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DOE OSTI2025

Uncertainty quantification for misspecified machine learned interatomic potentials

The use of high-dimensional regression techniques from machine learning has significantly improved the quantitative accuracy of interatomic potentials. Atomic simulations can now plausibly target quantitative predictions in a variety of settings, which has brought renewed interest in robust means to quantify uncertainties. In many practical settings where model complexity is constrained (e.g., due to performance considerations), misspecification — the inability of any one choice of model parameters to exactly match all training data — is a key contributor to errors that is often disregarded. Here, we employ a recent misspecification-aware regression technique to quantify parameter uncertainties, which is then propagated to a broad range of phase and defect properties in tungsten. The propagation is performed through both brute-force resampling and implicit Taylor expansion. The propagated misspecification uncertainties robustly quantify and bound errors on a broad range of material properties. We demonstrate application to recent foundational machine learning interatomic potentials, accurately predicting and bounding errors in MACE-MPA-0 energy predictions across the diverse materials project database.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Bayesian Inference with Latent Hamiltonian Neural Networks (L-HNNs)

When sampling for Bayesian inference, one popular approach is to use Hamiltonian Monte Carlo (HMC) and the No-U-Turn Sampler (NUTS). However, HMC and NUTS can require numerous numerical gradients of the target density and can prove slow in practice. We propose Hamiltonian neural networks (HNNs) with HMC and NUTS for solving Bayesian inference problems [1, 2]. Once trained, HNNs do not require gradients of the target density while sampling. Moreover, they satisfy important properties such as perfect time reversibility and Hamiltonian conservation, making them well suited for use within HMC and NUTS because stationarity can be shown. We also propose an HNN extension called latent HNNs (L-HNNs), which predict latent variable outputs. Compared to HNNs, L-HNNs offer improved expressivity and a reduction in integration errors. Finally, we propose employing L-HNNs in NUTS with an online error monitoring scheme to prevent degeneracy of the sampling in regions of low probability density. We demonstrate L-HNNs in NUTS with online error monitoring by using several example cases involving complex, heavy-tailed, and high local curvature probability densities. Overall, L-HNNs in NUTS with online error monitoring satisfactorily inferred these probability densities. Compared to traditional NUTS, L-HNNs in NUTS with online error monitoring improved the effective sample size (ESS) per gradient by an order of magnitude.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Evaluating the Potential and Challenges of an Uncertainty Quantification Method for Long Short–Term Memory Models for Soil Moisture Predictions

Recently, recurrent deep networks have shown promise to harness newly available satellite–sensed data for long–term soil moisture projections. However, to be useful in forecasting, deep networks must also provide uncertainty estimates. Here we evaluated Monte Carlo dropout with an input–dependent data noise term (MCD+N), an efficient uncertainty estimation framework originally developed in computer vision, for hydrologic time series predictions. MCD+N simultaneously estimates a heteroscedastic input–dependent data noise term (a trained error model attributable to observational noise) and a network weight uncertainty term (attributable to insufficiently constrained model parameters). Although MCD+N has appealing features, many heuristic approximations were employed during its derivation, and rigorous evaluations and evidence of its asserted capability to detect dissimilarity were lacking. To address this, we provided an in–depth evaluation of the scheme's potential and limitations. We showed that for reproducing soil moisture dynamics recorded by the Soil Moisture Active Passive (SMAP) mission, MCD+N indeed gave a good estimate of predictive error, provided that we tuned a hyperparameter and used a representative training data set. The input–dependent term responded strongly to observational noise, while the model term clearly acted as a detector for physiographic dissimilarity from the training data, behaving as intended. However, when the training and test data were characteristically different, the input–dependent term could be misled, undermining its reliability. Additionally, due to the data–driven nature of the model, data noise also influences network weight uncertainty, and therefore the two uncertainty terms are correlated. Altogether, this approach has promise, but care is needed to interpret the results.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Smart Methane Emission Detection System Development (Final Report)

Working with the Department of Energy's National Energy Technology Laboratory, Southwest Research Institute® (SwRI®) developed a system to identify methane leaks reliably, accurately, and autonomously at critical midstream sections of the natural gas distribution network in real-time for the purpose of mitigating methane emissions using Optical Gas Imaging (OGI) cameras. SwRI's Smart Leak Detection – Methane (SLED/M) adds a high degree of automation to the process of methane leak detection to minimize sources of human error, minimize response time to a leak event, and maximize midstream visibility. Furthermore, SwRI has been working towards integrating Quantitative OGI (QOGI) capabilities into this existing technology. By leveraging Deep Learning, SwRI now has the capability to estimate fugitive emission leak rates quickly and reliably, which allows operators to detect emissions, quantify leak rate, prioritize repairs, and validate the repairs in a single instrument. The next generation QOGI technology leverages the same cameras used in Leak Detection and Repair (LDAR) programs, with improvements in safety and speed for traditional quantification-based repairs, ultimately leading to less overhead cost for the operators. The goals for this research were to develop two types of models with the following goals: Run in real-time on the edge (≥ 12 Hz), Classification: Achieve less than 5% false positive detection, Classification: Achieve ≥ 95% methane plume detection rate, Regression: achieve ≤ 10 standard cubic feet per hour (scfh) prediction > 70% of the time. In order to achieve these results, multiple infrared (IR) and other sensors were investigated in tandem with the midwave IR (MWIR) OGI to provide additional information to train the underlying models. Information on atmospheric conditions including humidity, temperature, pressure, and solar radiation was provided by a weather station. Several machine learning and deep learning architectures and methods, including looking at quantized classification networks and regressions networks, were explored. As further data was collected, curated, and labeled, it allowed for more refined regressive networks to be adequately trained, leading to better insight into the true flow rates being observed. An important valuable deliverable of this research effort was the development of an advanced network which underwent multiple iterations capable of giving a continuous output. The current network has a predicted mean average percentage error (MAPE) of 12.3% just outside our target goal of 10.00%, but an accuracy of 97.78% at ±50 scfh, well within the overall goal for the Department of Energy (DOE) program. Upon closer inspection, it was observed that more than 10% of datapoints contributing to the MAPE predictions were the result of low flow rate predictions and are beyond the sensitivity of instrument measurement as a result of normal operational variation and noise.

03 NATURAL GAS↗

DOE OSTI2025

Surrogate-driven Variance-based Sensitivity Analysis of Thermal Storage Tanks in Integrated Energy Systems

Sensitivity analysis and uncertainty quantification are essential steps for enhancing the accuracy of computational models by identifying and mitigating uncertainties. This study focuses on these steps for the Thermal Energy Delivery System at Idaho National Laboratory, specifically targeting the thermocline tank. Using a Modelica/Dymola simulation model, the study perturbed various design parameters and boundary conditions, including shape factor, porosity, outlet temperature, inlet mass flow rate, and system pressure, to predict and quantify uncertainty in the tank’s ax- ial temperature. A dataset of over 1,000 simulations was generated, and surrogate models were developed using the pyMAISE (Michigan Artificial Intelligence Standard Environment) library, which is an Automatic Machine Learning library for nuclear engineering applications. The optimal model, a feedforward neural network with two hidden layers, achieved an R2 score above 0.99 and a mean absolute error below 1 Kelvin. Sensitivity analyses using Sobol indices and Fourier amplitude sensitivity testing methods on this surrogate model revealed that the inlet mass flow rate at initial timestamps and porosity significantly impacts predicted temperatures across all sensors and time steps.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Smart Methane Emission Detection System Development (Final Report)

Working with the Department of Energy’s National Energy Technology Laboratory, Southwest Research Institute® (SwRI®) developed a system to identify methane leaks reliably, accurately, and autonomously at critical midstream sections of the natural gas distribution network in real- time for the purpose of mitigating methane emissions using Optical Gas Imaging (OGI) cameras. SwRI’s Smart Leak Detection – Methane (SLED/M) adds a high degree of automation to the process of methane leak detection to minimize sources of human error, minimize response time to a leak event, and maximize midstream visibility. Furthermore, SwRI has been working towards integrating Quantitative OGI (QOGI) capabilities into this existing technology. By leveraging Deep Learning, SwRI now has the capability to estimate fugitive emission leak rates quickly and reliably, which allows operators to detect emissions, quantify leak rate, prioritize repairs, and validate the repairs in a single instrument. The next generation QOGI technology leverages the same cameras used in Leak Detection and Repair (LDAR) programs, with improvements in safety and speed for traditional quantification-based repairs, ultimately leading to less overhead cost for the operators. The goals for this research were to develop two types of models with the following goals: 1. Run in real-time on the edge (≥ 12 Hz) 2. Classification: Achieve less than 5% false positive detection 3. Classification: Achieve ≥ 95% methane plume detection rate 4. Regression: achieve ≤ 10 standard cubic feet per hour (scfh) prediction > 70% of the time In order to achieve these results, multiple infrared (IR) and other sensors were investigated in tandem with the midwave IR (MWIR) OGI to provide additional information to train the underlying models. Information on atmospheric conditions including humidity, temperature, pressure, and solar radiation was provided by a weather station. Several machine learning and deep learning architectures and methods, including looking at quantized classification networks and regressions networks, were explored. As further data was collected, curated, and labeled, it allowed for more refined regressive networks to be adequately trained, leading to better insight into the true flow rates being observed. An important valuable deliverable of this research effort was the development of an advanced network which underwent multiple iterations capable of giving a continuous output. The current network has a predicted mean average percentage error (MAPE) of 12.3% just outside our target goal of 10.00%, but an accuracy of 97.78% at ±50 scfh, well within the overall goal for the Department of Energy (DOE) program. Upon closer inspection, it was observed that more than 10% of datapoints contributing to the MAPE predictions were the result of low flow rate predictions and are beyond the sensitivity of instrument measurement as a result of normal operational variation and noise.

03 NATURAL GAS↗

DOE OSTI2020

Uncertainty analysis of correlated parameters in automated reaction mechanism generation

Abstract Uncertainty analysis is a useful tool for inspecting and improving detailed kinetic mechanisms because it can identify the greatest sources of model output error. Owing to the very nonlinear relationship between kinetic and thermodynamic parameters and computed concentrations, model predictions can be extremely sensitive to uncertainties in some parameters while uncertainties in other parameters can be irrelevant. Error propagation becomes even more convoluted in automatically generated kinetic models, where input uncertainties are correlated through kinetic rate rules and thermodynamic group values. Local and global uncertainty analyses were implemented and used to analyze error propagation in Reaction Mechanism Generator (RMG), an open‐source software for generating kinetic models. A framework for automatically assigning parameter uncertainties to estimated thermodynamics and kinetics was created, enabling tracking of correlated uncertainties. Local first‐order uncertainty propagation was implemented using sensitivities computed natively within RMG. Global uncertainty analysis was implemented using adaptive Smolyak pseudospectral approximations as implemented in the MIT Uncertainty Quantification Library to efficiently compute and construct polynomial chaos expansions to approximate the dependence of outputs on a subset of uncertain inputs. Cantera was used as a backend for simulating the reactor system in the global analysis. Analyses were performed for a phenyldodecane pyrolysis model. Local and global methods demonstrated similar trends; however, many uncertainties were significantly overestimated by the local analysis. Both local and global analyses show that correlated uncertainties based on kinetic rate rules and thermochemical groups drastically reduce a model's degrees of freedom and have a large impact on the determination of the most influential input parameters. These results highlight the necessity of incorporating uncertainty analysis in the mechanism generation workflow.

Gao, Connie W.↗

DOE OSTI2025

Preliminary Results on Bayesian Inverse UQ for OECD/NEA WPNCS Subgroup 14 Benchmark Exercise for Error Recovery and Experimental Coverage

The Organization for Economic Cooperation and Development (OECD) Working Party on Nucelar Criticality Safety (WPNCS) has proposed a benchmark exercise representative of neutronic behavior in criticality experiments. Here, the goal is to develop confidence in data assimilation techniques used to adjust nuclear data. Participants are given synthetic experimental models with associated measured data and asked to estimate the model parameters given the model and measurements as well as provide predictions for separate application models. In this work, we performed data assimilation using Bayesian inverse Uncertainty Quantification (UQ) with machine learning surrogate models to produce posterior parameter distributions for the requested parameters and posterior predictive distributions for the requested responses. Several experimental models are shown to insufficiently inform the posterior parameter distributions for the applications involved. However, given sufficient experimental data, posterior parameter estimates yielded reduced uncertainty in the response predictions of interest while covering the experimental data.

Bayesian Inference↗

DOE OSTI2025

Uncertainty quantification of a physics-informed model based on sparse identification of a Thermal Energy Distribution System

Integrated energy systems (IES)s are crucial for enhancing the economy and efficiency of power generation sources (e.g., nuclear energy) necessary to unleash American energy dominance. These systems can be integrated with thermal energy storage (TES) and intermittent renewable energies to optimize overall energy use, peak-load regulation, and demand-side responses. However, the stabilization of energy generation, transport, and utilization introduces operational complexities that exceed the challenges of managing each sub-component individually. Currently, though IESs rely on human operators for efficiency and stability, reducing human error risk and enhancing performance through automation is highly desirable. Recent advances at Idaho National Laboratory have demonstrated successful control of the Thermal Energy Distributed System (TEDS). However, the automatic control system depends on a deterministic Sparse Identification of Nonlinear Dynamics with Control (SINDyC) model, which are trained based on simulation data from physics-based simulations. Because of uncertainties in physics-based simulation, SINDyC model results in large discrepancies against experimental data and cannot be reliably used in automatic control. In this paper, we present an innovative approach to address these discrepancies by quantifying uncertainties and developing a more robust model. We first generated trajectories by using first-principles physics codes to encapsulate the experiment. Next, we trained thousands of models by randomly sampling these trajectories. We then collapsed all those models into one probabilistic SINDyC by fitting a multivariate Gaussian distribution onto the resulting coefficient’s distribution. Despite its simplicity, our approach successfully produced 95% confidence intervals that captured the experimental trajectories. It even did so with a higher probability and better U-pooling score across six of the seven relevant quantities of interest (QoIs), as compared to other classical approaches. In conclusion, ongoing research is focusing on generating new experimental trajectories to validate this approach, and on employing Bayesian calibration to refine parametric uncertainties and guide future model development efforts.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Quantifying the structural uncertainty of the aerosol mixing state representation in a modal model

Abstract. Aerosol mixing state is an important emergent property that affects aerosol radiative forcing and aerosol–cloud interactions, but it has not been easy to constrain this property globally. This study aims to verify the global distribution of aerosol mixing state represented by modal models. To quantify the aerosol mixing state, we used the aerosol mixing state indices for submicron aerosol based on the mixing of optically absorbing and non-absorbing species (χo), the mixing of primary carbonaceous and non-primary carbonaceous species (χc), and the mixing of hygroscopic and non-hygroscopic species (χh). To achieve a spatiotemporal comparison, we calculated the mixing state indices using output from the Community Earth System Model with the four-mode version of the Modal Aerosol Module (MAM4) and compared the results with the mixing state indices from a benchmark machine-learned model trained on high-detail particle-resolved simulations from the particle-resolved stochastic aerosol model PartMC-MOSAIC. The two methods yielded very different spatial patterns of the mixing state indices. In some regions, the yearly averaged χ value computed by the MAM4 model differed by up to 70 percentage points from the benchmark values. These errors tended to be zonally structured, with the MAM4 model predicting a more internally mixed aerosol at low latitudes and a more externally mixed aerosol at high latitudes compared to the benchmark. Our study quantifies potential model bias in simulating mixing state in different regions and provides insights into potential improvements to model process representation for a more realistic simulation of aerosols towards better quantification of radiative forcing and aerosol–cloud interactions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A fast multi-fidelity method with uncertainty quantification for complex data correlations: Application to vortex-induced vibrations of marine risers

Here we develop a fast multi-fidelity modeling method for very complex correlations between high- and low-fidelity data by working in modal space to extract the proper correlation function. We apply this method to infer the amplitude of motion of a flexible marine riser in cross-flow, subject to vortex-induced vibrations (VIV). VIV are driven by an absolute instability in the flow, which imposes a frequency (Strouhal) law that requires a matching with the impedance of the structure; this matching is easily achieved because of the rapid parametric variation of the added mass force. As a result, the wavenumber of the riser spatial response is within narrow bands of uncertainty. Hence, an error in wavenumber prediction can cause significant phase-related errors in the shape of the amplitude of response along the riser, rendering correlation between low- and high-fidelity data very complex. Working in modal space as outlined herein, dense data from low-fidelity data, provided by the semi-empirical computer code VIVA, can correlate in modal space with few high-fidelity data, obtained from experiments or fully-resolved CFD simulations, to correct both phase and amplitude and provide predictions that agree very well overall with the correct shape of the amplitude response. We also quantify the uncertainty in the prediction using Bayesian modeling and exploit this uncertainty to formulate an active learning strategy for the best possible location of the sensors providing the high fidelity measurements.

42 ENGINEERING↗

DOE OSTI2023

Count Every Trip: Finding the Uncertainty in Energy Estimates Made from Inferred Travel Modes

To properly inform transport policy and infrastructure changes, transportation related metrics need both measured values and uncertainties of those values. Travel monitoring smartphone apps can record people's travel behavior, but trip data quality is limited by sensor errors, user labeling rates and the accuracy of inference algorithms used for travel diary creation. We discuss the use of phone app recorded travel diary data to estimate energy consumption, and propose the use of propagation of variance to find error bars for such estimates. We define energy consumption for one trip as trip length times the energy intensity per distance unit of the travel mode used. We characterize trip length errors with relative error and inferred trip mode errors with confusion matrix columns. The resulting variances of each measurement are then propagated to the final calculated energy consumption. We tested our uncertainty methods on a dataset that used phone app data combined with prompted recall, consisting of 92,234 labeled trips for over 500,000 miles. Accounting for uncertainty using expected energy intensities and variance propagation gives a dataset-wide aggregate energy consumption percent error of about 9%, within one standard deviation from the truth. Future work could involve applying similar methods to other travel diary based metrics.

ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2024

Investigation of Ethane Dehydrogenation and Hydrogenolysis on Pt(111), Pt(211), and Pt(100): Bayesian Quantification and Correction of DFT-Based Enthalpic and Entropic Uncertainties

Computational investigations of heterogeneously catalyzed reactions using density functional theory (DFT) are often inaccurate, largely due to uncertainties in the choice of DFT functional (enthalpic uncertainty) and approximations for modeling adsorbate movement along the catalyst surface (entropic uncertainty). This work illustrates that both uncertainties are significant in the investigation of ethane dehydrogenation (EDH) and hydrogenolysis on Pt catalysts by considering the complete deconstruction of ethane on Pt(111), Pt(211), and Pt(100) using microkinetic modeling (MKM). Hence, this work uses both noncalibrated and Bayesian-calibrated MKMs to quantify and correct inaccuracies in macroscopic properties due to both uncertainties. A Bayesian approach to the correction of entropic errors was introduced using a “Modified Fermi Function (MFF)” to calibrate between the two bounds of entropy represented by the harmonic oscillator (HO) and free translator (FT) approximations. Regardless of enthalpic and entropic uncertainties, all three surfaces are capable of ethane activation; however, Pt(211) was found to be the most active and is largely responsible for methane production. Next, Pt(111) is largely responsible for acetylene production, and Pt(100) has the highest ethylene selectivity but is most susceptible to coking. By comparison of different calibrated models, the FT entropy approximation was found to better describe EDH under typical experimental conditions. Statistical evidence was found to support Pt(111) as the active site for EDH, assuming that one single site is responsible for the chemistry. On the three surfaces, competing second dehydrogenations to CH 2 CH 2 and CH 3 CH were observed as well as isomerization of CH 3 CH back to CH 2 CH 2 and deeper dehydrogenation of CH 3 CH. In conclusion, C–C cleavage was found to largely proceed via the CH 3 C intermediate on Pt(100) and Pt(111), while on Pt(211), it was via both CHC and CH 3 C.

Bayesian model selection↗

DOE OSTI2021

Chemometrics and Experimental Design for the Quantification of Nitrate Salts in Nitric Acid: Near-Infrared Spectroscopy Absorption Analysis

Implementing remote, real-time spectroscopic monitoring of radiochemical processing streams in hot cell environments requires efficiency and simplicity. The success of optical spectroscopy for the quantification of species in chemical systems highly depends on representative training sets and suitable validation sets. Selecting a training set (i.e., calibration standards) to build multivariate regression models is both time- and resource-consuming using standard one-factor-at-a-time approaches. This study describes the use of experimental design to generate spectral training sets and a validation set for the quantification of sodium nitrate (0–1 M) and nitric acid (0.1–10 M) using the near-infrared water band centered at 1440 nm. Partial least squares regression models were built from training sets generated by both D- and I-optimal experimental designs and a one-factor-at-a-time approach. The prediction performance of each model was evaluated by comparing the bias and standard error of prediction for statistical significance. D- and I-optimal designs reduced the number of samples required to build regression models compared with one-factor-at-a-time while also improving performance. Models must be confirmed against a validation sample set when minimizing the number of samples in the training set. The D-optimal design performed the best when considering both performance and efficiency by improving predictive capability and reducing number of samples in the training set by 64% compared with the one-factor-at-a-time approach. The experimental design approach objectively selects calibration and validation spectral data sets based on statistical criterion to optimize performance and minimize resources.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2025

Partnership Center for High-Fidelity Boundary Plasma Simulation (Final Report)

Within the Partnership Center for High-Fidelity Boundary Plasma Simulation (HBPS), work at UT-Austin was aimed at improved verification, validation, and uncertainty quantification (VVUQ) for edge plasma simulations and on performing gyrokinetics simulations of pedestal instabilities and turbulence in order to expand foundational understanding of pedestal transport. Regarding VVUQ, the accomplishments can be summarized as follows. First, it was shown that the Moment Preserving Constrained Resampling technique, when applied periodically in particle-in-cell simulations in the XGC code, can dramatically improve the accuracy of the simulation at essentially equivalent computational cost. Second, a technique for estimating model correlations, which are required to solve the model selection and sample allocation problem in multifidelity UQ techniques, without sampling the highest fidelity, most computationally expensive model, was developed and demonstrated. Third, previously developed methods for estimating statistical and discretization errors were applied to numerical methods relevant to edge plasma simulations, namely in particle-in-cell-based approaches, and shown to work. Finally, benchmark studies for comparing gyrokinetic codes were developed and performed, leading to reasonable agreement between four commonly used codes. Regarding physics studies, gyrokinetic simulations to investigate microtearing modes in the DIII-D pedestal were performed using the GENE code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Count Every Trip: Finding the Uncertainty in Energy Estimates Made from Inferred Travel Modes

ADVANCED PROPULSION SYSTEMS,MATHEMATICS AND COMPUT↗

DOE OSTI2023

Uncertain of uncertainties? A comparison of uncertainty quantification metrics for chemical data sets

Abstract With the increasingly more important role of machine learning (ML) models in chemical research, the need for putting a level of confidence to the model predictions naturally arises. Several methods for obtaining uncertainty estimates have been proposed in recent years but consensus on the evaluation of these have yet to be established and different studies on uncertainties generally uses different metrics to evaluate them. We compare three of the most popular validation metrics (Spearman’s rank correlation coefficient, the negative log likelihood (NLL) and the miscalibration area) to the error-based calibration introduced by Levi et al. ( Sensors 2022 , 22 , 5540). Importantly, metrics such as the negative log likelihood (NLL) and Spearman’s rank correlation coefficient bear little information in themselves. We therefore introduce reference values obtained through errors simulated directly from the uncertainty distribution. The different metrics target different properties and we show how to interpret them, but we generally find the best overall validation to be done based on the error-based calibration plot introduced by Levi et al. Finally, we illustrate the sensitivity of ranking-based methods (e.g. Spearman’s rank correlation coefficient) towards test set design by using the same toy model ferent test sets and obtaining vastly different metrics (0.05 vs. 0.65).

Rasmussen, Maria H.↗

DOE OSTI2020

Three dimensional cluster analysis for atom probe tomography using Ripley’s K-function and machine learning

The size and structure of spatial molecular and atomic clustering can significantly impact material properties and is therefore important to accurately quantify. Ripley’s K-function (K(r)), a measure of spatial correlation, can be used to perform such quantification when the material system of interest can be represented as a marked point pattern. This work demonstrates how machine learning models based on K (r)-derived metrics can accurately estimate cluster size and intra-cluster density in simulated three dimensional (3D) point patterns containing spherical clusters of varying size; over 90% of model estimates for cluster size and intra-cluster density fall within 11% and 18% error of the true values, respectively. These K (r)-based size and density estimates are then applied to an experimental APT reconstruction to characterize MgZn clusters in a 7000 series aluminum alloy. Here we find that the estimates are more accurate, consistent, and robust to user interaction than estimates from the popular maximum separation algorithm. Using K (r) and machine learning to measure clustering is an accurate and repeatable way to quantify this important material attribute.

36 MATERIALS SCIENCE↗