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DOE OSTI2015

van der Waals bilayer energetics: Generalized stacking-fault energy of graphene, boron nitride, and graphene/boron nitride bilayers

The structure, thermodynamics, and band gaps in graphene/graphene, boron nitride/boron nitride, and graphene/boron nitride bilayers are determined using several different corrections to first-principles approaches to account for the dispersion interactions. While the density functional dispersion correction, van der Waals density functional, meta–generalized gradient approximation, and adiabatic fluctuation-dissipation theorem methods (ACFDT-RPA) all lead to qualitatively similar predictions, the best accuracy is obtained through the application of the computationally expensive ACFDT-RPA method. We present an accurate ACFDT-RPA-based method to determine bilayer structure, generalized stacking-fault energy (GSFE), and band gaps as a function of the relative translation states of the two layers. The GSFE data clearly identify all of the stable and metastable bilayer translations as well as the barriers between them. Furthermore, this is key for predicting the sliding, formation, and adhesion energies for homo- and hetero-bilayers, as well as for the determination of defects in such multilayer van der Waals systems. These, in turn, provide an accurate approach for determining and manipulating the spatial variation of electronic structure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

A deterministic verification strategy for electrostatic particle-in-cell algorithms in arbitrary spatial dimensions using the method of manufactured solutions

As simulations of kinetic plasmas continue to increase in scope and complexity, a rigorous and straightforward method for verifying particle-in-cell (PIC) implementations is necessary to ensure their correctness. Here, in this paper, we present a deterministic method for the rigorous verification of multidimensional, multispecies, electrostatic particle-in-cell codes based on the method of manufactured solutions. Specifically, we prove that rigorous verification is possible through the exclusive examination of errors of grid quantities (i.e., moments and/or fields), allowing for a very light-weight and non-intrusive implementation in existing PIC codes. This is a marked improvement over earlier PIC verification approaches (only demonstrated with one species in 1D-1V), which rely on the comparison of cumulative distribution functions, and are invasive on the code base, introduce additional stochastic noise, are significantly more computationally expensive, and lack rigorous convergence properties. Interestingly, we show that different grid quantities feature different rates of convergence with the number of particles and mesh size, impacting the verification process. These theoretical results are confirmed numerically with a multi-species 2D-2V particle-in-cell code, including the ability of the method to detect order reduction due to an incorrect implementation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

A Sparse Grid Method for Bayesian Uncertainty Quantification with Application to Large Eddy Simulation Turbulence Models

There is wide agreement that the accuracy of turbulence models suffer from their sensitivity with respect to physical input data, the uncertainties of user-elected parameters, as well as the model inadequacy. However, the application of Bayesian inference to systematically quantify the uncertainties in parameters, by means of exploring posterior probability density functions (PPDFs), has been hindered by the prohibitively daunting computational cost associated with the large number of model executions, in addition to daunting computation time per one turbulence simulation. In this effort, we perform in this paper an adaptive hierarchical sparse grid surrogate modeling approach to Bayesian inference of large eddy simulation (LES). First, an adaptive hierarchical sparse grid surrogate for the output of forward models is constructed using a relatively small number of model executions. Using such surrogate, the likelihood function can be rapidly evaluated at any point in the parameter space without simulating the computationally expensive LES model. This method is essentially similar to those developed in Zhang et al. (Water Resour Res 49:6871–6892, 2013) for geophysical and groundwater models, but is adjusted and applied here for a much more challenging problem of uncertainty quantification of turbulence models. Through a numerical demonstration of the Smagorinsky model of two-dimensional flow around a cylinder at sub-critical Reynolds number, our approach is proven to significantly reduce the number of costly LES executions without losing much accuracy in the posterior probability estimation. Here, the model parameters are calibrated against synthetic data related to the mean flow velocity and Reynolds stresses at different locations in the flow wake. The influence of the user-elected LES parameters on the quality of output data will be discussed.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2015

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗

DOE OSTI2026

Assessing the Limitations of Self-Interaction-Corrected Functionals for Describing the Hydrated Electron

Simulating the hydrated electron using density functional theory is challenging due to the prevalence of self-interaction error in standard functionals. Hybrid functionals like PBEh(40) can reasonably describe the chemistry of an excess electron in water and partially mitigate self-interaction error by incorporating exact Hartree–Fock exchange, but they are computationally expensive making them impractical for large-scale and long-time ab initio molecular dynamics simulations. Explicit self-interaction correction schemes that are applied on an orbital-by-orbital basis offer a potential alternative when the correction is limited to the singly occupied molecular orbital obtained with a generalized gradient approximation functional. Here, we examine whether the Perdew–Zunger self-interaction correction scheme applied to the revPBE functional can provide a computationally efficient and physically sensible alternative to PBEh(40) for the hydrated electron. We find that functionals incorporating a self-interaction correction scheme should be viewed with caution when applied to the hydrated electron and its reactivity. Furthermore, we show that it is critical to consider extensive sampling and diverse chemical environments when validating their performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Structure and dynamics of aqueous solutions from PBE-based first-principles molecular dynamics simulations

Establishing an accurate and predictive computational framework for the description of complex aqueous solutions is an ongoing challenge for density functional theory based first-principles molecular dynamics (FPMD) simulations. In this context, important advances have been made in recent years, including the development of sophisticated exchange-correlation functionals. On the other hand, simulations based on simple generalized gradient approximation (GGA) functionals remain an active field, particularly in the study of complex aqueous solutions due to a good balance between the accuracy, computational expense, and the applicability to a wide range of systems. In such simulations we often perform them at elevated temperatures to artificially “correct” for GGA inaccuracies in the description of liquid water; however, a detailed understanding of how the choice of temperature affects the structure and dynamics of other components, such as solvated ions, is largely unknown. In order to address this question, we carried out a series of FPMD simulations at temperatures ranging from 300 to 460 K for liquid water and three representative aqueous solutions containing solvated Na + , K + , and Cl - ions. We show that simulations at 390–400 K with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional yield water structure and dynamics in good agreement with experiments at ambient conditions. Simultaneously, this computational setup provides ion solvation structures and ion effects on water dynamics consistent with experiments. These results suggest that an elevated temperature around 390–400 K with the PBE functional can be used for the description of structural and dynamical properties of liquid water and complex solutions with solvated ions at ambient conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

MICCO: An Enhanced Multi-GPU Scheduling Framework for Many-Body Correlation Functions

Calculation of many-body correlation functions is one of the critical kernels utilized in many scientific computing areas, especially in Lattice Quantum Chromodynamics (Lattice QCD). It is formalized as a sum of a large number of contraction terms each of which can be represented by a graph consisting of vertices describing quarks inside a hadron node and edges designating quark propagations at specific time intervals. Due to its computation- and memory-intensive nature, real-world physics systems (e.g., multi-meson or multi-baryon systems) explored by Lattice QCD prefer to leverage multi-GPUs. Different from general graph processing, many-body correlation function calculations show two specific features: a large number of computation-/data-intensive kernels and frequently repeated appearances of original and intermediate data. The former results in expensive memory operations such as tensor movements and evictions. The latter offers data reuse opportunities to mitigate the data-intensive nature of many-body correlation function calculations. However, existing graph-based multi-GPU schedulers cannot capture these data-centric features, thus resulting in a sub-optimal performance for many-body correlation function calculations. To address this issue, this paper presents a multi-GPU scheduling framework, MICCO, to accelerate contractions for correlation functions particularly by taking the data dimension (e.g., data reuse and data eviction) into account. This work first performs a comprehensive study on the interplay of data reuse and load balance, and designs two new concepts: local reuse pattern and reuse bound to study the opportunity of achieving the optimal trade-off between them. Based on this study, MICCO proposes a heuristic scheduling algorithm and a machine-learning-based regression model to generate the optimal setting of reuse bounds. Specifically, MICCO is integrated into a real-world Lattice QCD system, Redstar, for the first time running on multiple GPUs. The evaluation demonstrates MICCO outperforms other state-of-art works, achieving up to 2.25× speedup in synthesized datasets, and 1.49× speedup in real-world correlation functions.

Wang, Qihan↗

DOE OSTI2021

Deep Learning Explicit Differentiable Predictive Control Laws for Buildings

We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear model predictive control (MPC). Contrary to approximate MPC, DPC does not require supervision by an expert controller. Instead, a system dynamics model is learned from a small dataset of recorded observations of the perturbed system's dynamics and the control law is optimized offline by interaction with the learned system model. The DPC method is based on two sequential steps, i) system identification using a constrained neural state-space model, and ii) optimization of an explicit control law parametrized by another neural network in closed-loop simulation with the identified neural state-space model. The combination of a differentiable closed-loop system and penalty methods for constraint handling of system outputs and inputs allows us to optimize the control law's parameters directly by backpropagating economic MPC loss through the learned system model. By incorporating domain knowledge and leveraging established techniques from optimal control, our method leverages deep neural networks as nonlinear function approximators for system identification and control while avoiding concomitant costs of intractably large datasets, and computationally expensive over-parametrized models. The scalability, data efficiency, and constrained optimal control capability of the proposed DPC method are demonstrated in simulation using a multi-zone building emulator.

Drgona, Jan↗

DOE OSTI2025

Nonunitary Variational Quantum Eigensolver with the Localized Active Space Method and Cost Mitigation

Accurately describing strongly correlated systems with affordable quantum resources remains a central challenge for quantum chemistry applications on near and intermediate term quantum computers. The localized active space self-consistent field (LASSCF) approximates the complete active space self-consistent field (CASSCF) by generating active space-based wave functions within specific fragments while treating interfragment correlation with mean-field approach, hence is computationally less expensive. Hardware-efficient ansatzes (HEA) offer affordable and shallower circuits, yet they often fail to capture the necessary correlation. Previously, Jastrow-factor-inspired nonunitary qubit operators were proposed to use with HEA for variational quantum eigensolver (VQE) calculations (so-called nuVQE), as they do not increase circuit depths and recover correlation beyond the mean-field level for Hartree–Fock initial states. Here, in this study, we explore running nuVQE with LASSCF as the initial state. The method, named LAS-nuVQE, is shown to recover interfragment correlations, reach chemical accuracy with a small number of gates (<70) in both H 4 and square cyclobutadiene (C 4 H 4 ), and produces more accurate energetics than its HEA counterparts at all circuit depths. To further address the inherent symmetry-breaking in HEA, we implemented spin-constrained LAS-nuVQE to extend the capabilities of HEA further and show spin-pure results for square cyclobutadiene. We also mitigate the increased measurement overhead of nuVQE via Pauli grouping and shot-frugal sampling, reducing measurement costs by up to 2 orders of magnitude compared to ungrouped operator, and show that one can achieve better accuracy with a small number of shots (10 3–4 ) per one expectation value calculation compared to noiseless simulations with one or two orders of magnitude more shots. Finally, wall clock time estimates show that, with our measurement mitigation protocols, nuVQE becomes a cheaper and more accurate alternative than vanilla VQE with HEA. Taken together, these developments illustrate a practical pathway toward performing multireference chemical simulations with accuracy and affordable resources on today’s quantum hardware, achieving both accuracy and affordability in challenging correlated systems.

Wang, Qiaohong [Univ. of Chicago, IL (United State↗

DOE OSTI2023

Combining protein sequences and structures with transformers and equivariant graph neural networks to predict protein function

Abstract Motivation Millions of protein sequences have been generated by numerous genome and transcriptome sequencing projects. However, experimentally determining the function of the proteins is still a time consuming, low-throughput, and expensive process, leading to a large protein sequence-function gap. Therefore, it is important to develop computational methods to accurately predict protein function to fill the gap. Even though many methods have been developed to use protein sequences as input to predict function, much fewer methods leverage protein structures in protein function prediction because there was lack of accurate protein structures for most proteins until recently. Results We developed TransFun—a method using a transformer-based protein language model and 3D-equivariant graph neural networks to distill information from both protein sequences and structures to predict protein function. It extracts feature embeddings from protein sequences using a pre-trained protein language model (ESM) via transfer learning and combines them with 3D structures of proteins predicted by AlphaFold2 through equivariant graph neural networks. Benchmarked on the CAFA3 test dataset and a new test dataset, TransFun outperforms several state-of-the-art methods, indicating that the language model and 3D-equivariant graph neural networks are effective methods to leverage protein sequences and structures to improve protein function prediction. Combining TransFun predictions and sequence similarity-based predictions can further increase prediction accuracy. Availability and implementation The source code of TransFun is available at https://github.com/jianlin-cheng/TransFun.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2016

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

42 ENGINEERING↗

DOE OSTI2022

Real-space density kernel method for Kohn–Sham density functional theory calculations at high temperature

Kohn–Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. In this work, we present a density matrix based method for Kohn–Sham calculations at high temperatures that eliminates the need for diagonalization entirely, thus reducing the cost of such calculations significantly. Specifically, we develop real-space expressions for the electron density, electronic free energy, Hellmann–Feynman forces, and Hellmann–Feynman stress tensor in terms of an orthonormal auxiliary orbital basis and its density kernel transform, the density kernel being the matrix representation of the density operator in the auxiliary basis. Using Chebyshev filtering to generate the auxiliary basis, we next develop an approach akin to Clenshaw–Curtis spectral quadrature to calculate the individual columns of the density kernel based on the Fermi operator expansion in Chebyshev polynomials and employ a similar approach to evaluate band structure and entropic energy components. We implement the proposed formulation in the SPARC electronic structure code, using which we show systematic convergence of the aforementioned quantities to exact diagonalization results, and obtain significant speedups relative to conventional diagonalization based methods. Finally, we employ the new method to compute the self-diffusion coefficient and viscosity of aluminum at 116 045 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Boltzmann-conserving classical dynamics in quantum time-correlation functions: “Matsubara dynamics”

We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or “classical Wigner approximation”) results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their “Matsubara” values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ{sup 2} at ħ{sup 0} (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting “Matsubara” dynamics is inherently classical (since all terms O(ħ{sup 2}) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

EnZymClass: Substrate specificity prediction tool of plant acyl-ACP thioesterases based on ensemble learning

Characterizing the functional properties of plant acyl-ACP thioesterases (TEs), a key enzyme class used in the production of renewable oleochemicals in microbial hosts, experimentally, can be an expensive and time consuming process since it requires manual screening of thousands of candidates in a database. Using amino acid sequence to computationally predict an enzyme’s function might accelerate this process; however obtaining the necessary amount of information on previously characterized enzymes and their respective sequences required by standard Machine Learning (ML) based approaches to accurately infer sequence-function relationships can be prohibitive, especially with a low-throughput testing cycle. Experimental noise, unbalanced dataset where high sequence similarity does not always imply identical functional properties will further prevent robust prediction performance. Herein we present a ML method, Ensemble method for enZyme Classification (EnZymClass), that is specifically designed to address these issues. We used EnZymClass to classify TEs into short, long and mixed free fatty acid substrate specificity categories. While general guidelines for inferring substrate specificity have been proposed before, prediction of chain-length preference from primary sequence has remained elusive for plant acyl-ACP TEs. By applying EnZymClass to a subset of TEs in the ThYme database, we identified two medium chain TEs, ClFatB3 and CwFatB2, with previously uncharacterized activity in E. coli fatty acid production hosts.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

deeprob/ThioesteraseEnzymeSpecificity: EnZymClass-first-release

Banerjee, Deepro↗

DOE OSTI2017

Galactos: computing the anisotropic 3-point correlation function for 2 billion galaxies

The nature of dark energy and the complete theory of gravity are two central questions currently facing cosmology. A vital tool for addressing them is the 3-point correlation function (3PCF), which probes deviations from a spatially random distribution of galaxies. However, the 3PCF's formidable computational expense has prevented its application to astronomical surveys comprising millions to billions of galaxies. We present Galactos, a high-performance implementation of a novel, O( N 2 ) algorithm that uses a load-balanced k-d tree and spherical harmonic expansions to compute the anisotropic 3PCF. Our implementation is optimized for the Intel Xeon Phi architecture, exploiting SIMD parallelism, instruction and thread concurrency, and significant L1 and L2 cache reuse, reaching 39% of peak performance on a single node. Galactos scales to the full Cori system, achieving 9.8 PF (peak) and 5.06 PF (sustained) across 9636 nodes, making the 3PCF easily computable for all galaxies in the observable universe.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

2024 Second Half Semi Annual Report: Modeling plasticity-mediated flow in metals with pressurized cavities

The objective is to better predict the bulk-scale mechanical behavior of porous metals that have over pressurized cavities (e.g., irradiated metals with helium bubbles) by quantifying the complex coupling among cavity aspects (e.g., size distribution, inhomogeneous overpressure values, spatial arrangement) and metal properties (e.g., rate-dependency, crystallographic lattice). This requires up-scaling local mechanical fields from the single crystal scale and will be accomplished using a homogenization approach that combines full-field numerical simulations, analytical formalisms, and physics-informed machine learning to produce symbolically-defined constitutive equations (e.g., gauge functions). These equations will satisfy the objective because they enable computationally efficient predictions that approach the accuracy of computationally expensive full-field numerical simulations, abide by theoretical requirements (e.g., conservation of energy, work conjugacy), and retain the transparency of analytical models.

36 MATERIALS SCIENCE↗

NASA NTRS1991

Depth-size tradeoffs for neural computation

The tradeoffs between the depth (i.e., the time for parallel computation) and the size (i.e., the number of threshold gates) in neural networks are studied. The authors focus the study on the neural computations of symmetric Boolean functions and some arithmetic functions. It is shown that a significant reduction in the size is possible for symmetric functions and some arithmetic functions, at the expense of a small constant increase in depth. In the process, several neural networks which have the minimum size among all the known constructions have been developed. Results on implementing symmetric functions can be used to improve results about arbitrary Boolean functions. In particular, It is shown that any Boolean function can be computed in a depth-3 neural network with O(2n/2) threshold gates; it is also proven that a minimum number of threshold gates are required.

Siu, Kai-Yeung↗