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DOE OSTI2023

Context-aware learning of hierarchies of low-fidelity models for multi-fidelity uncertainty quantification

Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is computationally expensive. This work proposes a context-aware multi-fidelity Monte Carlo method that optimally balances the costs of training low-fidelity models with the costs of Monte Carlo sampling. It generalizes the previously developed context-aware bi-fidelity Monte Carlo method to hierarchies of multiple models and to more general types of low-fidelity models. When training low-fidelity models, the proposed approach takes into account the context in which the learned low-fidelity models will be used, namely for variance reduction in Monte Carlo estimation, which allows it to find optimal trade-offs between training and sampling to minimize upper bounds of the mean-squared errors of the estimators for given computational budgets. This is in stark contrast to traditional surrogate modeling and model reduction techniques that construct low-fidelity models with the primary goal of approximating well the high-fidelity model outputs and typically ignore the context in which the learned models will be used in upstream tasks. Further, the proposed context-aware multi-fidelity Monte Carlo method applies to hierarchies of a wide range of types of low-fidelity models such as sparse-grid and deep-network models. Numerical experiments with the gyrokinetic simulation code Gene show speedups of up to two orders of magnitude compared to standard estimators when quantifying uncertainties in small-scale fluctuations in confined plasma in fusion reactors. This corresponds to a runtime reduction from 72 days to four hours on one node of the Lonestar6 supercomputer at the Texas Advanced Computing Center.

42 ENGINEERING↗

DOE OSTI2024

Shielding Benchmark Comparison - MCNP6.2

This report documents the calculations performed for a shielding code comparison between various Department of Energy (DOE) sites. These shielding calculations were performed using an experiment drawn from the International Handbook of Evaluated Criticality Safety Benchmark Experiments, published by the Organisation for Economic Cooperation and Development/Nuclear Energy Agency (OECD/NEA). The benchmark selected for comparison is ALARM-CF-AIR-LAB-001 (“Neutron Fields in the Three-Section Concrete Labyrinth from Cf-252 Source, Benchmark ALARM CF AIR LAB-001”). The Y-12 submission for this code comparison was performed with Monte Carlo N Particle (MCNP) Transport Code System, Version 6.2 and Automated Variance Reduction Generator (ADVANTG).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Active learning with multifidelity modeling for efficient rare event simulation

Here, while multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model. We demonstrate our framework using several academic case studies (including some high-dimensional problems) and two finite element model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.

42 ENGINEERING↗

DOE OSTI2025

Covariance-Free Bifidelity Control Variates Importance Sampling for Rare Event Reliability Analysis

Multifidelity modeling has been steadily gaining attention as a tool to address the problem of exorbitant model evaluation costs that makes the estimation of failure probabilities a significant computational challenge for complex real-world problems, particularly when failure is a rare event. To implement multifidelity modeling, estimators that efficiently combine information from multiple models/sources are necessary. In past works, the variance reduction techniques of control variates (CV) and importance sampling (IS) have been leveraged for this task. In this paper, we present the CVIS framework—a creative take on a coupled CV and IS estimator for bifidelity reliability analysis. The framework addresses some of the practical challenges of the CV method by using an estimator for the control variate mean and sidestepping the need to estimate the covariance between the original estimator and the control variate through a clever choice for the tuning constant. Furthermore, the task of selecting an efficient IS distribution is also considered, with a view towards maximally leveraging the bifidelity structure and maintaining expressivity. Additionally, a diagnostic is provided that indicates both the efficiency of the algorithm as well as the relative predictive quality of the models utilized. Finally, the behavior and performance of the framework is explored through analytical and numerical examples.

Markov chain Monte Carlo↗

DOE OSTI2023

Optimizing shift selection in multilevel Monte Carlo for disconnected diagrams in lattice QCD

The calculation of disconnected diagram contributions to physical signals is a computationally expensive task in Lattice QCD. To extract the physical signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix, must be stochastically estimated. Because the variance of the stochastic estimator is typically large, variance reduction techniques must be employed. Multilevel Monte Carlo (MLMC) methods reduce the variance of the trace estimator by utilizing a telescoping sequence of estimators. Frequency Splitting is one such method that uses a sequence of inverses of shifted operators to estimate the trace of the inverse lattice Dirac operator, however there is no a priori way to select the shifts that minimize the cost of the multilevel trace estimation. Here we present a sampling and interpolation scheme that is able to predict the variances associated with Frequency Splitting under displacements of the underlying space time lattice. The interpolation scheme is able to predict the variances to high accuracy and therefore chooses shifts that correspond to an approximate minimum of the cost for the trace estimation. We show that Frequency Splitting with the chosen shifts displays significant speedups over multigrid deflation, and that these shifts can be used for multiple configurations within the same ensemble with no penalty to performance.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Interpolation as a means of shift selection for multilevel Monte Carlo with lattice displacements

The calculation of disconnected diagram contributions to physical signals is a computationally expensive task in Lattice QCD. To extract the physical signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix, must be stochastically estimated. Because the variance of the stochastic estimator is typically large, variance reduction techniques must be employed. Multilevel Monte Carlo (MLMC) methods reduce the variance of the trace estimator by utilizing a telescoping sequence of estimators. Frequency Splitting is one such method that uses a sequence of inverses of shifted operators to estimate the trace of the inverse of the lattice Dirac operator, however there is no a priori way to select the shifts that minimize the cost of the multilevel trace estimation. We present a sampling and interpolation scheme that is able to predict the variances associated with Frequency Splitting under displacements of the underlying space time lattice. The interpolation scheme is able to predict the variances to high accuracy and therefore choose shifts that correspond to an approximate minimum of the cost for the trace estimation. We show that Frequency Splitting with the chosen shifts displays significant speedups over multigrid deflation

Whyte, Travis↗

DOE OSTI2025

Denoising Autoencoder for Reconstructing Sensor Observation Data and Predicting Evapotranspiration: Noisy and Missing Values Repair and Uncertainty Quantification

Abstract Machine learning (ML) methods applied in scientific research often deal with interrelated features in high‐dimensional data. Reducing data noise and redundancy is needed to increase prediction accuracy and efficiency especially when dealing with data from field sensors. We explored an unsupervised learning method, the denoising autoencoder (DAE), to extract the underlying data structure from noisy raw data in the context of predicting hydrologic quantities from multiple field sensors. These sensors have intrinsic instrumental noise and occasional malfunctions that cause missing values. Our DAE neural network reconstructed meteorological sensor data containing noise and missing values to predict evapotranspiration in a mountainous watershed. The DAE reconstructed the sensor variables with a mean coefficient of determination value of 0.77 across 15 dimensions representing individual sensors. It reduced variance and bias uncertainties compared to a classical autoencoder model. The reconstruction quality varied across dimensions depending on their cross‐correlation and alignment with the underlying data structure. Uncertainties arising from the model structure were overall higher than those resulting from data corruption. We attached the DAE structure to a downstream ET‐prediction neural network in three formats and achieved reasonably accurate ET predictions . The use of the DAE notably reduced variance uncertainty in ET prediction. However, excessive variance reduction may be accompanied by an increase in bias due to the intrinsic bias‐variance tradeoff. Our method of evaluating and reducing uncertainties in aggregated data from different sources can be used to improve predictive models, process understanding, and uncertainty quantification for better water resource management. Plain Language Summary We present a machine learning method, namely the denoising autoencoder, which reduces the effects of data noise and missing values typically present in scientific data sets collected through sensor measurements. This method selects the most relevant information from noisy raw data collected by the instruments and fills in missing values. To demonstrate the effectiveness of our method, we applied it to predict evapotranspiration, a hydrologic variable that represents the water moved from the land surface to the atmosphere through a combination of evaporation and plant water use (transpiration). We also used a random sampling technique (the Monte Carlo method) to compare the uncertainty in the predictions when using the raw and noisy data versus the reconstructed data. The denoising process produced more accurate predictions of evapotranspiration with less uncertainty. Improved predictions of evapotranspiration can lead to a better understanding and accounting of water budgets. This ML approach is broadly suitable for a wide variety of applications that involve noisy sensor data with missing values. Key Points We used a denoising autoencoder (DAE) neural network to reduce noise in meteorological and soil sensor observations by on average We used Monte Carlo sampling to estimate the bias and variance of all model outputs, including uncertainty sources from data and the model We attached the DAE component to a downstream neural network to predict ET with the variance reduced by , compared to that without the DAE

denoising autoencoder↗

NASA NTRS2014

Long-Period Tidal Variations in the Length of Day

A new model of long-period tidal variations in length of day is developed. The model comprises 80 spectral lines with periods between 18.6 years and 4.7 days, and it consistently includes effects of mantle anelasticity and dynamic ocean tides for all lines. The anelastic properties followWahr and Bergen; experimental confirmation for their results now exists at the fortnightly period, but there remains uncertainty when extrapolating to the longest periods. The ocean modeling builds on recent work with the fortnightly constituent, which suggests that oceanic tidal angular momentum can be reliably predicted at these periods without data assimilation. This is a critical property when modeling most long-period tides, for which little observational data exist. Dynamic ocean effects are quite pronounced at shortest periods as out-of-phase rotation components become nearly as large as in-phase components. The model is tested against a 20 year time series of space geodetic measurements of length of day. The current international standard model is shown to leave significant residual tidal energy, and the new model is found to mostly eliminate that energy, with especially large variance reduction for constituents Sa, Ssa, Mf, and Mt.

LOD tidal oscillations↗

DOE OSTI2024

Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Dispersion-enhanced sequential batch sampling for adaptive contour estimation

In computer simulation and optimal design, sequential batch sampling offers an appealing way to iteratively stipulate optimal sampling points based upon existing selections and efficiently construct surrogate modeling. Nonetheless, the issue of near duplicates poses tremendous quandary for sequential learning. It refers to the situation that selected critical points cluster together in each sampling batch, which are individually but not collectively informative towards the optimal design. Near duplicates severely diminish the computational efficiency as they barely contribute extra information towards update of the surrogate. To address this issue, we impose a dispersion criterion on concurrent selection of sampling points, which essentially forces a sparse distribution of critical points in each batch, and demonstrate the effectiveness of this approach in adaptive contour estimation. Specifically, we adopt Gaussian process surrogate to emulate the simulator, acquire variance reduction of the critical region from new sampling points as a dispersion criterion, and combine it with the modified expected improvement (EI) function for critical batch selection. The critical region here is the proximity of the contour of interest. This proposed approach is vindicated in numerical examples of a two-dimensional four-branch function, a four-dimensional function with a disjoint contour of interest and a time-delay dynamic system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Weak-form latent space dynamics identification

Recent work in data-driven modeling has demonstrated that a weak formulation of model equations enhances the noise robustness of a wide range of computational methods. In this paper, we demonstrate the power of the weak form to enhance the LaSDI (Latent Space Dynamics Identification) algorithm, a recently developed data-driven reduced order modeling technique. We introduce a weak form-based version WLaSDI (Weak-form Latent Space Dynamics Identification). WLaSDI first compresses data, then projects onto the test functions and learns the local latent space models. Notably, WLaSDI demonstrates significantly enhanced robustness to noise. With WLaSDI, the local latent space is obtained using weak-form equation learning techniques. Compared to the standard sparse identification of nonlinear dynamics (SINDy) used in LaSDI, the variance reduction of the weak form guarantees a robust and precise latent space recovery, hence allowing for a fast, robust, and accurate simulation. We demonstrate the efficacy of WLaSDI vs. LaSDI on several common benchmark examples including viscid and inviscid Burgers', radial advection, and heat conduction. For instance, in the case of 1D inviscid Burgers' simulations with the addition of up to 100% Gaussian white noise, the relative error remains consistently below 6% for WLaSDI, while it can exceed 10,000% for LaSDI. Similarly, for radial advection simulations, the relative errors stay below 15% for WLaSDI, in stark contrast to the potential errors of up to 10,000% with LaSDI. Moreover, speedups of several orders of magnitude can be obtained with WLaSDI. For example applying WLaSDI to 1D Burgers' yields a 140X speedup compared to the corresponding full order model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Shutdown dose rate analysis with the Shift Monte Carlo radiation transport code and modular verification workflow

Calculation of the shutdown dose rate is crucial for safe fusion reactor operations. The Rigorous-two-step (R2S) method is a method that requires connected neutron transport, activation, and gamma transport. Shift has integrated variance reduction with a deterministic solver Denovo, supports multiple geometry formats, and is scalable. These features make it an attractive transport solver choice for an R2S workflow. An R2S workflow for the Shift Monte Carlo code is developed and compared to the existing Oak Ridge National Laboratory Shutdown Dose Rate Code Suite (ORCS) workflow. Also, a Python framework for integrating two R2S workflows is developed to mix and match each step in the R2S workflow for improved collaboration and verification experience. In this study, results show that the Shift-Denovo R2S workflow and the ORCS workflow calculate the shutdown dose rate of the ITER Shutdown Dose Rate benchmark problem with an average relative error of 2.285%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Global stochastic optimization of stellarator coil configurations

In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case of the National Compact Stellarator Experiment (NCSX) project. Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the sample average approximation; and Adam, equipped with a control variate for variance reduction. Numerical simulations performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than 0.1% of the cost of previous work, which considered solely local stochastic optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Decay Dose Shielding Analysis with Hybrid Unstructured Mesh/Constructive Solid Geometry Monte Carlo Calculation and ADVANTG Acceleration

Here, the target segments of the Oak Ridge National Laboratory Second Target Station (STS) neutron production facility become highly activated due to spallation reactions or nuclei transmutation by primary protons and emitted neutrons. Once the target segments are removed from their location within the core vessel, decay dose rates must be accurately quantified to determine the shielding configurations of remote-handling tools and transport casks and to aid in planning maintenance activities. For this analysis, we utilized a hybrid unstructured mesh (UM)/constructive solid geometry approach for calculating spallation products and neutron fluxes, activation calculations using the AARE package that includes the CINDER2008 activation code to calculate the decay photon source at different cooling times, and the ADVANTG code to accelerate the final decay photon transport calculation. Both Type 316 stainless steel (SS-316) and lead were investigated as candidates for shielding materials. The decay photon transport calculation through the thick SS-316 or lead shields exhibited between 25 and 30 orders-of-magnitude attenuations in the radial direction, depending on the shield. Such a difficult shielding calculation required advanced variance reduction. ADVANTG has some missing features, which limits its usability in spallation neutron source applications. It does not support volumetric sources created for MCNP6.2 UM capability. An approximate source was created for this problem. Not only was this approximate source needed for running the ADVANTG calculation to generate the weight windows, but also it was essential to develop source biasing (SB) parameters that were crucial for dramatically accelerating the decay photon transport in this problem. With this approximate source, the analysis was completed in a very reasonable computational time, and the design of the STS remote-handling equipment was finalized. This paper compares the efficiency of Monte Carlo simulations with different weight window and SB parameters calculated using different approximate ADVANTG calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Analysis of Second Target Station Target Removal Dose Rates

The Second Target Station (STS) project at Oak Ridge National Laboratory’s spallation neutron source is a crucial initiative for maintaining U.S. leadership in neutron sciences. The STS aims to create the world’s brightest pulsed cold neutron source, enabling cutting-edge research across various scientific disciplines. To ensure safe and efficient maintenance operations, understanding the effects of shutdown dose rates from activated components within the STS target systems is essential. This study establishes a computational framework for calculating decay gamma sources and subsequent shutdown dose rates utilizing advanced methods to account for all activation channels, including high-energy interactions down to thermal neutron capture. This study describes a novel integration of multiple tools and provides an effective means of analyzing activation and shutdown dose rates at spallation neutron facilities. A custom-developed script automates the decay gamma source generation process, ensuring proper sampling during the variance reduction phase, which is critical for accurate predictions of shutdown dose rates.

Transmutation↗

DOE OSTI2025

Evaluation of PBR Spent Fuel Criticality and Dose Rate Compliance for Storage and Transportation

Spent tri-structural isotropic (TRISO)–based fuels have a strong track record in storage and transportation without documented incidents. This work seeks to reduce uncertainty to aid in more informed spent fuel management of TRISO-based fuels by modeling both fresh and spent pebble bed reactor (PBR) fuel and comparing the results to the regulatory standards from 10 CFR 71. SCALE was used for all modeling due to it having fast and accurate methods for handling PBR fuel modeling, as well as having an efficient method for shielding calculations in monaco with automated variance reduction using importance calculations (MAVRIC), which utilizes the consistent adjoint-driven importance sampling (CADIS) and the forward-weighted consistent adjoint-driven importance sampling (FW-CADIS) methods. KENO-VI was used for all criticality calculations, TSUNAMI was used for uncertainty quantification on k-effective, TRITON and the Oak Ridge isotope generation code (ORIGEN) were both used for depletion of the fuel, and MAVRIC was used for shielding calculations. For criticality assessments, this study focused on the requirement that the value of the neutron multiplication factor, k-effective (k-eff), would not exceed a peak value of 0.95, including uncertainty, with 95% confidence. Criticality was initially examined by modeling fresh fuel from three different designs—HTR-10 fuel, PBMR-400 fuel, and demonstration fuel representative of a TRISO-fueled modern high-temperature gas reactor (HTGR) design, henceforth referred to as Demo HTGR—and placing them into various sized containers with conditions described in 10 CFR 71 to quantify the peak k-eff state. When the peak value of 0.95 k-eff was exceeded, mitigation methods were examined in those scenarios. Burnup credit, pebble displacement in areas of strong neutron multiplication, and random pebble replacement using pebbles of various compositions and replacement fractions were examined. In summary, the criticality of PBR fuels can be well accounted for by restricting container size, taking credit for burnup, or by displacing/replacing pebbles. Uncertainty of the k-eff due to nuclear data uncertainties was recorded at ~0.6644%Δk/k, or roughly 664% mil (pcm). The nuclear data–induced uncertainty was relatively small and should not require significant modification in the design to be accounted for. Revisions to the evaluated nuclear data file values have been shown to have a larger impact than nuclear data–induced uncertainty. For dose rate aspects, U.S. Nuclear Regulatory Commission regulations require a maximum dose rate of 10 millirem per hour (mrem/h) at 2 meters. In examining the dose rate behavior of spent PBR fuel, the representative Demo HTGR fuel was modeled exclusively due to it possessing the highest target burnup of the examined fuels. Equilibrium cycle modeling methods were used to produce a higher-fidelity discharge isotopic composition than simple assumptions, such as reflected pebbles. The discharge composition was used as a source term in the fixed-source transport shielding calculations, and dose rates were calculated at 2 m for the shortest possible cooling time. The low concentration of fuel material led to dose rates that were in line with regulatory limits, despite the high burnup when compared to traditional light water reactor fuels. In conclusion, the methods employed in this study would require more work to further verify and validate and are limited to the criticality and dose rate analyses performed.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Applications of flow models to the generation of correlated lattice QCD ensembles

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these correlations can be exploited for variance reduction in the computation of observables. Three different proof-of-concept applications are demonstrated using a novel residual flow architecture: continuum limits of gauge theories, the mass dependence of QCD observables, and hadronic matrix elements based on the Feynman–Hellmann approach. In all three cases, it is shown that statistical uncertainties are significantly reduced when machine-learned flows are incorporated as compared with the same calculations performed with uncorrelated ensembles or direct reweighting. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

A Machine Learning–Based Tire Life Prediction Framework for Increasing Life of Commercial Vehicle Tires

In the commercial freight industry, tire retreading decisions are often conservative due to limited knowledge of a tire’s remaining service life. This practice leads to increased costs and material waste. This paper proposes a machine learning–based approach for estimating tire casing life and retreadability, focusing on usage data rather than wear information. This approach could extend the tire’s lifespan and reduce landfill waste. Data integration from diverse tire casing measurement sources presents challenges, including imbalanced removal data. Our methodology addresses these challenges by using historical inspection, telematics, and finite element modeling (FEM) datasets. We introduce “Tire Casing Energy” as a comprehensive usage input and apply a Variance-Reduction Synthetic Minority Oversampling Technique (VR-SMOTE) for data imbalance rectification. A random forest model is used to estimate the state of the tire casing and the casing removal probability, with Bayesian optimization applied for hyperparameter tuning, enhancing model accuracy. Here, the proposed prediction framework is able to differentiate different truck fleets and tire locations based on their usage parameters. With the aid of this machine learning model, the importance and sensitivity of different tire usage parameters can be obtained, which is beneficial to maximize tire life.

Data balancing↗