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DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗

DOE OSTI2023

Modeling Ring Current Proton Fluxes Using Artificial Neural Network and Van Allen Probe Measurements

Abstract Terrestrial ring current dynamics are a critical part of the near‐space environment, in that they directly drive geomagnetic field variations that control particle drifts, and define geomagnetic storms. The present study aims to specify a global and time‐varying distribution of ring current proton using geomagnetic indices and solar wind parameters with their history as input. We train an artificial neural network (ANN) model to reproduce proton fluxes measured by the Radiation Belt Storm Probes Ion Composition Experiment instrument onboard Van Allen Probes. By choosing optimal feature parameters and their history length, the model results show a high correlation and a small error between model specifications and satellite measurements. The modeled results well capture energy‐dependent proton dynamics in association with geomagnetic storms, including inward radial diffusion, acceleration and decay. Our ANN model produces proton fluxes with their corresponding 3D spatiotemporal variations, capturing the latitudinal distribution and local time asymmetry that are consistent with observations and that can further inform theory.

Li, Jinxing↗

DOE OSTI2026

Investigation of Causal Relationships of the Cross‐Scale Wave Coupling Through Information Theoretical Approach

On 2015 October 2, MMS spacecraft observed an electron micro-injection event near the southern hemispheric high-altitude cusp, coinciding with intense wave activity across several frequency bands. Here, we investigated the MMS magnetic field and plasma during this event to explore cross-scale coupling among the wave modes. Employing the Hilbert-Huang transform, we perform an empirical mode decomposition to extract frequencies and amplitudes of the intrinsic mode functions (IMFs). In this analysis, we establish both linear and nonlinear relationships and examine the information transfer between the IMFs. Notably, the transfer entropy suggests that high frequency ion cyclotron waves may be driven by the mirror mode structures. Our case study effectively demonstrates the utility of the information theory based tools for studying cross-scale wave coupling phenomena.

Rivera, Elmer C. [Andrews University, Berrien Spri↗

DOE OSTI2023

Electronic signatures of Lorentzian dynamics and charge fluctuations in lithiated graphite structures

Lithium graphite intercalation compounds (Li-GICs) are essential materials for modern day portable electronics and obtaining insights into their atomic structure and thermodynamics is of fundamental interest. Here we explore the electronic and atomic states of Li-GICs at varying degrees of Lithium loading (i.e., “staging”) by means of ab-initio molecular dynamics simulations and simulated X-ray adsorption spectroscopy (XAS). We analyze the atomic correlation functions and shows that the enhancements of the Li-ion entropy with increased staging result from Lorentzian lithium-ion dynamics and charge fluctuations, which activate low-energy phonon modes. The associated electronic signatures are modulations of the unoccupied π*/σ* orbital energy levels and unambiguous fingerprints in Carbon K-edge XAS spectra. Thus, we extend the canonical view of XAS, establishing that these “static” measurements in fact encode the signature of the thermodynamic response and relaxation dynamics of the system. This causal link between atomic structure, spectroscopy, thermodynamics, and information theory can be generally exploited to better understand stability in solid-state electrochemical systems.

25 ENERGY STORAGE↗

DOE OSTI2023

Accurate prediction of oxygen vacancy concentration with disordered A-site cations in high-entropy perovskite oxides

Abstract Entropic stabilized ABO 3 perovskite oxides promise many applications, including the two-step solar thermochemical hydrogen (STCH) production. Using binary and quaternary A-site mixed {A}FeO 3 as a model system, we reveal that as more cation types, especially above four, are mixed on the A-site, the cell lattice becomes more cubic-like but the local Fe–O octahedrons are more distorted. By comparing four different Density Functional Theory-informed statistical models with experiments, we show that the oxygen vacancy formation energies ( $${E}_{V}^{f}$$ E V f ) distribution and the vacancy interactions must be considered to predict the oxygen non-stoichiometry ( δ ) accurately. For STCH applications, the $${E}_{V}^{f}$$ E V f distribution, including both the average and the spread, can be optimized jointly to improve Δ δ (difference of δ between the two-step conditions) in some hydrogen production levels. This model can be used to predict the range of water splitting that can be thermodynamically improved by mixing cations in {A}FeO 3 perovskites.

08 HYDROGEN↗

DOE OSTI2025

Anomalous thermal transport in Eshelby twisted van der Waals nanowires

Dislocations in van der Waals (vdW) layered nanomaterials induce strain and structural changes that substantially impact thermal transport. Understanding these effects could enable the manipulation of dislocations for improved thermoelectric and optoelectronic applications, but experimental insights remain limited. Here, in this study, we use synthetic Eshelby twisted vdW GeS nanowires (NWs) with single screw dislocations as a model system to explore the interplay between dislocation-induced structural modifications and lattice thermal conductivity. Our measurements reveal a monoclinic structure stabilized by the dislocation, leading to a substantial drop in thermal conductivity for larger-diameter NWs (70% at room temperature), supported by first-principles calculations. Interestingly, we also find an anomalous enhancement of thermal conductivity with decreasing diameter in twisted NWs, contrary to typical trends in non-twisted GeS NWs. This is attributed to increased conductivity near the NW cores due to compressive strain around the central dislocations, and aligns with a density-functional-theory-informed core–shell model. Our results highlight the critical role of dislocations in thermal conduction, providing fundamental insights for defect and strain engineering in advanced thermal applications.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Entropy removal of medical diagnostics

Shannon entropy is a core concept in machine learning and information theory, particularly in decision tree modeling. To date, no studies have extensively and quantitatively applied Shannon entropy in a systematic way to quantify the entropy of clinical situations using diagnostic variables (true and false positives and negatives, respectively). Decision tree representations of medical decision-making tools can be generated using diagnostic variables found in literature and entropy removal can be calculated for these tools. This concept of clinical entropy removal has significant potential for further use to bring forth healthcare innovation, such as quantifying the impact of clinical guidelines and value of care and applications to Emergency Medicine scenarios where diagnostic accuracy in a limited time window is paramount. This analysis was done for 623 diagnostic tools and provided unique insights into their utility. For studies that provided detailed data on medical decision-making algorithms, bootstrapped datasets were generated from source data to perform comprehensive machine learning analysis on these algorithms and their constituent steps, which revealed a novel and thorough evaluation of medical diagnostic algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

The hidden influence of terrestrial groundwater on salt marsh function and resilience

Salt marshes are hotspots of nutrient processing and carbon sequestration. So far, studies addressing spatiotemporal variability in and drivers of salt marsh biogeochemical function, carbon storage and resilience have focused on ocean-driven surface hydrologic influences, neglecting effects of terrestrial hydrology through subsurface connections. Here we evaluate drivers of salt marsh redox potential, a proxy for biogeochemical state, through wavelet analyses and information theory using data from seven marshes. The results point to terrestrial groundwater level as a dominant control on redox variability across all sites. Because redox is a key driver of biogeochemical processes, and specifically oxidation of organic matter that sequesters carbon and maintains marsh elevation, these terrestrial influences are critical to understanding marsh function and evolution. Further, the newly identified links between onshore groundwater levels and marsh redox conditions shift the traditional paradigm and suggest that terrestrial hydrology is a primary control on salt marsh carbon sequestration potential and resilience.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Multiscale analysis of large twist ferroelectricity and swirling dislocations in bilayer hexagonal boron nitride

With its atomically thin structure and intrinsic ferroelectric properties, heterodeformed bilayer hexagonal boron nitride (hBN) has gained prominence in next-generation non-volatile memory applications. However, studies to date have focused almost exclusively on small-twist bilayer hBN, leaving the question of whether ferroelectricity can persist under small heterostrain and large heterodeformation entirely unexplored. In this work, we establish the crystallographic origin of ferroelectricity in bilayer hBN configurations heterodeformed relative to high-symmetry configurations such as AA-stacking and 21.786789° twisted configurations (Σ7), using Smith normal form bicrystallography. We then demonstrate out-of-plane ferroelectricity in bilayer hBN across configurations vicinal to both the AA and Σ7 stackings. Atomistic simulations reveal that AA-vicinal systems support ferroelectricity under both small twist and small strain, with polarization switching in the latter governed by the deformation of swirling dislocations rather than the straight interface dislocations seen in the former. For Σ7-vicinal systems, where existing interatomic potentials underperform particularly under extreme out-of-plane compression, we develop a density-functional-theory-informed continuum framework—the bicrystallography-informed frame-invariant multiscale (BFIM) model, which captures out-of-plane ferroelectricity in heterodeformed configurations vicinal to Σ7 stacking. Interface dislocations in these large heterodeformed bilayer configurations exhibit markedly smaller Burgers vectors compared to interface dislocations in small-twist and small-strain bilayer hBN. The BFIM model reproduces experimental results and provides a powerful, computationally efficient framework for predicting ferroelectricity in large-unit-cell heterostructures where atomistic simulations are prohibitively expensive.

Ahmed, Md Tusher [Univ. of Illinois at Urbana-Cham↗

DOE OSTI2021

Asymptotic reversibility of thermal operations for interacting quantum spin systems via generalized quantum Stein’s lemma

Abstract For quantum spin systems in any spatial dimension with a local, translation-invariant Hamiltonian, we prove that asymptotic state convertibility from a quantum state to another one by a thermodynamically feasible class of quantum dynamics, called thermal operations, is completely characterized by the Kullback–Leibler (KL) divergence rate, if the state is translation-invariant and spatially ergodic. Our proof consists of two parts and is phrased in terms of a branch of the quantum information theory called the resource theory. First, we prove that any states, for which the min and max Rényi divergences collapse approximately to a single value, can be approximately reversibly converted into one another by thermal operations with the aid of a small source of quantum coherence. Second, we prove that these divergences collapse asymptotically to the KL divergence rate for any translation-invariant ergodic state. We show this via a generalization of the quantum Stein’s lemma for quantum hypothesis testing beyond independent and identically distributed situations. Our result implies that the KL divergence rate serves as a thermodynamic potential that provides a complete characterization of thermodynamic convertibility of ergodic states of quantum many-body systems in the thermodynamic limit, including out-of-equilibrium and fully quantum situations.

Physics↗

DOE OSTI2023

Gaps labeling theorem for the bubble-diamond self-similar graphs

Abstract Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information theory, we present a detailed spectral analysis for a new class of fractal-type diamond graphs, referred to as bubble-diamond graphs, and provide a gap-labeling theorem in the sense of Bellissard for the corresponding probabilistic graph Laplacians using the technique of spectral decimation. Labeling the gaps in the Cantor set by the normalized eigenvalue counting function, also known as the integrated density of states, we describe the gap labels as orbits of a second dynamical system that reflects the branching parameter of the bubble construction and the decimation structure. The spectrum of the natural Laplacian on limit graphs is shown generically to be pure point supported on a Cantor set, though one particular graph has a mixture of pure point and singularly continuous components.

Physics↗

DOE OSTI2025

Real classical shadows

Efficiently learning expectation values of a quantum state using classical shadow tomography has become a fundamental task in quantum information theory. In a classical shadows protocol, one measures a state in a chosen basis $\mathcal{W}$ after it has evolved under a unitary transformation randomly sampled from a chosen distribution $\mathcal{U}$. In this work we study the case where $\mathcal{U}$ corresponds to either local or global orthogonal Clifford gates, and $\mathcal{W}$ consists of real-valued vectors. Our results show that for various situations of interest, this ‘real’ classical shadow protocol improves the sample complexity over the standard scheme based on general Clifford unitaries. For example, when one is interested in estimating the expectation values of arbitrary real-valued observables, global orthogonal Cliffords typically decrease the required number of samples by a factor of two. More dramatically, for k-local observables composed only of real-valued Pauli operators, sampling local orthogonal Cliffords leads to a reduction by an exponential-in-k factor in the sample complexity over local unitary Cliffords. Finally, we show that by measuring in a basis containing complex-valued vectors, orthogonal shadows can, in the limit of large system size, exactly reproduce the original unitary shadows protocol.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Frustrated mixed-spin ladders: Evidence for a bond-order wave phase between rung-singlet and Haldane phases

In frustrated spin ladders, the interplay of frustration and correlations leads to the familiar Haldane (H) and rung-singlet (RS) phases. The nature of the transition between these two phases is still under debate. In this paper we tackle this issue using tools of quantum information theory. We consider frustrated mixed-spin-(1, 1/2) ladders with antiferromagnetic leg, rung and diagonal couplings, and calculate various quantities, such as the entanglement entropy (EE), the Schmidt gap, and the level degeneracy of the entanglement spectrum (ES). We use two numerical techniques, the infinite time-evolving block decimation (iTEBD) and the density matrix renormalization group (DMRG). We demonstrate that there exists an intermediate phase in which the ES levels do not exhibit the characteristic degeneracies of the H and RS phases. To understand the underlying physics in this phase, here we investigate short-range spin correlations along legs, rungs and diagonals and show that in this intermediate phase long-wavelength modulations occur, akin to bond-order waves.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Green's function knockout formalism

Knockout nuclear reactions, in which a nucleon is removed from a nucleus as a result of the collision with another nucleus, have been widely used as an experimental tool, both to populate isotopes further removed from stability and to obtain information about the single-particle nature of the nuclear spectrum. In order to fully exploit the experimental information, theory is needed for the description of both the structure of the nuclei involved, and the dynamics associated with the nucleon removal mechanisms. Here, the standard approach, using theoretical shell-model spectroscopic factors for the structure description coupled with an eikonal model of reaction, has been successful when used in the context of the removal of valence nucleons in nuclei close to stability. However, it has been argued that the reaction theory might need to be revisited in the case of exotic nuclei, more specifically for highly asymmetric nuclei in which the deficient species (neutrons or protons) is being removed. We present here a new formalism for the nucleon-removal and -addition reaction through knockout and transfer reactions, that treats consistently structure and reaction properties using dispersive optical potentials. In particular, our formalism includes the dynamical effects associated with the removal of a nucleon from the projectile, which might explain the long standing puzzle of the quenching of spectroscopic factors in nuclei with extreme neutrons-to-protons ratios.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Theoretical methods to design and test quantum simulators for the compact Abelian Higgs model

The lattice compact Abelian Higgs model is a nonperturbative regularized formulation of low-energy scalar quantum electrodynamics. In 1+1 dimensions, this model can be quantum simulated using a ladder-shaped optical lattice with Rydberg-dressed atoms. In this setup, one spatial dimension is used to carry the angular momentum of the quantum rotors. One can use truncations corresponding to spin-2 and spin-1 to build local Hilbert spaces associated with the links of the lattice. We argue that ladder-shaped configurable arrays of Rydberg atoms can be used for the same purpose. We make concrete proposals involving two and three Rydberg atoms to build one local spin-1 space (a qutrit). We show that the building blocks of the Hamiltonian calculations are models with one and two spins. We compare target and simulators using perturbative and numerical methods. The two-atom setup provides an easily controllable simulator of the one-spin model while the three-atom setup involves solving nonlinear equations. We discuss approximate methods to couple two spin-1 spaces. The article provides analytical and numerical tools necessary to design and build the proposed simulators with current technology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Bootstrapping gauge theories

We consider asymptotically free gauge theories with gauge group S U ( N c ) and N f quarks with mass m q ≪ Λ QCD that undergo chiral symmetry breaking and confinement. We propose a bootstrap method to compute the S matrix of the pseudo-Goldstone bosons (pions) that dominate the low-energy physics. For the important case of N c = 3 , N f = 2 , a numerical implementation of the method gives the phase shifts of the S 0 , P 1 and S 2 waves in good agreement with experimental results. The method incorporates gauge theory information ( N c , N f , m q , Λ QCD ) by using the form-factor bootstrap recently proposed by Karateev, Kuhn and Penedones together with a finite energy version of the Shifman-Vainshtein-Zakharov (SVZ) sum rules. At low energy we impose constraints from chiral symmetry breaking. The only low-energy numerical inputs are the pion mass m π and the quark and gluon condensates. Published by the American Physical Society 2024

He, Yifei (ORCID:0000000213666157)↗

DOE OSTI2021

Revisiting Huffman Coding: Toward Extreme Performance on Modern GPU Architectures

Today's high-performance computing (HPC) applications are producing vast volumes of data, which are challenging to store and transfer efficiently during the execution, such that data compression is becoming a critical technique to mitigate the storage burden and data movement cost. Huffman coding is arguably the most efficient Entropy coding algorithm in information theory, such that it could be found as a fundamental step in many modern compression algorithms such as DEFLATE. On the other hand, today's HPC applications are more and more relying on the accelerators such as GPU on supercomputers, while Huffman encoding suffers from low throughput on GPUs, resulting in a significant bottleneck in the entire data processing. In this paper, we propose and implement an efficient Huffman encoding approach based on modern GPU architectures, which addresses two key challenges: (1) how to parallelize the entire Huffman encoding algorithm, including codebook construction, and (2) how to fully utilize the high memory-bandwidth feature of modern GPU architectures. The detailed contribution is fourfold. (1) We develop an efficient parallel codebook construction on GPUs that scales effectively with the number of input symbols. (2) We propose a novel reduction based encoding scheme that can efficiently merge the codewords on GPUs. (3) We optimize the overall GPU performance by leveraging the state-of-the-art CUDA APIs such as Cooperative Groups. (4) We evaluate our Huffman encoder thoroughly using six real-world application datasets on two advanced GPUs and compare with our implemented multi-threaded Huffman encoder. Experiments show that our solution can improve the encoding throughput by up to 5.0x and 6.8x on NVIDIA RTX 5000 and V100, respectively, over the state-of-the-art GPU Huffman encoder, and by up to 3.3x over the multi-thread encoder on two 28-core Xeon Platinum 8280 CPUs.

Tian, Jiannan↗

DOE OSTI2020

Explainable and trustworthy artificial intelligence for correctable modeling in chemical sciences

Data science has primarily focused on big data, but for many physics, chemistry, and engineering applications, data are often small, correlated and, thus, low dimensional, and sourced from both computations and experiments with various levels of noise. Typical statistics and machine learning methods do not work for these cases. Expert knowledge is essential, but a systematic framework for incorporating it into physics-based models under uncertainty is lacking. Here, we develop a mathematical and computational framework for probabilistic artificial intelligence (AI)–based predictive modeling combining data, expert knowledge, multiscale models, and information theory through uncertainty quantification and probabilistic graphical models (PGMs). We apply PGMs to chemistry specifically and develop predictive guarantees for PGMs generally. Our proposed framework, combining AI and uncertainty quantification, provides explainable results leading to correctable and, eventually, trustworthy models. The proposed framework is demonstrated on a microkinetic model of the oxygen reduction reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗