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At least 307 records · Page 17

Bayesian prior construction for uncertainty quantification in first-principles statistical mechanics

First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or molecular dynamics simulations. Inexpensive surrogates such as cluster expansions enable otherwise intractable calculations by interpolating data from higher accuracy methods, such as Density Functional Theory (DFT). Surrogate models introduce uncertainty into downstream calculations, in addition to any uncertainty inherent to DFT calculations. Bayesian frameworks address this by quantifying uncertainty and incorporating expert knowledge through priors. However, constructing effective priors remains challenging. This work introduces and describes practical strategies for building Bayesian cluster expansions, focusing on basis truncation, hyperparameter selection, and ground state replication. We analyze multiple basis truncation schemes, compare cross-validation to the evidence-approximation for hyperparameter optimization, and provide methods to find and enforce ground-state-preserving models through priors. Additionally, we compare the uncertainties between different approximations to DFT (LDA, PBE, SCAN) against the uncertainty introduced with the use of cluster expansion surrogate models. These approaches are demonstrated on the BCC Li x Mg 1-x and Li x Al 1-x alloys, which are both of interest for solid-state Li batteries. Our results provide guidelines for constructing and utilizing Bayesian cluster expansions, thereby improving the transparency of materials modeling. Furthermore, the approaches and insights developed in this work can be transferred to a wide range of cluster expansion surrogate models, including the atomic cluster expansion and related machine-learned interatomic potential architectures.

Alloy theory↗

Machine-Learning Accelerated Studies of Materials with High Performance and Edge Computing

In the studies of materials, experimental measurements often serve as the reference to verify physics theory and modeling; while theory and modeling provide a fundamental understanding of the physics and principles behind. However, the interactions and cross validation between them have long been a challenge even to-date. Not only that inferring a physics model from experimental data is itself a difficult inverse problem, another major challenge is the orders-of-magnitude longer wall-clock time required to carry out high-fidelity computer modeling to match the timescale of experiments. We envisage that by combining high performance computing, data science, and edge computing technology, the current predicament can be alleviated, and a new paradigm of data-driven physics research will open up. For example, we can accelerate computer simulations by first performing the large-scale modeling on high performance computers and train a machine-learned surrogate model. This computationally inexpensive surrogate model can then be transferred to the computing units residing closely to the experimental facilities to perform high-fidelity simulations at a much higher throughout. The model will also be more amenable to analyzing and validating experimental observations in comparable time scales at a much lower computational cost. Further integration of these accelerated computer simulations with an outer machine learning loop can also inform and direct future experiments, while making the inverse problem of physics model inference more tractable. We will demonstrate a proof-of-concept by using a quantum Monte Carlo application, Dynamical Cluster Approximation (DCA++), to machine-learn a surrogate model and accelerate the study of quantum correlated materials.

Li, Ying Wai↗

Interpretation of borehole strain measurements using surrogate modeling-based optimization

Interpreting strain data measured during well testing requires inverting poroelastic forward models set up to represent an aquifer or reservoir. One approach is to use stochastic methods to conduct the inversion. Subsurface parameters such as elastic modulus, permeability, and geometry of heterogeneities are estimated by searching the parameter space. This is feasible, but cumbersome, requiring more than a week of computation using many hundreds of computer nodes in one of our earlier analyses. This motivated us to consider alternative methods, including an artificial neural network (ANN) as a surrogate model.

Roudini, Soheil↗

Computational materials reliability assessment of hydrogen fueled gas turbine power generation engines

The use of blended fuel sources in land based gas turbine engines drives variations in the resulting operational profile (temperatures and pressures) which can impact engine reliability. Furthermore, variability in the manufacture of components affects the resulting microstructure which directly impacts material performance and reliability. Currently, data-driven models are typically used for maintaining and inspecting fleets of engines. Without explicitly capturing material and operational sources of variability conservatism must be used in developing component-level reliability models. Therefore, there exists an opportunity to use information from materials-scale physics models to better inform reliability modeling and reduce conservatism; the impact is more cost-efficient operation and maintenance of current and future fleets. Specifically, this work establishes a computational framework for evaluating the probabilistic high temperature creep performance of hot-section Ni-based superalloys where uncertainty comes from both microstructural and operational variability. A novel high-fidelity physics model which phenomenologically captures grain-boundary sensitive phenomena has been established. A probabilistic calibration procedure was used to calibrate the model and capture uncertainty in the parameterized model coefficients. A design of experiments methodology was established for identifying informative microstructural digital representations for suitable for forward model evaluation. Results show that training a machine-learning surrogate using this design criteria outperforms random selection of microstructural representations. Finally, two surrogate models were developed: (1) a deterministic surrogate model which predicts the local field response given microstructure, constitutive model parameters, and operating conditions (stress, temperature) and (2) a probabilistic model, where uncertainty comes from constitutive law uncertainty, built using denoising diffusion probabilistic models which samples responses given (1) microstructure and (2) operating conditions. These surrogate models enable partner Siemens Energy to rapidly perform UQ analysis specific to creep deformation across a range of microstructures and operating conditions. The impact is that these ML and physics codes can be used to establish more advanced reliability models for the inspection, servicing, and maintenance of land based gas turbine engines.

36 MATERIALS SCIENCE↗

Anisotropic yield models for lattice unit cell structures exploiting orthotropic symmetry

We report numerical homogenization enables efficient computational analysis and design of multiscale structures made of micro-architected materials including lattice unit cells. However, predicting yield is nontrivial because it requires accurate and efficient predictions of the maximum stress inside the homogenized unit cells. To address this challenge, we develop a macroscale anisotropic yield function for micro-architected materials. The yield function depends on the three-dimensional macroscale stress state and the parameters describing a family of micro-architectures, such as the radii of the struts in a lattice unit cell. To ensure accuracy, we determine the maximum stress using three-dimensional continuum finite-element analysis. To ensure efficiency, we construct surrogate models from the aforementioned high-fidelity results for yield prediction. To reduce simulation costs and surrogate modeling complexity, we leverage orthotropic symmetry commonly found in lattice unit cells. In this paper, we provide a thorough presentation of group representations and the systematic procedure to exploit orthotropic domain symmetry in homogenization and surrogate modeling. We illustrate the use of linear homogenization results to predict yield in specific unit cells without further simulations. We furthermore show that surrogate modeling presents a viable option for anisotropic yield prediction in a continuously parametrized family of micro-architectures. More specifically, despite the dimensionality and degree of nonlinearity in the maximum micro von Mises stress within the unit cell, the surrogate models can predict it with less than 5% error at least 90% of the time. Moreover, the largest under-prediction error, which is more critical than the over-prediction error, is typically less than 10%.

42 ENGINEERING↗

A Bayesian Multi-fidelity Neural Network to Predict Nonlinear Frequency Backbone Curves

The use of structural mechanics models during the design process often leads to the development of models of varying fidelity. Often low-fidelity models are efficient to simulate but lack accuracy, while the high-fidelity counterparts are accurate with less efficiency. Here, this paper presents a multi-fidelity surrogate modeling approach that combines the accuracy of a high-fidelity finite element model with the efficiency of a low-fidelity model to train an even faster surrogate model that parameterizes the design space of interest. The objective of these models is to predict the nonlinear frequency backbone curves of the Tribomechadynamics Research Challenge benchmark structure which exhibits simultaneous nonlinearities from frictional contact and geometric nonlinearity. The surrogate model consists of an ensemble of neural networks that learn the mapping between low and high-fidelity data through nonlinear transformations. Bayesian neural networks are used to assess the surrogate model's uncertainty. Once trained, the multi-fidelity neural network is used to perform sensitivity analysis to assess the influence of the design parameters on the predicted backbone curves. Additionally, Bayesian calibration is performed to update the input parameter distributions to correlate the model parameters to the collection of experimentally measured backbone curves.

42 ENGINEERING↗

Surrogate-driven design optimization with uncertainty constraints in Monte Carlo simulations

In multi-objective design tasks, the computational cost increases rapidly when high-fidelity simulations are used to evaluate objective functions. Surrogate models help mitigate this cost by approximating the simulation output, simplifying the design process. However, under high uncertainty, surrogate models trained on noisy data can produce inaccurate predictions, as their performance depends heavily on the quality of training data. This study investigates the impact of data uncertainty on two multi-objective design problems modelled using Monte Carlo transport simulations: a neutron moderator and an ion-to-neutron converter. For each, a grid search was performed using five different tally uncertainty levels to generate training data for neural network surrogate models. These models were then optimized using NSGA-III. The recovered Pareto-fronts were analyzed across uncertainty levels: in the moderator problem, normalized hypervolume dropped from 0.886 at 1.0% uncertainty to 0.748 at 10% uncertainty, while in the converter problem it remained near 0.50 for all cases. Average simulation times were also compared to evaluate the trade-off between accuracy and computational cost. Results show that the influence of simulation uncertainty is strongly problem-dependent. In the neutron moderator case, higher uncertainties led to exaggerated objective sensitivities and distorted Pareto-fronts, reducing normalized hypervolume. In contrast, the ion-to-neutron converter task was less affected—low-fidelity simulations produced results similar to those from high-fidelity data. These findings suggest that a fixed-fidelity approach is not optimal. Surrogate models can recover the Pareto-front under noisy conditions, and multi-fidelity studies help identify suitable uncertainty levels for each problem to balance efficiency and accuracy.

07 ISOTOPE AND RADIATION SOURCES↗

The case for digital twins in metal additive manufacturing

The digital twin (DT) is a relatively new concept that is finding increased acceptance in industry. A DT is generally considered as comprising a physical entity, its virtual replica, and two-way digital data communications in-between. Its primary purpose is to leverage the process intelligence captured within digital models—or usually their faster-solving surrogates—towards generating increased value from the physical entities. The surrogate models are created using machine learning based on data obtained from the field, experiments and digital models, which may be physics-based or statistics-based. Anomaly detection and correction, and diagnostic closed-loop process control are examples of how a process DT can be deployed. In the manufacturing industry, its use can achieve improvements in product quality and process productivity. Metal additive manufacturing (AM) stands to gain tremendously from the use of DTs. This is because the AM process is inherently chaotic, resulting in poor repeatability. However, a DT acting in a supervisory role can inject certainty into the process by actively keeping it within bounds through real-time control commands. Closed-loop feedforward control is achieved by observing the process through sensors that monitor critical parameters and, if there are any deviations from their respective optimal ranges, suitable corrective actions are triggered. The type of corrective action (e.g. a change in laser power or a modification to the scanning speed) and its magnitude are determined by interrogating the surrogate models. Because of their artificial intelligence (AI)-endowed predictive capabilities, which allow them to foresee a future state of the physical twin (e.g. the AM process), DTs proactively take context-sensitive preventative steps, whereas traditional closed-loop feedback control is usually reactive. Apart from assisting a build process in real-time, a DT can help with planning the build of a part by pinpointing the optimum processing window relevant to the desired outcome. Again, the surrogate models are consulted to obtain the required information. In this article, we explain how the application of DTs to the metal AM process can significantly widen its application space by making the process more repeatable (through quality assurance) and cheaper (by getting builds right the first time).

36 MATERIALS SCIENCE↗

Data-driven emulation of modal aerosol microphysics via neural operator-based modeling

The complexity and the small characteristic scales of aerosol microphysical processes pose a big challenge for accurate and efficient Earth system simulations at regional and global scales. In this work, we construct and evaluate a surrogate model: the aerosol deep operator network (ADON), a physics-inspired dual-net architecture for emulating the aerosol microphysics parameterization suite in the version 2 of the Energy Earth System Model (E3SMv2). The current version of the surrogate model is trained on a dataset comprising 9.8 million samples obtained from a global E3SMv2 simulation with the horizontal resolution of about one degree under cloud-free conditions. Incorporating domain spatial and temporal coordinates, as well as principle components extracted from training data, the dual-net surrogate model effectively captures the intricate representations of aerosol and the relationship with atmospheric state variables, achieving an R-squared score over $$95.7\%$$ for all the lognormal aerosol modes in the extrapolated regime. The validated model provides feature importance of input variables and their impact on the predictive capacity of the surrogate model in relation to the E3SM. The computational cost of online inference time deployed on CPUs and GPUs with lower precisions highlights ADON’s efficiency and potential in robust predictive modeling for large-scale Earth system computations.

Bai, Zhe↗

Investigating the influence of particle distribution on force and torque statistics using hierarchical machine learning

An accurate representation of hydrodynamic force and torque experienced by every particle in a distribution can be obtained from particle resolved (PR) simulations. These unique quantities are influenced by the deterministic position of surrounding particles. However, systems simulated with this methodology are typically limited to particles due to the involved computational cost. This resource requirement is a major bottleneck in analyzing the effect of variations in particle distribution. Here, this article attempts to address this bottleneck by availing relatively inexpensive deep learning models. The surrogate models that we employ in this article use a physics‐based hierarchical framework and symmetry‐preserving neural networks to achieve robustness with limited training data. This article first performs additional generalizability tests on PR data of distinct distributions that are not involved in the training process. The models are then deployed on several different particle distributions. Impact of clustering and structure on the observed statistics are investigated.

42 ENGINEERING↗

Neural message-passing for objective-based uncertainty quantification and optimal experimental design

Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be high. In such cases, based on a Bayesian paradigm, we can design robust operators retaining the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to enhance the performance of such operators maximally. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) provides an effective means for quantifying uncertainty in complex systems, the high computational cost of estimating MOCU has been a challenge in applying it to real-world scientific/engineering problems. In this work, we propose a novel scheme to reduce the computational cost for objective-UQ via MOCU based on a data-driven approach. We adopt a neural message-passing model for surrogate modeling, incorporating a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance robust synchronization performance through uncertainty reduction. We show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, without any visible performance loss compared to the state-of-the-art. The proposed approach applies to general OED tasks, beyond the Kuramoto model.

97 MATHEMATICS AND COMPUTING↗

Digital twin framework for PIP-II linac: AI-driven multi-scale modeling from ion source to 800 MeV

The PIP-II superconducting linac at Fermilab is designed to deliver multi-megawatt proton beams for neutrino physics and other high-intensity applications. To expedite commissioning and enhance operational reliability, we have developed an EPICS-based data flow framework that seamlessly integrates digital twins (DT) with physical twins (PT). These digital twins comprise high-fidelity beam dynamics models or data-driven surrogate models connected to their physical counterparts through real-time diagnostics and advanced machine-learning algorithms.Central to this framework is Linac_Gen, an accelerated simulation tool that incorporates convolutional neural networks, random forests, and genetic algorithms to provide up to a tenfold speedup in optimizing the accelerator geometry model. An EPICS translator layer ensures interoperability by efficiently mapping lattice parameters across diverse simulation platforms.Our EPICS-based framework supports multiple operational modes—monitoring, passive learning, closed-loop control, and online learning—covering the entire machine lifecycle. By leveraging HPC resources and multi-objective optimization techniques, the digital twin enables adaptive trajectory correction, real-time fault detection, and predictive modeling of beam stability. This comprehensive approach paves the way for robust, high-intensity operation and data-driven accelerator R&D at Fermilab.

Pathak, Abhishek [Fermilab]↗

Bayes_Opt-SWMM: A Gaussian process-based Bayesian optimization tool for real-time flood modeling with SWMM

Real-time flood model plays a pivotal role in averting urban flood damage, particularly when there is minimal lead time for preparatory measures. However, urban flood modeling in real-time often contends with inherent uncertainties arising from input data uncertainty and parameter ambiguities. Here this study introduces a real-time calibration (RTC) tool called Bayes_Opt-SWMM, specifically tailored for real-time urban flood modeling and uncertainty optimization. This tool leverages the Gaussian process-based Bayesian optimization algorithm and interfaces seamlessly with the Stormwater Management Model (SWMM). It integrates real-time model forcing data and flood monitoring collected through sensors and gauges which are strategically placed within critical locations of urban drainage systems. Our approach hinges on the Surrogate Model based Uncertainty Optimization (SMUO) concept, providing an avenue for enhancing real-time flood modeling. Bayes_Opt-SWMM runs the optimization process using a surrogate model called Gaussian Process emulator with two inference methods: (1) the Gaussian Process (GP) model and (2) Markov Chain Monte Carlo (MCMC) algorithm in GP model (GP_MCMC). Furthermore, three acquisition functions, namely Expected Improvement (EI), Maximum Probability of Improvement (MPI), and Lower Confidence Bound (LCB), facilitate optimal parameter fitting within the surrogate models. The efficiency of GP-based surrogate models in learning SWMM model parameters, leads to an improved uncertainty quantification and accelerated real-time flood modeling in urban areas. Overall, Bayes_Opt-SWMM emerges as a cost-effective and valuable tool for real-time flood modeling and monitoring, with significant potential for managing intelligent storm water systems in urban environments.

54 ENVIRONMENTAL SCIENCES↗

Energy-efficient, Large-scale Molecular Dynamics Simulations via Hardware- and Algorithm-level Optimization

This work aims to develop a framework for energy-efficient computing that will enable molecular dynamics (MD) simulations of large-scale phenomena with atomic precision and simultaneously remove computational bottlenecks limiting the speed of MD simulations. We seek to implement such an approach through the development of surrogate models for the interatomic force calculation combined with the use of mixed numerical precision formats. For a model system of neutral atoms (only pairwise interactions), significant force calculation efficiency improvements were achieved, without detrimental effects on atomic structures or average energies, using single precision, by developing a surrogate model (deep neural network), and by quantizing this surrogate model. For a model system of charged atoms, the reciprocal-space calculation of electrostatic interactions was identified as the main bottleneck, and the development of a surrogate model should be pursued to achieve an estimated one-order-of-magnitude additional speedup.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Uncertainty quantification and sensitivity analysis of a nuclear thermal propulsion reactor startup sequence

The research presented in this article describes progress in applying stochastic methods, uncertainty quantification, parametric studies, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated via the radiation transport code Griffin to simulate neutronics. Our goal is to develop a reduced-order (surrogate) model that can be rapidly sampled with perturbations to multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums (CDs), which is itself controlled by a hybrid proportional-integral-derivative (PID) controller actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time [Λ] and effective delayed neutron fraction [ β eff ] from a transient Griffin simulation executed via Griffin’s improved quasi-static solver to provide the kinetic parameters) as inputs to functions that control the CD rotation angle. By investigating numerous stochastic approaches, we developed a dual-purpose surrogate model of the NTP system, using polynomial regression in the Multiphysics Object-Oriented Simulation Environment (MOOSE) Stochastic Tools Module (STM). The trained model can be rapidly sampled while simultaneously perturbing various input parameters, such as coefficients on the PID control or temperature (directly affecting the neutron cross section). The surrogate model delivers accurate (within 5%) results at speeds orders of magnitude faster (minutes, not days of computational time) than the base model. Once the surrogate model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs as well as the effects of these inputs on the model output. For example, coefficients used in the PID control system may vary due to some type of physical interference, or uncertainty may exist in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters, and operational boundaries can be determined. The goal of this work is to support development of an advanced control system for operating CDs in a functioning NTP system. This work is a scoping study of the MOOSE STM.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

Iterative sampling of expensive simulations for faster deep surrogate training

Deep neural network (DNN) surrogates of expensive physics simulations are enabling a rapid change in the way that common experimental design and analysis tasks are approached. Surrogate models allow simulations to be performed in parallel and separately from downstream tasks, thereby enabling analyses that would be impossible with the simulation in-the-loop; surrogates based on DNNs can effectively emulate diverse non-scalar data of the types collected in fusion and laboratory-astrophysics experiments. The challenge is in training the surrogate model, for which large ensembles of physics simulations must be run, preferably without wasting computational effort on uninteresting simulations. Here, in this paper, we present an iterative sampling scheme that can preferentially propose simulations in interesting regions of parameter space without neglecting unexplored regions, allowing high-quality and wide-ranging surrogate models to be trained using 2–3 times fewer simulations compare to space-filling designs. Our approach uses an explicit importance function defined on the simulation output space, balanced against a measure of simulation density which serves as a proxy for surrogate accuracy. It is easy to implement and can be tuned to find interesting simulations early in the study, allowing surrogates to be trained quickly and refined as new simulations become available; this represents an important step towards the routine generation of deep surrogate models quickly enough to be truly relevant to experimental work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fusion RF Modeling Machine Learning (FusionML_RF) v1.0

FusionML_RF consists of multiple codes and trained machine learning (ML) models that perform low-cost output modeling from the Genray-CQL3D. Three machine learning techniques (multilayer perceptron, random forest, and Gaussian process) provide fast surrogate models for lower hybrid current drive (LHCD) simulations. For example, completing a single GENRAY/CQL3D simulation without radial diffusion of fast electrons requires several minutes of wall-clock time. On the other hand, these ML models achieve ~ms of inference time with high accuracy across the input parameter space. This software collection consists of multiple components. (1) codes that use ML methods and precomputed Genray-CQL3D simulation output to build regression models that enable approximate computations of Genray-CLQ3D outputs from arbitrary but physically meaningful input parameters (surrogate modeling); (2) three trained models created by the team, using a database of 16,000+ GENRAY/CQL3D simulations, to study the performance of ML models for surrogate modeling; (3) codes that load the trained models and simulation data, and then compute mean squared error between the models' predictions and the ground truth of simulation output data. This collection is being made available in conjunction with a scientific publication about the work to promote reusability and provide an artifact of the scientific work.

Bai, Zhe↗

An active learning framework for the rapid assessment of galvanic corrosion

The current present in a galvanic couple can define its resistance or susceptibility to corrosion. However, as the current is dependent upon environmental, material, and geometrical parameters it is experimentally costly to measure. To reduce these costs, Finite Element (FE) simulations can be used to assess the cathodic current but also require experimental inputs to define boundary conditions. Due to these challenges, it is crucial to accelerate predictions and accurately predict the current output for different environments and geometries representative of in-service conditions. Machine learned surrogate models provides a means to accelerate corrosion predictions. However, a one-time cost is incurred in procuring the simulation and experimental dataset necessary to calibrate the surrogate model. Therefore, an active learning protocol is developed through calibration of a low-cost surrogate model for the cathodic current of an exemplar galvanic couple (AA7075-SS304) as a function of environmental and geometric parameters. The surrogate model is calibrated on a dataset of FE simulations, and calculates an acquisition function that identifies specific additional inputs with the maximum potential to improve the current predictions. This is accomplished through a staggered workflow that not only improves and refines prediction, but identifies the points at which the most information is gained, thus enabling expansion to a larger parameter space. The protocols developed and demonstrated in this work provide a powerful tool for screening various forms of corrosion under in-service conditions.

36 MATERIALS SCIENCE↗