weak t3 in which the layer with λ 1 ≠ 0 exhibits long-range charge order, but the “metallic layer” with λ –1 = 0, to which it is hybridized, does not.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Hybrid Particle Swarm-Interpolation Algorithm for Improved Critical Experiment Design

The typical goal of designing a critical experiment is twofold: a system that is both critical and optimized for some other value. This value could be an energy-integrated sensitivity, percent fissions in a certain energy range, or some other value that can be calculated by a transport code. By simulating different combinations of reflector, moderator, and fuel thicknesses a designer can identify such a desirable configuration. The domain of all possible combinations of these thicknesses is referred to as the experiment search space. As more dimensions are added, the search space increases in size exponentially. For a three-dimensional case, which includes three thickness values between zero and ten centimeters to the nearest tenth of a millimeter, a total of 1,000 3 , configurations exists. Rather than check each configuration individually, which would be extremely computationally expensive, it has been shown to be more efficient to use a conventional particle swarm optimization (PSO) algorithm to identify critical and optimal configurations. This work presents the theory and implementation of a novel hybrid PSO interpolation algorithm to perform these optimizations faster than a conventional PSO algorithm. To demonstrate this, an example optimization will be carried out by the conventional and hybrid PSO algorithms and their performances will be compared.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Impact of solvent forces and broken symmetry on the assembly of designed proteins at a liquid-solid interface

The era of protein design has enabled the creation of hybrid protein-inorganic interfaces, leading to both surface-directed self-assembly of de novo protein architectures and protein-directed formation of inorganic materials. However, the resulting patterns of protein assembly are often unexpected, implying that essential interactions are not accounted for in current design platforms. Here, we use high-speed atomic force microscopy (AFM) analyzed through machine learning to follow the assembly of protein nanorods in aqueous electrolytes on two types of mica exhibiting disparate symmetry elements, which are imprinted on the overlying hydration structure. Using Monte Carlo simulations, we reproduce the observed phases and show that an observed smectic phase, previously thought to be unstable for non-interacting rods in two dimensions, emerges when crystal symmetry introduces a directional bias. The findings demonstrate the importance of incorporating solvent forces as modulated by the hydration structure inherent to interfacial systems when designing protein assemblies at liquid-crystal interfaces. Coupling physics-based simulations that can account for these factors to de novo protein design algorithms can lead to improved design platforms for bio-inspired, hybrid materials.

bioinspired materials↗

DOE OSTI2023

Studying the hadron structure with PANDA and CLAS using machine learning techniques

The hadron spectroscopy and structure are currently very active fields of research to study the non-perturbative regime of quantum chronodynamics. The first one studies the complex structure of excited hadrons by looking at their decay products, while the latter uses lepton scattering on nucleons. Both methods require reconstruction algorithms with great efficiency and good particle identification and background rejection rates. This work aims to provide these by either improving the existing methods or developing new ones. The first part of this document presents a feasibility study of a predicted hybrid charmonium state for the PANDA experiment. Lattice QCD calculations predict the ground state hybrid charmonium to be a spin exotic with quantum numbers of JP C = 1?+ at a mass of around 4.3 GeV with a width to be around 20 MeV. A machine learning based data analysis scheme is proposed to further improve the signal efficiency and the background reduction, alongside with improvements of the analysis software (PandaRoot), that are vital for this study. These improvements include a reworked clustering algorithm for the electromagnetic calorimeter (EMC) and an optimized monte carlo matching for neutral particles. The second part of this document is about studying the proton structure. A multidimensional study of the structure function ratio Fsin(?)LU /FUU has been performed for K±, based on the measurement of beam-spin asymmetries. It uses the high statistics data recorded with the CLAS12 spectrometer at Jefferson Laboratory. Fsin(?)LU is a twist-3 quantity that provides information about the quark gluon correlations in the proton. This document will present for the first time a simultaneous analysis of two kaon channels over a large kinematic range of z, xB , PT and Q2 with virtualities Q2 ranging from 1 GeV2 up to 8 GeV2 using machine learning techniques for improved particle identification.

Kripko, Aron↗