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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Visual feedback and guided balance training in an immersive virtual reality environment for lower extremity rehabilitation

Balance training is essential for physical rehabilitation procedures, as it can improve functional mobility and enhance cognitive coordination. However, conventional balance training methods may have limitations in terms of motivation, real-time objective feedback, and personalization, which a virtual reality (VR) setup may provide a better alternative. In this work, we present an immersive VR training environment for lower extremity balance rehabilitation with real-time guidance and feedback. The VR training environment immerses the user in a 3D ice rink model where a virtual coach (agent) leads them through a series of balance poses, and the user controls a trainee avatar with their own movements. Here we developed two coaching styles: positive-reinforcement and autonomous-supportive, and two viewpoints of the trainee avatar: first-person and third-person. The proposed environment was evaluated in a user study with healthy, non-clinical participants (n = 16, 24.4 ± 5.7 years old, 9 females). Our results show that participants showed stronger performance in the positive-reinforcement style compared to the autonomous-supportive style. Additionally, in the third-person viewpoint, the participants exhibited more stability in the positive-reinforcement style compared to the autonomous-supportive style. For viewpoint, participants exhibited stronger performance in the first-person viewpoint compared to third-person in the autonomous-supportive style, while they were comparable in the positive-reinforcement style. We observed no significant effects on the foot height and number of mistakes. Furthermore, we report the analysis of user performance with balance training poses and subjective measures based on questionnaires to assess the user experience, usability, and task load. The proposed VR balance training could offer an interactive, adaptive, and engaging environment and open new potential research directions for lower extremity rehabilitation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Scalable balanced training of conditional generative adversarial neural networks on image data

Here, we propose a distributed approach to train deep convolutional generative adversarial neural network (DC-CGANs) models. Our method reduces the imbalance between generator and discriminator by partitioning the training data according to data labels, and enhances scalability by performing a parallel training where multiple generators are concurrently trained, each one of them focusing on a single data label. Performance is assessed in terms of inception score, Fréchet inception distance, and image quality on MNIST, CIFAR10, CIFAR100, and ImageNet1k datasets, showing a significant improvement in comparison to state-of-the-art techniques to training DC-CGANs. Weak scaling is attained on all the four datasets using up to 1000 processes and 2000 NVIDIA V100 GPUs on the OLCF supercomputer Summit.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Development of lean, efficient, and fast physics-framed deep-learning-based proxy models for subsurface carbon storage

In this work, we present deep-learning-based surrogate models for CCUS developed with four different algorithms and a physics-framed two-phase flow problem involving displacement of water by CO 2 . The deep-learning models were trained using 3D datasets describing the pressure plume, CO 2 saturation plume, and water extraction rate generated by numerical simulation. The hyperparameters defining the architecture of the neural networks were optimized to determine the slimmest network size and training parameters that give the most efficient performance at the least training cost. To develop a robust model that closely mimics the governing physical laws, the discretized form of the two-phase fluid transport equation was used to formulate the supervised deep-learning task. The algorithms investigated in this study predicted the data to above 95% accuracy, with the multi-layer perceptron model demonstrating the best performance by balancing training speed, prediction time, and prediction accuracy with lean network capacity. Furthermore, the surrogate models simultaneously predict reservoir pressure and CO 2 saturation in every grid block, including the surface well extraction rate and bottomhole pressure, at all simulation times for a given static model realization in just a few seconds on a standard desktop computer. A key outcome of this study is that limits can be placed on network design parameters to avoid over designing neural networks, with associated efficiencies in training and prediction times. This is very useful because large volumes of data may be generated in CCUS projects and over-design of neural network architectures imposes penalties that are antithetical to the goal of near-real time forecasting.

58 GEOSCIENCES↗
DOE OSTI2026

HARMONY: Large-Scale Architecture Search for Efficient Hybrid Language Models

As large language models scale to trillions of parameters, their computational and memory requirements present critical challenges for efficient training and deployment. While Mixture of Experts (MoE) architectures enable efficient scaling through sparse parameter activation, and state-space models like Mamba offer linear-time complexity, principled methods for combining these paradigms remain undeveloped. We introduce HARMONY (Hybrid Architecture Research for Mamba, Optimized with Neural efficiencY), a multi-objective evolutionary neural architecture search framework for discovering efficient hybrid language models that integrate Transformer attention mechanisms, Mixture-of-Experts routing, and Mamba state-space components. Through large-scale distributed search using 16,384 MI250X GPUs on the Frontier supercomputer, HARMONY explores a comprehensive design space encompassing six attention variants (MHA, MQA, GQA, MLA, SWA, and Mamba-2), variable MoE configurations with both routed and shared experts, and extensive Mamba hyperparameters. Our framework discovers heterogeneous architectures that balance training performance with computational efficiency through multi-objective optimization incorporating latency penalties and fitness-based selection. Analysis of discovered architectures reveals that optimal hybrid designs favor heterogeneous component mixing rather than homogeneous patterns, with Mamba-2 and Multi-Head Latent Attention (MLA) emerging as preferred mechanisms. Discovered architectures demonstrate superior training efficiency: our best configuration achieves a final perplexity of 1.0874 with 2.38B parameters while processing 4,320 tokens/second, outperforming significantly larger manually designed models. Full-scale evaluation shows HARMONY's top architectures achieve better loss trajectories than equivalently-sized models using state-of-the-art configurations including Mixtral, Jamba, and Samba. Additionally, we demonstrate 91% weak scaling efficiency when training discovered 36B-parameter models across 1,024 GPUs. HARMONY is released as an open framework with comprehensive tools for building and training hybrid models using expert-data-pipeline parallelism, democratizing access to automated architecture design for next-generation language models.

Herron, Emily [ORNL] (ORCID:0000000273008172)↗
DOE OSTI2023

Deep reinforcement learning for class imbalance fault diagnosis of equipment in nuclear power plants

In equipment fault diagnosis in nuclear power plants, there may be far more samples in one class (e.g., a health state) than in another class (e.g., a fault state). The distribution of data in each class is highly skewed. Most machine learning algorithms are suitable for balanced training datasets. When faced with imbalanced samples, these algorithms tend to provide good identification for the majority classes and bias for the minority classes. However, the misclassification of minority classes can lead to high costs. To address the above problem, this paper develops a deep reinforcement learning-based diagnosis method that models fault diagnosis as a sequential decision-making process. At each time step, the agent receives the state of the environment represented by the training samples and then takes a diagnosis action guided by a policy. If the action is correct/incorrect, the agent receives a positive/negative reward. The reward for minority classes is higher than that for majority classes. The agent’s goal is to obtain as many cumulative rewards as possible in the process, i.e., to identify the sample as correctly as possible. Six demonstration scenarios are constructed, depending on the selected fault datasets and the designed model structures. Experiments show that the proposed method achieves a higher weighted-averaged F1 score than the classical supervised learning method in most cases of class imbalance. Finally, the proposed method has potential applications in the field of class imbalance fault diagnosis of equipment in nuclear power plants.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Merger identification through photometric bands, colours, and their errors

Aims. We present the application of a fully connected neural network (NN) for galaxy merger identification using exclusively photometric information. Our purpose is not only to test the method’s efficiency, but also to understand what merger properties the NN can learn and what their physical interpretation is. Methods. We created a class-balanced training dataset of 5860 galaxies split into mergers and non-mergers. The galaxy observations came from SDSS DR6 and were visually identified in Galaxy Zoo. The 2930 mergers were selected from known SDSS mergers and the respective non-mergers were the closest match in both redshift and r magnitude. The NN architecture was built by testing a different number of layers with different sizes and variations of the dropout rate. We compared input spaces constructed using: the five SDSS filters: u, g, r, i, and z; combinations of bands, colours, and their errors; six magnitude types; and variations of input normalization. Results. We find that the fibre magnitude errors contribute the most to the training accuracy. Studying the parameters from which they are calculated, we show that the input space built from the sky error background in the five SDSS bands alone leads to 92.64 ± 0.15% training accuracy. We also find that the input normalization, that is to say, how the data are presented to the NN, has a significant effect on the training performance. Conclusions. We conclude that, from all the SDSS photometric information, the sky error background is the most sensitive to merging processes. This finding is supported by an analysis of its five-band feature space by means of data visualization. Moreover, studying the plane of the g and r sky error bands shows that a decision boundary line is enough to achieve an accuracy of 91.59%.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

High dimensional binary classification under label shift: phase transition and regularization

Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of the label shift, e.g., balancing the training data. However, these methods often consider the underparametrized regime, where the sample size is much larger than the data dimension. The research under the overparametrized regime is very limited. Here, to bridge this gap, we propose a new asymptotic analysis of the Fisher Linear Discriminant classifier for binary classification with label shift. Specifically, we prove that there exists a phase transition phenomenon: Under certain overparametrized regime, the classifier trained using imbalanced data outperforms the counterpart with reduced balanced data. Moreover, we investigate the impact of regularization to the label shift: The aforementioned phase transition vanishes as the regularization becomes strong.

binary classification↗
DOE OSTI2025

When more data hurts: Optimizing data coverage while mitigating diversity-induced underfitting in an ultrafast machine-learned potential

Machine-learned interatomic potentials (MLIPs) are becoming an essential tool in materials modeling. However, optimizing the generation of training data used to parametrize the MLIPs remains a significant challenge. This is because MLIPs can fail when encountering local environments too different from those present in the training data. The difficulty of determining a priori the environments that will be encountered during molecular dynamics simulation necessitates diverse, high-quality training data. Here, this study investigates how training data diversity affects the performance of MLIPs using the Ultra-Fast force field (UF 3 ) to model amorphous silicon nitride. We employ expert and autonomously generated data to create the training data and fit four force field variants to subsets of the data. Our findings reveal a critical balance in training data diversity: insufficient diversity hinders generalization, while excessive diversity can exceed the MLIP's learning capacity, reducing simulation accuracy. Specifically, we found that the UF 3 variant trained on a subset of the training data, in which nitrogen-rich structures were removed, offered vastly better prediction and simulation accuracy than any other variant. By comparing these UF 3 variants, we highlight the nuanced requirements for creating accurate MLIPs, emphasizing the importance of application-specific training data to achieve optimal performance in modeling complex material behaviors.

ab initio molecular dynamics↗
DOE OSTI2022

Photometric redshift estimation with convolutional neural networks and galaxy images: Case study of resolving biases in data-driven methods

Deep-learning models have been increasingly exploited in astrophysical studies, but these data-driven algorithms are prone to producing biased outputs that are detrimental for subsequent analyses. In this work, we investigate two main forms of biases: class-dependent residuals, and mode collapse. We do this in a case study, in which we estimate photometric redshift as a classification problem using convolutional neural networks (CNNs) trained with galaxy images and associated spectroscopic redshifts. We focus on point estimates and propose a set of consecutive steps for resolving the two biases based on CNN models, involving representation learning with multichannel outputs, balancing the training data, and leveraging soft labels. The residuals can be viewed as a function of spectroscopic redshift or photometric redshift, and the biases with respect to these two definitions are incompatible and should be treated individually. We suggest that a prerequisite for resolving biases in photometric space is resolving biases in spectroscopic space. Experiments show that our methods can better control biases than benchmark methods, and they are robust in various implementing and training conditions with high-quality data. Our methods hold promises for future cosmological surveys that require a good constraint of biases, and they may be applied to regression problems and other studies that make use of data-driven models. Nonetheless, the bias-variance tradeoff and the requirement of sufficient statistics suggest that we need better methods and optimized data usage strategies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

A Computational Framework to design 3D stiffness gradient acoustic metamaterials for impedance matching

Acoustic waves play a crucial role in various applications, including medical imaging, non-destructive testing, and sonar systems. One of the significant challenges in these applications is impedance matching, which is essential for minimizing reflections and maximizing the transfer of acoustic energy between different media. Acoustic metamaterials offer a promising solution to this challenge. In addition to impedance control, gradient stiffness can enhance structural efficiency and enable spatial control of wave propagation, making it a valuable feature in acoustic metamaterial design. In this pa- per, we present our developed computational method to design 3D stiffness gradient acoustic metamaterials for impedance matching. The key steps in our approach include generating initial designs using a periodic covariance function to provide unit cells that are both periodic on the boundaries and randomly formed inside the unit cell. Furthermore, we integrated manufacturing constraints into the design process, ensuring that the structures are interconnected for fabrication. We propose two computational optimization algorithms: GenUnit, based on a non-dominated sorting genetic algorithm (NSGA-II), and MLMatch, which leverages differentiable machine learning. The two approaches are not separate contributions but complementary com- ponents of a unified framework. GenUnit requires no training data and directly interfaces with physics-based simulations, making it highly accurate but slower for large-scale exploration. In contrast, MLMatch is data-hungry during training but, once trained, enables near-instantaneous inference and broad design-space coverage. Together, they form a hybrid strategy: ML- Match rapidly explores the global design space, and GenUnit provides local refinement with high-fidelity accuracy. This balance between training cost, inference time, and precision is the motivation for including both methods in the same study. We applied this dual-algorithm framework to generate two metallic-based metamaterial designs that match the acoustic impedance of water while exhibiting a controlled gradient in stiffness (from stiff to soft). The stiffness gradient is particularly advantageous in applications where one side of the structure must interface with soft or sensitive surfaces, such as human tissue or delicate components. Here, this work paves the way for improved materials in various acoustic applications, particularly in ultrasound devices, by providing better impedance.

Metamaterial↗
DOE OSTI2021

Energy Budget Constraints on the Time History of Aerosol Forcing and Climate Sensitivity

Abstract An observationally constrained time series of historical aerosol effective radiative forcing (ERF) from 1750 to 2019 is developed in this study. We find that the time history of aerosol ERFs diagnosed in CMIP6 models exhibits considerable variation and explore how the time history of aerosol forcing influences the probability distributions of present‐day aerosol forcing and emergent metrics such as climate sensitivity. Using a simple energy balance model, trained on CMIP6 climate models and constrained by observed near‐surface warming and ocean heat uptake, we derive estimates for the historical aerosol forcing. We find 2005–2014 mean aerosol ERF to be −1.1 (−1.8 to −0.5) W m −2 relative to 1750. Assuming recently published historical emissions from fossil fuel and industrial sectors and biomass burning emissions from SSP2‐4.5, aerosol ERF in 2019 is −0.9 (−1.5 to −0.4) W m −2 . There is a modest recovery in aerosol forcing (+0.025 W m −2 decade −1 ) between 1980 and 2014. This analysis also gives a 5%–95% range of equilibrium climate sensitivity of 1.8°C –5.1°C (best estimate 3.1°C) with a transient climate response of 1.2°C –2.6°C (best estimate 1.8°C).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Training a Quantum Annealing Based Restricted Boltzmann Machine on Cybersecurity Data

A restricted Boltzmann machine (RBM) is a generative model that could be used in effectively balancing a cybersecurity dataset because the synthetic data a RBM generates follows the probability distribution of the training data. RBM training can be performed using contrastive divergence (CD) and quantum annealing (QA). QA-based RBM training is fundamentally different from CD and requires samples from a quantum computer. We present a real-world application that uses a quantum computer. Specifically, we train a RBM using QA for cybersecurity applications. The D-Wave 2000Q has been used to implement QA. RBMs are trained on the ISCX data, which is a benchmark dataset for cybersecurity. For comparison, RBMs are also trained using CD. CD is a commonly used method for RBM training. Our analysis of the ISCX data shows that the dataset is imbalanced. We present two different schemes to balance the training dataset before feeding it to a classifier. The first scheme is based on the undersampling of benign instances. The imbalanced training dataset is divided into five sub-datasets that are trained separately. A majority voting is then performed to get the result. Our results show the majority vote increases the classification accuracy up from 90.24% to 95.68%, in the case of CD. For the case of QA, the classification accuracy increases from 74.14% to 80.04%. In the second scheme, a RBM is used to generate synthetic data to balance the training dataset. We show that both QA and CD-trained RBM can be used to generate useful synthetic data. Balanced training data is used to evaluate several classifiers. Among the classifiers investigated, K-Nearest Neighbor (KNN) and Neural Network (NN) perform better than other classifiers. They both show an accuracy of 93%. Our results show a proof-of-concept that a QA-based RBM can be trained on a 64-bit binary dataset. The illustrative example suggests the possibility to migrate many practical classification problems to QA-based techniques. Further, we show that synthetic data generated from a RBM can be used to balance the original dataset.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

3D Deep Learning Joint Inversion of Active Seismic Full Waveform and Passive Seismic Traveltime Data for Reservoir Imaging and Uncertainty Quantification

Here, we present deep learning (DL) networks for three-dimensional (3D) joint inversion of active seismic full waveform and passive seismic traveltime data to image reservoirs and their properties and quantify imaging uncertainties. Active seismic full-waveform data can provide high-resolution monitoring images but are collected only intermittently because of their high acquisition cost. In contrast, passive seismic data can be gathered at relatively low cost between regular active surveys, although their imaging quality can be compromised by factors such as low signal-to-noise ratios and limited ray coverage of the target. Although these datasets are routinely acquired together at CO 2 storage sites, their combined inversion within a 3D DL framework has not been previously demonstrated. To our knowledge, this is the first study to address this gap, combining the strength of both data types. For efficient data storage and DL training with large 3D seismic datasets, we use a 3D data matrix in which a random number of passive seismic traveltime data are stored as parabolic envelopes using one-hot encoding and a 3D full-waveform data matrix in which multiple shot gathers are summed. Two network architectures are evaluated: a single-encoder U-Net for single-data type inversion and a dual-encoder U-Net for joint inversion of active and passive seismic data. We also evaluate the single-encoder U-Net for joint inversion by concatenating full-waveform data and traveltime data. We propose a systematic approach for selecting an optimal dropout rate that balances regularization during training and Monte Carlo dropout-based uncertainty quantification during prediction by examining the correlation coefficient between standard deviation and prediction error, along with the training misfit, across a range of dropout rates. 3D DL inversion experiments include five different network configurations, with evaluations under ideal, noisy and dropout-enabled conditions. Both model and data uncertainties are assessed, as well as their combined effects. Across all conditions, the networks consistently predict accurate CO 2 saturation models with low prediction errors, such as a structural similarity index of 0.993 and CO 2 difference of 1.1%. Uncertainty estimates show strong spatial correlation with prediction errors, confirming the effectiveness of the proposed dropout selection approach. The results demonstrate that our DL approach, utilizing compact data representations and appropriate uncertainty quantification, yields accurate subsurface images under various inversion conditions and provides valuable insights into the reliability of predictions.

Um, Evan Schankee [Lawrence Berkeley National Labo↗
DOE OSTI2022

KGML-ag: a modeling framework of knowledge-guided machine learning to simulate agroecosystems: a case study of estimating N<sub>2</sub>O emission using data from mesocosm experiments

Abstract. Agricultural nitrous oxide (N2O) emission accounts for a non-trivial fraction of global greenhouse gas (GHG) budget. To date, estimating N2O fluxes from cropland remains a challenging task because the related microbial processes (e.g., nitrification and denitrification) are controlled by complex interactions among climate, soil, plant and human activities. Existing approaches such as process-based (PB) models have well-known limitations due to insufficient representations of the processes or uncertainties of model parameters, and due to leverage recent advances in machine learning (ML) a new method is needed to unlock the “black box” to overcome its limitations such as low interpretability, out-of-sample failure and massive data demand. In this study, we developed a first-of-its-kind knowledge-guided machine learning model for agroecosystems (KGML-ag) by incorporating biogeophysical and chemical domain knowledge from an advanced PB model, ecosys, and tested it by comparing simulating daily N2O fluxes with real observed data from mesocosm experiments. The gated recurrent unit (GRU) was used as the basis to build the model structure. To optimize the model performance, we have investigated a range of ideas, including (1) using initial values of intermediate variables (IMVs) instead of time series as model input to reduce data demand; (2) building hierarchical structures to explicitly estimate IMVs for further N2O prediction; (3) using multi-task learning to balance the simultaneous training on multiple variables; and (4) pre-training with millions of synthetic data generated from ecosys and fine-tuning with mesocosm observations. Six other pure ML models were developed using the same mesocosm data to serve as the benchmark for the KGML-ag model. Results show that KGML-ag did an excellent job in reproducing the mesocosm N2O fluxes (overall r2=0.81, and RMSE=3.6 mgNm-2d-1 from cross validation). Importantly, KGML-ag always outperforms the PB model and ML models in predicting N2O fluxes, especially for complex temporal dynamics and emission peaks. Besides, KGML-ag goes beyond the pure ML models by providing more interpretable predictions as well as pinpointing desired new knowledge and data to further empower the current KGML-ag. We believe the KGML-ag development in this study will stimulate a new body of research on interpretable ML for biogeochemistry and other related geoscience processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Technoeconomic Analysis Round Robin of a Retrofit of the Ivanpah Concentrating Solar Plant with a Molten-Salt System with Thermal Energy Storage

While the fidelity of technoeconomic analysis (TEA) models for concentrating solar thermal systems has improved in recent years, there is a lack of consensus on the specific inputs used to forecast performance of a newly built tower system due to a lack of validations and post-mortems available to the public. This effort is a joint initiative between multiple international organizations to validate and compare their TEA models. The specific case study is a proposed retrofit of one unit of the Ivanpah Solar Energy Generating System to include molten-salt storage, replacing the steam generation system with a molten-salt receiver, salt-to-steam heat exchanger train, and new balance of plant while keeping the existing steam turbine, solar field, and interconnection in place, using plant data for calibration. This manuscript discusses several of the agreed-upon assumptions for this study as well as a preliminary analysis from prior work that motivates the study.

14 SOLAR ENERGY↗
DOE OSTI2024

AGR-5/6/7 Partial Mass Balance

AGR-5/6/7 goals and test train configuration, status of AGR-5/6/7 mass balance work, preliminary results of Ag-110m, Cs-134, and Eu-154.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

3D-ReG: A 3D ReRAM-based Heterogeneous Architecture for Training Deep Neural Networks

Deep neural network (DNN) models are being expanded to a broader range of applications. The computational capability of traditional hardware platforms cannot accommodate the growth of model complexity. Among recent technologies to accelerate DNN, resistive memory (ReRAM)-based processing-in-memory (PIM) emerged as a promising solution for DNN inference due to its high efficiency for matrix-based computation. We face two major technical challenges in extending the use of ReRAM-based accelerators for training: (1) full-precision data is essential in back-propagation; (2) the need to support both feed-forward and back-propagation aggravates the data-movement burden. We propose a heterogeneous architecture named as 3D-ReG, which leverages full-precision GPU to ensure training accuracy and low-overhead 3D integration to provide low-cost data movements. Moreover, we introduce conservative and aggressive task-mapping schemes, which partition the computation phases in different ways to balance execution efficiency and training accuracy. We evaluate 3D-ReG implemented with two 3D integration technologies, through-silicon vias (TSVs) and monolithic inter-tier vias (MIVs), and compare them with GPU-only and PIM-only counterparts. Various GPU-only platforms using two main-memory technologies (DRAM, ReRAM) and three interconnect technologies (2D, TSV, MIV) are evaluated as well. Experimental results show that 3D-ReG can achieve on average 5.64× training speedup and 3.56× higher energy efficiency compared with the GPU with DRAM as main memory, at the cost of 0.05%–3.39% accuracy drop. We define a new metric, gain-loss ratio (GLR), which quantitatively evaluates the capability of a DNN training hardware in terms of the model accuracy and hardware efficiency. The results of our comparison show that the aggressive task-mapping scheme on MIV-based 3D-ReG outperforms the other methods.

Computer Science↗
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↗