From Monte Carlo to machine learning: how computational methods advance the study of statistical physics
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Li, Ying Wai↗
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Information and Statistics in Nuclear Experiment and Theory (ISNET)
As with all empirical sciences, nuclear physics operates in the virtuous cycle of the scientific method: observations inspire theoretical models; models lead to new predictions; predictions are tested in experiments; experiments lead to new observations; and so on. Evaluating what we are inferring, and how certain we are of it, is key to this process. These requirements, and a general interest in applying novel statistical, mathematical, and computational techniques, led to the formation of a dedicated research community entitled “Information and Statistics in Nuclear Experiment and Theory (ISNET)” (https://isnet-series.github.io/), which now includes more than 300 members. While the community’s interests lean toward nuclear theory, the unifying theme for this group is the inference of knowledge from data.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
A Stochastic Reduced-Order Model for Statistical Microstructure Descriptors Evolution
Integrated computational materials engineering (ICME) models have been a crucial building block for modern materials development, relieving heavy reliance on experiments and significantly accelerating the materials design process. However, ICME models are also computationally expensive, particularly with respect to time integration for dynamics, which hinders the ability to study statistical ensembles and thermodynamic properties of large systems for long time scales. To alleviate the computational bottleneck, we propose to model the evolution of statistical microstructure descriptors as a continuous-time stochastic process using a non-linear Langevin equation, where the probability density function (PDF) of the statistical microstructure descriptors, which are also the quantities of interests (QoIs), is modeled by the Fokker–Planck equation. In this work, we discuss how to calibrate the drift and diffusion terms of the Fokker–Planck equation from the theoretical and computational perspectives. The calibrated Fokker–Planck equation can be used as a stochastic reduced-order model to simulate the microstructure evolution of statistical microstructure descriptors PDF. Considering statistical microstructure descriptors in the microstructure evolution as QoIs, we demonstrate our proposed methodology in three integrated computational materials engineering (ICME) models: kinetic Monte Carlo, phase field, and molecular dynamics simulations.
97 MATHEMATICS AND COMPUTING↗
Lagrangian conditional statistics and flow topology in edge plasma turbulence
Lagrangian statistics and particle transport in edge plasma turbulence are investigated using the Hasegawa–Wakatani model and its modified version. The latter shows the emergence of pronounced zonal flows. Different values of the adiabaticity parameter are considered. The main goal is to characterize the role of coherent structures, i.e., vortices and zonal flows, and their impact on the Lagrangian statistics of particles. Computationally intensive long time simulations following ensembles of test particles over hundreds of eddy turnover times are considered in statistically stationary turbulent flows. The flow topology is characterized using the Lagrangian Okubo–Weiss criterion in order to split the flow into topologically different domains. In elliptic and hyperbolic regions, the probability density functions (PDFs) of the residence time have self-similar algebraic decaying tails. However, in the intermediate regions, the PDFs exhibit exponentially decaying tails. Topologically conditioned PDFs of the Lagrangian velocity, and acceleration and density fluctuations are likewise computed. The differences between the classical Hasegawa–Wakatani system and its modified version are assessed, and the role of zonal flows is highlighted. Here, the density flux spectrum, which characterizes the contributions of different length scales, is studied, and its inertial scaling is found to be in agreement with predictions based on dimensional arguments. Analyzing the angular change of particle tracers at different time scales, corresponding to coarse grained curvature, completes the study, and these multiscale geometric statistics quantify the directional properties of the particle motion in different flow regimes.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Physics-Informed Gaussian Process Regression for States Estimation and Forecasting in Power Grids
Real-time state estimation and forecasting are critical for the efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data. In the PhI-GPR method, we propose to compute the prior statistics offline by solving stochastic differential equations (SDEs) governing the power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertainty in wind mechanical power. Here, we assume that the power grid dynamics are governed by swing equations, with the wind mechanical power fluctuating randomly in time. We solve these equations for the mean and covariances of the power grid states using the Monte Carlo simulation method. We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate observed and unobserved states. For the considered problem, PhI-GPR has computational advantages over the ensemble Kalman filter (EnKF) method: In PhI-GPR, ensembles are computed offline and independently of the data acquisition process, whereas for EnFK, ensembles are computed online with data acquisition, rendering real-time forecast more challenging. We also demonstrate that the PhI-GPR forecast is more accurate than the EnKF forecast when the random mechanical wind power is non-Markovian. In contrast, the two methods produce similar forecasts for the Markovian mechanical wind power. For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR; both forecasts are significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Density functional theory-based surrogate kinetic models for heterogeneous reactions of hydrocarbon intermediates on silicon carbide
The increasing demand for high-performance materials in advanced technologies highlights the importance of achieving a fundamental understanding and potential control of silicon carbide (SiC) deposition processes. However, existing models often lack sufficient theoretical detail, relying heavily on empirical data and offering limited predictive capability. In particular, the complex surface chemistry governing SiC growth remains poorly understood. This study addresses these challenges by employing density functional theory (DFT) to investigate key heterogeneous reactions involving hydrocarbon intermediates on SiC surfaces, including dehydrogenation, hydrogenation, and carbon deposition. Transition state searches were conducted to identify reaction pathways and energy barriers. While first-principles calculations offer high accuracy, they are computationally intensive. To extend the utility of these first-principles results, vibrational analyses were performed using phonon-based statistical thermochemistry to compute temperature-dependent reaction rates which were used to develop Arrhenius-type surrogate kinetic models. Furthermore, the resulting framework provides a more rigorous, physically grounded basis for integrating atomistic insights into continuum-scale modeling, ultimately enabling improved prediction and optimization of SiC film growth in high-performance material systems.
Density Functional Theory↗
Challenges and opportunities for machine learning potentials in transition path sampling: alanine dipeptide and azobenzene studies
ML potentials enable fast TPS simulations ( e.g. , for alanine dipeptide) but may fail for complex cases like azobenzene isomerization. Adequate reference data and domain expertise are crucial for selecting test trajectories.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Black-box statistical prediction of lossy compression ratios for scientific data
Lossy compressors are increasingly adopted in scientific research, tackling volumes of data from experiments or parallel numerical simulations and facilitating data storage and movement. In contrast with the notion of entropy in lossless compression, no theoretical or data-based quantification of lossy compressibility exists for scientific data. Users rely on trial and error to assess lossy compression performance. As a strong data-driven effort toward quantifying lossy compressibility of scientific datasets, we provide a statistical framework to predict compression ratios of lossy compressors. Our method is a two-step framework where (i) compressor-agnostic predictors are computed and (ii) statistical prediction models relying on these predictors are trained on observed compression ratios. Proposed predictors exploit spatial correlations and notions of entropy and lossyness via the quantized entropy. We study 8+ compressors on 6 scientific datasets and achieve a median percentage prediction error less than 12%, which is substantially smaller than that of other methods while achieving at least a 8.8× speedup for searching for a specific compression ratio and 7.8× speedup for determining the best compressor out of a collection.
97 MATHEMATICS AND COMPUTING↗
Methods for Explainable Artificial Intelligence
We explored ways of quantifying information in a neural network. This can be used to determine the right size of a network or to infer the way in which a network is processing information. The first year and a half was somewhat exploratory while the last half of the project focused on approaches that seemed to show the most promise. The introduce a new way of computing explainable artificial intelligence (XAI) saliency maps that is several orders of magnitude faster than methods with similar fidelity We call it FastCAM. The method works be combining a Class Activation Map (CAM) method such as GradCAM with a forward activation map computed with a statistic we call SMOE Scale. The addition of the forward activation maps to CAM methods seems to always improve their fidelity. At the same time, computational overhead is not increased by very much. While Gradients with SmoothGrad scores better on some fidelity measures, it is overall not as good and requires more than 1500 times to compute. We demonstrate two completed applications of FastCAM on tasks outside of the LDRD at LLNL. The source code for FastCAM is currently being implanted into Captum, the official XAI toolkit for the popular deep learning toolkit PyTorch. The LDRD currently has 13 publications released to the public. 10 of them are journal length.
97 MATHEMATICS AND COMPUTING↗
Statistical Mechanics on Lattices (smol) v0.0.1
smol is a Python implementation of the Cluster Expansion Method and extensions of this methodology; which is used to fit applied lattice models from first principle calculations for subsequent use in Monte Carlo simulations for computing thermodynamic and statistical properties of atomic configuration. smol has a several notable advantages over other similar software packages. The first being its Python implementation which makes it easy to use even for users with little software and coding skills. Despite being implemented in Python, essential Monte Carlo routines are implemented in Cython such that performance is not compromised and is competitive even to similar software implemented in C/C++. Furthermore, the package has specific functionality for handling complex ionic materials (such as cathodes and electrolytes) that is not readily available in other packages. Lastly, the software has a flexible and modular design with the intention of making it fast and efficient to develop and extend the methodology.
Barroso-Luque, Luis↗
Probabilistic learning and updating of a digital twin for composite material systems
This paper presents an approach for characterizing and estimating statistical dependence between a large number of observables in a composite material system. Conditional regression is carried out using the estimated joint density function, permitting a systematic exploration of interdependence between fine scale and coarse observables that can be used for both prognosis and design of complex material systems. An example demonstrates the integration of experimental data with a computational database. The statistical approach is based on the probabilistic learning on manifolds recently developed by the authors. This approach leverages intrinsic structure detected through diffusion on graphs with projected stochastic differential equations to generate samples constrained to that structure.
42 ENGINEERING↗
Extrapolation of the Rainflow-Counted Load Ranges for Fatigue Assessment of the Wind Turbine's Blades
Wind turbine design standards recommend the use of statistical modeling coupled with extrapolation of the short-term load data to long-term periods for fatigue reliability assessment. However, statistical error and computational expense can limit the accuracy of such approaches. In the case of wind turbine blades, the errors are more significant because of the high material fatigue exponent that makes the damage estimations more sensitive to variations. In addition, due to different excitation sources, the flapwise load range histogram is not unimodal, and thus its statistical modeling is complex. In the present work, we provide three methods for statistical modeling of the flapwise bending moment ranges including a novel approach based on frequency-based separation of the modes. The first two methods are simplified approaches for modeling the most crucial load ranges using unimodal distributions and the third method involves multimodal distribution fitting. The research is based on 3600 10-minute aeroelastic simulations of DTU 10MW case study wind turbine from which a benchmark damage equivalent load (DEL) is calculated. The DEL calculated by each of the three proposed methods is compared to this reference. The results show that the conventional approach based on using 6 seeds as well as using mixture models fitted on the limited data lead to under-conservative results with errors up to 23%. On the other hand, the simplified unimodal approaches provided in this work can provide conservative estimations of the fatigue damage with mean values 5% and 12% higher than the benchmark. However, the variability of the DEL estimates is higher when using unimodal extrapolation of the load ranges, and the data can be conservative by 17.5%. The proposed unimodal fits suggested for modeling and extrapolation of the blade's load ranges provide less errors relatively and most importantly conservative DEL estimations while maintaining computational efficiency.
blade fatigue↗
Physics-informed machine learning of the correlation functions in bulk fluids
The Ornstein–Zernike (OZ) equation is the fundamental equation for pair correlation function computations in the modern integral equation theory for liquids. In this work, machine learning models, notably physics-informed neural networks and physics-informed neural operator networks, are explored to solve the OZ equation. The physics-informed machine learning models demonstrate great accuracy and high efficiency in solving the forward and inverse OZ problems of various bulk fluids. The results highlight the significant potential of physics-informed machine learning for applications in thermodynamic state theory.
97 MATHEMATICS AND COMPUTING↗
Tools for Water Ingress Testing
The Safety Storage and Engineering Team, as part of the Production Support Services division (PSS-2), is tasked with ensuring the safety of containers used for handling and storage of nuclear materials. As part of this work, water ingress tests are conducted to evaluate the water-tightness of containers intended for in-glovebox use. In collaboration, the statistics group of the Computer and Computational Sciences Division (CCS-6) provided support in developing a statistically defensible approach for determining appropriate sample sizes for water ingress testing. Water ingress testing involves multiple measurements on multiple containers. Our approach uses a simple random effects model to analyze a pilot data set, implementing prediction limits to evaluate the efficacy of collecting additional data. Although this study capitalizes on available data, our approach can be used with estimates of the ratio of between and within variability and average values, often available from past testing or expert knowledge. An interactive Shiny tool was developed as a final user-friendly product for future testing. The Shiny interface is an open-source package providing a framework for building web applications. Raw data exploration and prediction interval-based sample size assessments can quickly be conducted by the engineering team without needing to interact with the underlying code.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Passive method to measure strength of turbulence
Disclosed is a method to passively measure and calculate the strength of turbulence via the index of refraction structure constant Cn2 from video imagery gathered by an imaging device, such as a video camera. Processing may occur with any type computing device utilizing a processor executing machine executable code stored on memory. This method significantly simplifies instrumentation requirements, reduces cost, and provides rapid data output. This method combines an angle of arrival methodology, which provides scale factors, with a new spatial/temporal frequency domain method. As part of the development process, video imagery from high speed cameras was collected and analyzed. The data was decimated to video rates such that statistics could be computed and used to confirm that this passive method accurately characterizes the atmospheric turbulence. Cn2 accuracy from this method compared well with scintillometer data through two full orders of magnitude and more capability is expected beyond this verification.
O'Neill, Mary Morabito↗
Transient hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation. II. Isomer-resolved unimolecular dynamics
Transient carbon-centered hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation are characterized by their time- and energy-resolved unimolecular dissociation dynamics to hydroxyl (OH) and cyclic ether products. Two distinct •QOOH isomers are examined with radical sites at a primary carbon of one of the methyl groups (β-Me) or a secondary carbon (β-Et) of the ethyl group. Energy-dependent unimolecular rates are obtained from the time-dependent appearance of OH products for the two isomers and compared with statistical microcanonical rates computed using RRKM theory, including heavy-atom tunneling, based on high-level theoretical calculations. A benchmark-corrected approach is utilized to compute high-accuracy stationary-point energies, most importantly, transition-state barriers, for the •QOOH_Me and •QOOH_Et isomers in isopentane oxidation, building on higher-level reference calculations for the oxidation of ethane (C 2 H 5 O 2 ) and propane (C 3 H 7 O 2 ), respectively. Here, the measured rates are compared with RRKM calculations incorporating the benchmark-corrected transition-state parameters, a vibrationally adiabatic multidimensional hindered-rotor treatment of key torsions, and quantum tunneling. Agreement between experiment and theory validates the statistical description and shows faster decay for •QOOH_Et due to its lower barrier. Both β-QOOH isomers decay almost exclusively to OH + cyclic ether products under the conditions studied.
Oxidation processes↗
Signatures of a liquid–liquid transition in an ab initio deep neural network model for water
Significance Water is central across much of the physical and biological sciences and exhibits physical properties that are qualitatively distinct from those of most other liquids. Understanding the microscopic basis of water’s peculiar properties remains an active area of research. One intriguing hypothesis is that liquid water can separate into metastable high- and low-density liquid phases at low temperatures and high pressures, and the existence of this liquid–liquid transition could explain many of water’s anomalous properties. We used state-of-the-art approaches in computational quantum chemistry, statistical mechanics, and machine learning and obtained evidence consistent with a liquid–liquid transition, supporting the argument for the existence of this phenomenon in real water.
36 MATERIALS SCIENCE↗
Hydrogen Dispersion Modeling for Development of Smart Distributed Monitoring
Studying hydrogen dispersion is crucial for ensuring the safe and effective deployment of hydrogen as an energy carrier. This study presents a comprehensive CFD modeling framework for simulating hydrogen dispersion at a real-world hydrogen production, storage, and utilization facility. Utilizing the Hydrogen Research Facility under the Advanced Research on Integrated Energy Systems (ARIES) at the National Renewable Energy Laboratory's (NREL) Flatirons campus, controlled hydrogen releases at 27 kg-H2/hr were simulated. The model incorporated site-specific atmospheric conditions, including hourly wind speeds and temperatures recorded between 8 AM and 8 PM from October to December 2023. To reduce computational demands, a statistical reduction technique was applied to condense the dataset to 100 representative scenarios, validated by statistical tests for wind speeds and power law coefficients. Simulations were conducted using the Reynolds-Averaged Navier-Stokes equations. Results demonstrated that wind speed substantially influences hydrogen dispersion, with low wind conditions forming concentrated clouds and higher wind speeds stretching the plume. Additionally, clustering analysis informed optimal sensor placement at various elevations with up to 10 sensor locations on each elevation. This framework offers a robust approach for understanding hydrogen behavior in ambient conditions and informing detection strategies.
08 HYDROGEN↗