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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

The expressivity of classical and quantum neural networks on entanglement entropy

Abstract Analytically continuing the von Neumann entropy from Rényi entropies is a challenging task in quantum field theory. While then-th Rényi entropy can be computed using the replica method in the path integral representation of quantum field theory, the analytic continuation can only be achieved for some simple systems on a case-by-case basis. In this work, we propose a general framework to tackle this problem using classical and quantum neural networks with supervised learning. We begin by studying several examples with known von Neumann entropy, where the input data is generated by representing$${\text {Tr}}\rho _A^n$$ Tr ρ A n with a generating function. We adopt KerasTuner to determine the optimal network architecture and hyperparameters with limited data. In addition, we frame a similar problem in terms of quantum machine learning models, where the expressivity of the quantum models for the entanglement entropy as a partial Fourier series is established. Our proposed methods can accurately predict the von Neumann and Rényi entropies numerically, highlighting the potential of deep learning techniques for solving problems in quantum information theory.

Physics↗
DOE OSTI2024

Nanoparticle self-assemblies with modern complexity

Thanks to decades of tireless efforts, nanoparticle assemblies have reached at an extremely high level of controllability, sophistication, and complexity, with new insights provided by integration with graph theory, cutting-edge characterization, and machine learning (ML)-based computation and modeling, as well as with ever-diversifying applications in energy, catalysis, biomedicine, optics, electronics, magnetics, organic biosynthesis, and quantum technology. Nanoparticle assemblies can be crystalline, known as superlattices or supracrystals. Their assembly entails a transition from disorder—dispersed nanoparticles—to order, which can be achieved through classical nucleation pathways or nonclassical pathways via prenucleation precursors or particle aggregation. Further, the periodic lattices allow facile manipulations of electrons, phonons, photons, and even spins, leading to advanced device components and metamaterials. Meanwhile, aperiodic assemblies out of nanoparticles, such as gels, networks, and amorphous solids, also start to attract attentions. Despite the loss of periodicity, symmetry-lowering or symmetry-breaking three-dimensional (3D) structures emerge with unique properties, such as chiroptical activity, topological mechanical strength, and quantum entanglement. Real-space imaging such as electron microscopy and X-ray based tomography methods are utilized to characterize these complex structures, while mathematical tools such as graph theories are in need to describe such complex structures. This issue aims to provide a timely review of the efforts in this greatly broadened materials design space including experiment, simulation, theory, and applications. Nine top experts (and their teams) from four countries deliver six review papers, summarizing fundamental mechanistic understandings of nanoparticle assemblies, highlighted with the developments of state-of-the-art in situ characterization tools and ML-assisted reverse engineering, and newly emergent applications of nanoarchitectures.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Convex Q-Learning in Continuous Time with Application to Dispatch of Distributed Energy Resources

Convex Q-learning is a recent approach to reinforcement learning, motivated by the possibility of a firmer theory for convergence, and the possibility of making use of greater a priori knowledge regarding policy or value function structure. This paper explores algorithm design in the continuous time domain, with a finite-horizon optimal control objective. The main contributions are (i) The new Q-ODE: a model-free characterization of the Hamilton-Jacobi-Bellman equation. (ii) A formulation of Convex Q-learning that avoids approximations appearing in prior work. The Bellman error used in the algorithm is defined by filtered measurements, which is necessary in the presence of measurement noise. (iii) Convex Q-learning with linear function approximation is a convex program. It is shown that the constraint region is bounded, subject to an exploration condition on the training input. (iv) The theory is illustrated in application to resource allocation for distributed energy resources, for which the theory is ideally suited.

Lu, Fan↗
DOE OSTI2023

Constraining chaos: Enforcing dynamical invariants in the training of reservoir computers

Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants—such as the Lyapunov exponent spectrum and the fractal dimension—in the systems of interest, enabling longer and more stable forecasts when operating with limited data. The technique is demonstrated in detail using reservoir computing, a specific kind of recurrent neural network. Finally, results are given for the Lorenz 1996 chaotic dynamical system and a spectral quasi-geostrophic model of the atmosphere, both typical test cases for numerical weather prediction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Development of interatomic potential and effect of ordering on defect properties in CrMnV

Developing materials that can withstand extreme environments, such as high radiation doses and elevated temperatures, is crucial for next-generation particle accelerators, including the 2.4 MW Long-Baseline Neutrino Facility. High-Entropy Alloys have emerged as promising candidates for beam window materials due to their superior mechanical strength, corrosion resistance, and radiation tolerance. In this study, we focus on the Cr–Mn–V alloy system, developing and employing machine-learning interatomic potentials (MLIPs) to investigate the formation of an ordered phase and its influence on defect properties. Using hybrid Monte Carlo-Molecular Dynamics simulations, we observe the formation of a B2-ordered phase at lower temperatures, consistent with Density Functional Theory (DFT) predictions. Ordered structures display a bimodal distribution of migration energies and reduced mean square displacement values, indicating suppressed vacancy diffusion. Our results also show that the migration energy barrier varies based on the atomic species, with Mn and V exhibiting the highest and lowest average barriers, respectively. These findings suggest that atomic ordering inhibits defect mobility, potentially enhancing the radiation resistance of CrMnV alloys. The validated MLIP provides a reliable framework for simulations that are faster than traditional DFT while maintaining the accuracy required to study defect and ordering properties.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Extended Fayans energy density functional: optimization and analysis

The Fayans energy density functional (EDF) has been very successful in describing global nuclear properties (binding energies, charge radii, and especially differences of radii) within nuclear density functional theory. In a recent study, supervised machine learning methods were used to calibrate the Fayans EDF. Building on this experience, in this work we explore the effect of adding isovector pairing terms, which are responsible for different proton and neutron pairing fields, by comparing a 13D model without the isovector pairing term against the extended 14D model. At the heart of the calibration is a carefully selected heterogeneous dataset of experimental observables representing ground-state properties of spherical even–even nuclei. To quantify the impact of the calibration dataset on model parameters and the importance of the new terms, we carry out advanced sensitivity and correlation analysis on both models. The extension to 14D improves the overall quality of the model by about 30%. The enhanced degrees of freedom of the 14D model reduce correlations between model parameters and enhance sensitivity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Cartesian equivariant representations for learning and understanding molecular orbitals

Qualitative and quantitative orbital properties such as bonding/antibonding character, localization, and orbital energies are critical to how chemists understand reactivity, catalysis, and excited-state behavior. Despite this, representations of orbitals in deep learning models have been very underdeveloped relative to representations of molecular geometries and Hamiltonians. Here, we apply state-of-the-art equivariant deep learning architectures to the task of assigning global labels to orbitals, namely energies characterizations, given the molecular coefficients from Hartree–Fock or density functional theory. The architecture we have developed, the Cartesian Equivariant Orbital Network (CEONET), shows how molecular orbital coefficients are readily featurized as equivariant node features common to all graph-based machine-learned potentials. We find that CEONET performs well at predicting difficult quantitative labels such as the orbital energy and orbital entropy. Furthermore, we find that the CEONET representation provides an intuitive latent space for differentiating orbital character for the qualitative assignment of e.g. bonding or antibonding character. In addition to providing a useful representation for further integrating deep learning with electronic structure theory, we expect CEONET to be useful for automatizing and interpreting the results of advanced electronic structure methods such as complete active space self-consistent field theory. In particular, the ability of CEONET to infer multireference character via the orbital entropy paves the way toward the machine-learned selection of active spaces.

chemical reactions↗
DOE OSTI2024

Structural and mechanical properties of monolayer amorphous carbon and boron nitride

Amorphous materials exhibit various characteristics that are not featured by crystals and can sometimes be tuned by their degree of disorder (DOD). Here, we report results on the mechanical properties of monolayer amorphous carbon (MAC) and monolayer amorphous boron nitride (maBN) with different DOD. The pertinent structures are obtained by kinetic-Monte-Carlo (kMC) simulations using machine-learning potentials (MLP) with density-functional-theory (DFT)-level accuracy. An intuitive order parameter, namely the areal fraction F x occupied by crystallites within the continuous random network, is proposed to describe the DOD. We find that F x captures the essence of the DOD: Samples with the same F x but different sizes and arrangements of crystallites, obtained using two distinct kMC procedures, have virtually identical radial distributions functions as well as bond-length and bond-angle distributions. Furthermore, by simulating the fracture process with molecular dynamics, we found that the mechanical responses of MAC and maBN before fracture are mainly determined by F x and are insensitive to the sizes and specific arrangements and to some extent the numbers and area distributions of the crystallites. The behavior of cracks in the two materials is analyzed and found to mainly propagate in meandering paths in the CRN region and to be influenced by crystallites in distinct ways that toughen the material. Furthermore, the present results reveal the relation between structure and mechanical properties in amorphous monolayers and may provide a universal toughening strategy for 2D materials.

2-dimensional systems↗
DOE OSTI2022

Learning Distributed Geometric Koopman Operator for Sparse Networked Dynamical Systems

Koopman operator theory provides an alternative to study nonlinear networked dynamical systems by mapping the state space to an abstract higher dimensional space where the system evolution is linear. Recent works show the application of graph neural networks (GNNs) to learn state to object-centric embeddings and achieve centralized block-wise computation of Koopman operator (KO) under additional assumptions on the underlying agents properties and constraints on the KO structure. However, the computational complexity of learning the Koopman increases exponentially for networked systems where the number of possible system states grows in a combinatorial fashion with the number of nodes. The learning challenge is further amplified for sparse networks by two factors: 1) sample sparsity for learning the Koopman operator in the non-linear space, and 2) the divergence in the dynamics of individual nodes or from one subgraph to another. Our work aims to address these challenge by formulating the representation learning of networked dynamical systems into a multi-agent paradigm and learning the Koopman operator in a distributive manner. The computational as well as performance advantages of distributed Koopman is predominant for sparse networks whereas for fully connected networks, it is shown to coincide with the centralized one. The empirical study on rope system, network of oscillators and a synthetic power system show comparable and superior performance along with computational benefits with the state-of-the-art methods.

Mukherjee, Sayak↗
DOE OSTI2023

Deep nonparametric estimation of intrinsic data structures by chart autoencoders: Generalization error and robustness

Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled near a low-dimensional manifold, we employ chart autoencoders, which encode data into low-dimensional latent features on a collection of charts, preserving the topology and geometry of the data manifold. Our paper establishes statistical guarantees on the generalization error of chart autoencoders, and we demonstrate their denoising capabilities by considering n noisy training samples, along with their noise-free counterparts, on a d-dimensional manifold. By training autoencoders, we show that chart autoencoders can effectively denoise the input data with normal noise. We prove that, under proper network architectures, chart autoencoders achieve a squared generalization error in the order of n–$\frac{2}{d+2}$log 4 n, which depends on the intrinsic dimension of the manifold and only weakly depends on the ambient dimension and noise level. We further extend our theory on data with noise containing both normal and tangential components, where chart autoencoders still exhibit a denoising effect for the normal component. As a special case, our theory also applies to classical autoencoders, as long as the data manifold has a global parametrization. Furthermore, our results provide a solid theoretical foundation for the effectiveness of autoencoders, which is further validated through several numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Progress in Normalizing Flows for 4d Gauge Theories

Normalizing flows have arisen as a tool to accelerate Monte Carlo sampling for lattice field theories. This work reviews recent progress in applying normalizing flows to 4-dimensional nonabelian gauge theories, focusing on two advancements: an architectural improvement referred to as learned active loops, and the application of correlated ensemble methods to QCD with N f = 2 dynamical fermions.

Abbott, Ryan [Massachusetts Institute of Technolog↗
DOE OSTI2022

Benchmarking structural evolution methods for training of machine learned interatomic potentials

When creating training data for machine-learned interatomic potentials (MLIPs), it is common to create initial structures and evolve them using molecular dynamics (MD) to sample a larger configuration space. Here, we benchmark two other modalities of evolving structures, contour exploration (CE) and dimer-method (DM) searches against MD for their ability to produce diverse and robust density functional theory training data sets for MLIPs. We also discuss the generation of initial structures which are either from known structures or from random structures in detail to further formalize the structure-sourcing processes in the future. The polymorph-rich zirconium-oxygen composition space is used as a rigorous benchmark system for comparing the performance of MLIPs trained on structures generated from these structural evolution methods. Using Behler–Parrinello neural networks as our MLIP models, we find that CE and the DM searches are generally superior to MD in terms of spatial descriptor diversity and statistical accuracy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Learning the generating functional for variance reduction in lattice QCD

The generating functional in quantum field theory provides the natural framework for constructing correlation functions as derivatives with respect to source operators. We present a methodology that leverages machine-learned normalizing flows to reduce the variance of arbitrary $N$-point correlation functions of bosonic operators in lattice gauge field theory calculations by encoding a representation of the generating functional. We show that it is possible to systematically approach noiseless estimators of correlation functions in this framework. We demonstrate this methodology with applications to calculations of glueball correlation functions and Wilson loops in Quantum Chromodynamics and Yang-Mills theory. The results show up to three orders of magnitude variance reduction.

Abbott, Ryan [Columbia U.] (ORCID:0000000258778005↗
DOE OSTI2022

Exact constraints and appropriate norms in machine-learned exchange-correlation functionals

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human-designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently, efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to de-orbitalize the strongly constrained and appropriately normed (SCAN) functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding the use of the orbital-dependent kinetic energy density. The performance and transferability of the machine-learned functional are demonstrated for molecular and periodic systems.

Artificial neural networks↗
DOE OSTI2024

Nuclear Quantum Effects on the Electronic Structure of Water and Ice

The electronic properties and optical response of ice and water are intricately shaped by their molecular structure, including the quantum mechanical nature of the hydrogen atoms. Despite numerous previous studies, a comprehensive understanding of the nuclear quantum effects (NQEs) on the electronic structure of water and ice at finite temperatures remains elusive. Here, we utilize molecular simulations that harness efficient machine-learning potentials and many-body perturbation theory to assess how NQEs impact the electronic bands of water and hexagonal ice. By comparing path-integral and classical simulations, we find that NQEs lead to a larger renormalization of the fundamental gap of ice, compared to that of water, ultimately yielding similar bandgaps in the two systems, consistent with experimental estimates. Our calculations suggest that the increased quantum mechanical delocalization of protons in ice, relative to water, is a key factor leading to the enhancement of NQEs on the electronic structure of ice.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Li + /H + Exchange in Solid-State Oxide Li-Ion Conductors

Understanding the moisture stability of oxide Li-ion conductors is important for their practical applications in solid-state batteries. Unlike sulfide or halide conductors, oxide conductors generally better resist degradation when in contact with water but can still undergo topotactic Li + /H + exchange (LHX). Here, we combine density functional theory (DFT) calculations with a machine-learning interatomic potential model to investigate the thermodynamic driving force of the LHX reaction for two representative oxide Li-ion conductor families: garnets and NASICONs. Li-stuffed garnets exhibit a strong driving force for proton exchange due to their high Li chemical potential. In contrast, NASICONs demonstrate a higher resistance against proton exchange due to the lower Li chemical potential and the lower O–H bond covalency for polyanion-bonded oxygens. Our findings reveal a critical trade-off: Li stuffing enhances conductivity but increases moisture susceptibility. This study underscores the importance of designing Li-ion conductors that possess both high conductivity and high stability in practical environments.

Li, Zhuohan [Lawrence Berkeley National Laboratory↗
DOE OSTI2025

Uncovering the True Active Sites in Ni–N–C Catalysts for CO 2 Electroreduction

Understanding and designing active sites in single-atom catalysts (SACs) requires going beyond static models to capture their dynamic evolution under realistic electrochemical conditions. Here, in this work, we develop an integrated theoretical framework that accounts for operational conditions, by combining grand canonical density functional theory (GC-DFT) with machine-learning-accelerated sampling, to uncover structure–activity–stability relationships in Ni–N–C SACs for the CO 2 reduction reaction (CO 2 RR). A library of NiN x C 4–x (x = 0–4) motifs─representing coordination defects likely formed during high-temperature synthesis─was systematically evaluated. Under working conditions, these sites were found to undergo hydrogenation, and NiN 3 C 1_ H 1 was identified as the most probable active site. At reducing potentials, hydrogen adsorbs spontaneously at C–Ni bridge sites rather than Ni top sites, while subsurface hydrogen facilitates bent CO 2 adsorption crucial for activation. High CO 2 RR selectivity toward CO arises from site separation: Ni centers drive CO2RR, while the hydrogen evolution reaction (HER) occurs at the C–Ni bridge or N sites and from thermodynamic suppression of HER at moderate hydrogen coverage. At more negative potentials, a shift in the CO 2 RR rate-determining process (RDP) and Ni out-of-surface displacement induced by coadsorption of H and H 2 O jointly reduce activity and selectivity. Thus, both the high CO2RR selectivity of Ni–N–C catalysts and its reversal with more negative potentials can be rationalized by accounting for hydrogenated surfaces. This highlights the necessity of modeling realistic; in situ conditions. This framework provides generalizable insights into the dynamic behavior of active sites in SACs, offering guidance for the rational design of active and robust catalysts for a wide range of electrochemical reactions.

25 ENERGY STORAGE↗
DOE OSTI2025

Computing chemical potentials with machine-learning-accelerated simulations to accurately predict thermodynamic properties of molten salts

The successful design and deployment of next-generation nuclear technologies heavily rely on thermodynamic data for relevant molten salt systems. However, the lack of accurate force fields and efficient methods has limited the quality of thermodynamic predictions from atomistic simulations. Here we propose an efficient free energy framework for computing chemical potentials, which is the central free energy quantity behind many thermodynamic properties. We accelerate our simulations without sacrificing accuracy by using machine learning interatomic potentials trained on density functional theory (DFT) data. Using lithium chloride as our model system, we compute chemical potentials with DFT-accuracy for solid and liquid phases by transmuting ions into noninteracting particles. Notably, in the liquid phase, we demonstrate consistency whether we transmute one ion pair or the entire system into ideal gas particles. By locating the temperature where the chemical potential of solid and liquid phases cross, we predict a melting point of 880 ± 18 K for lithium chloride, which is remarkably close to the experimental value of 883 K. With this successful demonstration, we lay the foundation for high-throughput thermodynamic predictions of many properties that can be derived from the chemical potentials of the minority and majority components in molten salts.

Gibson, Luke D. [Oak Ridge National Laboratory (OR↗