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At least 1,171 records · Page 65

DOE Express Quantum Computing Application Teams (QCAT FY20 Report)

The QCOR project consists of 4 main research tasks: 1) scientific applications and algorithm development for machine learning (ML) and quantum theories of condensed matter systems and lattice gauge theories; 2) high-level quantum-classical (HLQC) language and domain specific language (DSL) development; 3) compiler and interfaces development for the HLQC language; and 4) hardware-level control, optimization, and algorithms libraries. In the succeeding sections we report on progress towards our research tasks during the 2020 calendar year.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

RayStation: External beam treatment planning system

RaySearch Laboratories is a world leader in the field of advanced software and creator of the RayStation treatment planning system for radiation therapy. The aim with RayStation is to deliver an unmatched user experience and leading functionality. Unique features described here include multiatlas based autosegmentation for contouring, deformable registration with 2 different algorithms, multicriteria optimization, Plan Explorer, fallback planning, ultrafast computation speed, and 4-dimensional (4D) adaptive radiation therapy. RayStation can be used to plan for electrons and photons on traditional linacs, for protons on various delivery systems, and for Accuray's helical TomoTherapy system. This paper describes some of these modalities, with reference to clinical cases and including descriptions of the impact on workflow.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

A Generation-Storage Coordination Dispatch Strategy for Power System Based on Causal Reinforcement Learning

In the backdrop of global energy transformation, power systems integrating high proportions of renewable energy sources are facing unprecedented challenges in operational stability and dispatch efficiency. To address these challenges, this study introduces a generation-storage coordination real-time dispatch strategy based on Causal Power System Dynamic Reinforcement Learning (CPSDRL). Diverging from traditional reinforcement learning approaches, CPSDRL innovatively incorporates causal inference within the state prediction model - the crux of model-based reinforcement learning - thereby establishing the Power Causal Dynamic Model (PCDM). Assisted by the prior knowledge of power systems, the model significantly enhances prediction accuracy and reliability through a two-stage training process. Utilizing PCDM, this study further applies a direct policy search algorithm to optimize the real-time dispatch strategy. Experimental results indicate that the proposed method improves the stability of generation-storage coordination real-time dispatch and exhibits competitive advantages in sample efficiency and computational speed, compared to traditional model-based and model-free reinforcement learning algorithms. This method is expected to enhance the practicality and adaptability of causal reinforcement learning techniques in power system scheduling and control.

causal reinforcement learning↗

Towards a Scalable and Adaptive Application Support Platform for Large-Scale Distributed E-Sciences in High-Performance Network Environments

The advent of large-scale collaborative scientific applications has demonstrated the potential for broad scientific communities to pool globally distributed resources to produce unprecedented data acquisition, movement, and analysis. System resources including supercomputers, data repositories, computing facilities, network infrastructures, storage systems, and display devices have been increasingly deployed at national laboratories and academic institutes. These resources are typically shared by large communities of users over Internet or dedicated networks and hence exhibit an inherent dynamic nature in their availability, accessibility, capacity, and stability. Scientific applications using either experimental facilities or computation-based simulations with various physical, chemical, climatic, and biological models feature diverse scientific workflows as simple as linear pipelines or as complex as a directed acyclic graphs, which must be executed and supported over wide-area networks with massively distributed resources. Application users oftentimes need to manually configure their computing tasks over networks in an ad hoc manner, hence significantly limiting the productivity of scientists and constraining the utilization of resources. The success of these large-scale distributed applications requires a highly adaptive and massively scalable workflow platform that provides automated and optimized computing and networking services. This project is to design and develop a generic Scientific Workflow Automation and Management Platform (SWAMP), which contains a web-based user interface specially tailored for a target application, a set of user libraries, and several easy-to-use computing and networking toolkits for application scientists to conveniently assemble, execute, monitor, and control complex computing workflows in heterogeneous high-performance network environments. SWAMP will enable the automation and management of the entire process of scientific workflows with the convenience of a few mouse clicks while hiding the implementation and technical details from end users. Particularly, we will consider two types of applications with distinct performance requirements: data-centric and service-centric applications. For data-centric applications, the main workflow task involves large-volume data generation, catalog, storage, and movement typically from supercomputers or experimental facilities to a team of geographically distributed users; while for service-centric applications, the main focus of workflow is on data archiving, preprocessing, filtering, synthesis, visualization, and other application-specific analysis. We will conduct a comprehensive comparison of existing workflow systems and choose the best suited one with open-source code, a flexible system structure, and a large user base as the starting point for our development. Based on the chosen system, we will develop and integrate new components including a black box design of computing modules, performance monitoring and prediction, and workflow optimization and reconfiguration, which are missing from existing workflow systems. A modular design for separating specification, execution, and monitoring aspects will be adopted to establish a common generic infrastructure suited for a wide spectrum of science applications. We will further design and develop efficient workflow mapping and scheduling algorithms to optimize the workflow performance in terms of minimum end-to-end delay, maximum frame rate, and highest reliability. We will develop and demonstrate the SWAMP system in a local environment, the grid network, and the 100Gpbs Advanced Network Initiative (ANI) testbed. The demonstration will target scientific applications in climate modeling and high energy physics and the functions to be demonstrated include workflow deployment, execution, steering, and reconfiguration. Throughout the project period, we will work closely with the science communities in the fields of climate modeling and high energy physics including Spallation Neutron Source (SNS) and Large Hadron Collider (LHC) projects to mature the system for production use.

97 MATHEMATICS AND COMPUTING↗

An optimization of the FPGA trigger based on the artificial neural network for a detection of neutrino-origin showers

Observations of ultra-high energy neutrinos became a priority in experimental astro-particle physics. Up to now, the Pierre Auger Observatory did not find any candidate on a neutrino event. This imposes competitive limits to the diffuse flux of ultra-high energy neutrinos in the EeV range and above. A very low rate of events potentially generated by neutrinos is a significant challenge for a detection technique and requires both sophisticated algorithms and high-resolution hardware. A trigger based on a artificial neural network was implemented into the Cyclone{sup R} V E FPGA 5CEFA9F31I7. The prototype Front-End boards for Auger-Beyond-2015 with Cyclone{sup R} V E can test the neural network algorithm in real pampas conditions in 2015. Showers for muon and tau neutrino initiating particles on various altitudes, angles and energies were simulated in CORSICA and Offline platforms giving pattern of ADC traces in Auger water Cherenkov detectors. The 3-layer 12-10-1 neural network was taught in MATLAB by simulated ADC traces according the Levenberg-Marquardt algorithm. Results show that a probability of a ADC traces generation is very low due to a small neutrino cross-section. Nevertheless, ADC traces, if occur, for 1-10 EeV showers are relatively short and can be analyzed by 16-point input algorithm. For 100 EeV range traces are much longer, but with significantly higher amplitudes, which can be detected by standard threshold algorithms. We optimized the coefficients from MATLAB to get a maximal range of potentially registered events and for fixed-point FPGA processing to minimize calculation errors. Currently used Front-End boards based on no-more produced ACEXR PLDs and obsolete Cyclone{sup R} FPGAs allow an implementation of relatively simple threshold algorithms for triggers. New sophisticated trigger implemented in Cyclone{sup R} V E FPGAs with large amount of DSP blocks, embedded memory running with 120 - 160 MHz sampling may support to discover neutrino events in the Pierre Auger Observatory. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Cooperative Load Scheduling for Multiple Aggregators Using Hierarchical ADMM

Demand response (DR) serves an important role in improving the efficiency and stability of power systems. In recent years, with advances in communication and smart device technologies, many aggregators have emerged to facilitate end customer participation in DR programs. These aggregators, equipped with customized optimal control algorithms, are capable of providing various grid services. Among them is load scheduling during DR events, namely following a load signal provided by the utility company while minimizing overall customer discomfort. However, as the number of aggregators keeps increasing, it becomes challenging for utility companies to conduct load scheduling for multiple aggregators and generate reference signals for each of them. This paper proposes an optimization framework using hierarchical alternating direction method of multipliers (H-ADMM) to optimally generate load following signals for multiple aggregators. Under this framework, utility and multiple aggregators work in a cooperative manner, aiming at minimizing an overall system cost from different levels of the power system hierarchy, while protecting user privacy. A case study has been conducted in a system with multiple aggregators, based on control of HVAC loads. Experimental results validate the effectiveness of the proposed algorithm.

ADMM↗

Cooperative Load Scheduling for Multiple Aggregators Using Hierarchical ADMM

Demand response (DR) serves an important role in improving the efficiency and stability of power systems. In recent years, with advances in communication and smart device technologies, many aggregators have emerged to facilitate end customer participation in DR programs. These aggregators, equipped with customized optimal control algorithms, are capable of providing various grid services. Among them is load scheduling during DR events, namely following a load signal provided by the utility company while minimizing overall customer discomfort. However, as the number of aggregators keeps increasing, it becomes challenging for utility companies to conduct load scheduling for multiple aggregators and generate reference signals for each of them. This paper proposes an optimization framework using hierarchical alternating direction method of multipliers (H-ADMM) to optimally generate load following signals for multiple aggregators. Under this framework, utility and multiple aggregators work in a cooperative manner, aiming at minimizing an overall system cost from different levels of the power system hierarchy, while protecting user privacy. A case study has been conducted in a system with multiple aggregators, based on control of HVAC loads. Experimental results validate the effectiveness of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗

Cooperative Load Scheduling for Multiple Aggregators Using Hierarchical ADMM: Preprint

Demand response (DR) serves an important role in improving the efficiency and stability of power systems. In recent years, with advances in communication and smart device technologies, many aggregators have emerged to facilitate end customer participation in DR programs. These aggregators, equipped with customized optimal control algorithms, are capable of providing various grid services. Among them is load scheduling during DR events, namely following a load signal provided by the utility company while minimizing overall customer discomfort. However, as the number of aggregators keeps increasing, it becomes challenging for utility companies to conduct load scheduling for multiple aggregators and generate reference signals for each of them. This paper proposes an optimization framework using hierarchical alternating direction method of multipliers (H-ADMM) to optimally generate load following signals for multiple aggregators. Under this framework, utility and multiple aggregators work in a cooperative manner, aiming at minimizing an overall system cost from different levels of the power system hierarchy, while protecting user privacy. A case study has been conducted in a system with multiple aggregators, based on control of HVAC loads. Experimental results validate the effectiveness of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗

Interaction networks for the identification of boosted H → $b\overline b$ decays

We develop an algorithm based on an interaction network to identify high-transverse-momentum Higgs bosons decaying to bottom quark-antiquark pairs and distinguish them from ordinary jets that reflect the configurations of quarks and gluons at short distances. The algorithm's inputs are features of the reconstructed charged particles in a jet and the secondary vertices associated with them. Describing the jet shower as a combination of particle-to-particle and particle-to-vertex interactions, the model is trained to learn a jet representation on which the classification problem is optimized. The algorithm is trained on simulated samples of realistic LHC collisions, released by the CMS Collaboration on the CERN Open Data Portal. The interaction network achieves a drastic improvement in the identification performance with respect to state-of-the-art algorithms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Understanding the Hierarchy of Dense Subgraphs in Stationary and Temporally Varying Setting

Graphs are widely used to model relationships in a wide variety of domains such as sociology, bioinformatics, infrastructure, the WWW, to name a few. One of the key observations is that while real-world graphs are often globally sparse, they are locally dense. In other words, the average degree is often quite small (say at most 10 in a million vertex graph), but vertex neighborhoods are often dense. Finding dense subgraphs is a critical aspect of graph mining It has been used for finding communities and spam link farms in web graphs, graph visualization, real-time story identification, DNA motif detection in biological networks, finding correlated genes, epilepsy prediction, finding price value motifs in financial data, graph compression, distance query indexing, and increasing the throughput of social networking site servers. However, most standard formulations of this problem (like clique, quasi-clique, k-densest subgraph) are NP-hard. Furthermore, current dense subgraph finding algorithms usually optimize some objective, and only find a few such subgraphs without providing any structural relations, whereas the goal is rarely to find the "true optimum," but to identify many (if not all) dense substructures, understand their distribution in the graph, and ideally determine relationships among them. In this project, we first aim to devise algorithms and provide 3 implementations with nice visualizations to find the hierarchy between dense subgraphs, and then understand the structure of the hierarchy to gain more insight on the hidden patterns in real-world networks. Another important aspects in graph analysis is the temporal nature of networks. Networks evolve over time and in many applications data arrives at a high velocity, and thus it is important to design algorithms that can process data efficiently. We report three main results towards identifying dense structures in large evolving graphs. First, we will show how the hierarchical connectedness structure can be maintained efficiently, where connectedness is defined by increasing levels of connectivity strength. Next, we present dense structure can be identified in bipartite graphs without building projection graphs. And finally, we present a new method for peeling algorithms This new approach avoids sequential nature of peeling algorithms and is amenable to parallelization, which is crucial for processing high velocity data.

97 MATHEMATICS AND COMPUTING↗

Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws

We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimization-based technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match high-fidelity data. The optimal kernel therefore acts as a homogenized nonlocal continuum model that accurately reproduces wave motion in a smaller-scale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several one-dimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce high-fidelity data for a composite material in applications that are substantially different from the problems used as training data.

97 MATHEMATICS AND COMPUTING↗

Optimization of a Residential Air Source Heat Pump using Refrigerants with GWP <150 for Improved Performance and Reduced Emission

Using low-GWP refrigerants can reduce the Green House Gas (GHG) emission of heat pump systems. Heat exchangers and compressors are the key components and have a prominent impact on system performance, significant research is devoted to reducing the cost of the heat exchangers while achieving the same or better system performance with refrigerant charge reduction.To better understand the environmental impacts of optimized systems with low-GWP refrigerants, Life Cycle Climate Performance (LCCP) evaluation method was used to evaluate the direct and indirect emissions of the system over the course of its lifetime from manufacturing to disposal. The DOE/ORNL Heat Pump Design Model (HPDM) is used to evaluate the performance of heat pumps. Multi-objective optimizations using Particle Swarm Optimization (PSO) algorithm are performed on a 3-ton R410A residential air source heat pump on market. Seven R410A alternatives, i.e., R32, R454B, R454C, R455A, R457A, R1234yf and R1234ze(E) are investigated. The last five fluids have GWP lower than 150.As a result, 5.5%-12.8% seasonal energy efficiency ratio 2 (SEER2) improvement is achieved, and the optimized systems reduce life cycle CO2 emission by 8.5%-28.6% with GWP lower than 150 refrigerants. The optimal heat exchangers can fit into the original R410A fan-coil units; therefore, the proposed design method establishes a production and installation path to produce cost-effective low-GWP heat pumps easily accepted by end users.

Li, Zhenning↗

SNNVis: Visualizing Graph Embedding of Evolutionary Optimization for Spiking Neural Networks

While Spiking Neural Networks (SNNs) show a lot of promise, it is difficult to optimize them because applying traditional gradient-based optimization techniques is difficult. Even though evolutionary algorithms (EAs) have been shown to promise to optimize SNNs, understanding the relationship between evolving the characteristics of SNNs and their performance to improve the optimization algorithm is challenging because of the complex characteristics and huge population size. We propose visual analytics with novel graph embedding for evolutionary SNNs to address the challenges. While existing graph embedding techniques have limitations in preserving the specific features of the nodes and edges, our approach maintains them. Also, we develop visual analytics for understanding the relationship between the network performance and the features of nodes and edges and exploring and analyzing the evolving SNNs to build insights into improving the EA.

Chae, Junghoon [ORNL] (ORCID:0000000206016746)↗

Data-Enabled Fusion Technology (Final Scientific/Technical Report)

Advancing Scientific Understanding in Fusion Energy and Machine Learning This research represented a significant step forward in machine learning (ML) applications for fusion energy experiments. The project integrated advanced data-driven modeling, optimization techniques, and artificial intelligence to enhance the predictive capabilities and operational efficiency of plasma-based fusion systems. Specifically, tasks focused on ML-enhanced diagnostics, operator guidance tools, and predictive modeling helped improve the ability to interpret complex fusion experiments. Key areas of advancement included: 1) data-driven plasma control, i.e., using ML algorithms to optimize experimental conditions and classify plasma behaviors based on historical data; 2) spectroscopy and diagnostics, i.e., applying AI models to extract previously inaccessible insights from experimental spectroscopy data; and 3) configuration mapping and operator guidance, i.e., developing a predictive framework to assist scientists in identifying the most effective experimental parameters, reducing reliance on manual adjustments. By refining these ML-driven techniques, the project contributed to the broader scientific community’s understanding of plasma dynamics and fusion energy viability. Technical Effectiveness and Economic Feasibility The methods investigated demonstrated high technical effectiveness, as reflected in milestones assessing the predictive accuracy, performance, and optimization of fusion configurations. The development of an Operator Guidance Tool (OGT), for example, led to more precise control of plasma conditions by learning from experimental data and offering real-time adjustments. From an economic standpoint, DeFT provided: 1) the ability to reduce trial-and-error experimentation, which lowered operational costs; 2) improved data interpretation methods, which enabled more efficient resource allocation in large-scale fusion research projects; and 3) the automation of key diagnostic tasks, which reduced manual labor and human error, increasing overall efficiency. 13 The final assessments of predictive models and optimization strategies demonstrated that these approaches were scalable and could be implemented across multiple fusion energy research programs. Public Benefit and Societal Impact This project contributed directly to the broader goal of achieving sustainable and commercially viable fusion energy, which had profound implications for clean energy production and climate change mitigation. The integration of AI-driven solutions into fusion research: 1) sped up scientific discovery, accelerating progress towards achieving energy breakthroughs; 2) reduced the cost of experimentation, making fusion research more accessible; and 3) provided a framework for future AI applications in high-energy physics, benefiting adjacent fields like space exploration, material science, and renewable energy. Additionally, by fostering collaborations between AI researchers and plasma physicists, this project promoted interdisciplinary innovation that could lead to broader applications beyond fusion research.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

TH-E-17A-07: Improved Cine Four-Dimensional Computed Tomography (4D CT) Acquisition and Processing Method

Purpose: Artifacts arising from the 4D CT acquisition and post-processing methods add systematic uncertainty to the treatment planning process. We propose an alternate cine 4D CT acquisition and post-processing method to consistently reduce artifacts, and explore patient parameters indicative of image quality. Methods: In an IRB-approved protocol, 18 patients with primary thoracic malignancies received a standard cine 4D CT acquisition followed by an oversampling 4D CT that doubled the number of images acquired. A second cohort of 10 patients received the clinical 4D CT plus 3 oversampling scans for intra-fraction reproducibility. The clinical acquisitions were processed by the standard phase sorting method. The oversampling acquisitions were processed using Dijkstras algorithm to optimize an artifact metric over available image data. Image quality was evaluated with a one-way mixed ANOVA model using a correlation-based artifact metric calculated from the final 4D CT image sets. Spearman correlations and a linear mixed model tested the association between breathing parameters, patient characteristics, and image quality. Results: The oversampling 4D CT scans reduced artifact presence significantly by 27% and 28%, for the first cohort and second cohort respectively. From cohort 2, the inter-replicate deviation for the oversampling method was within approximately 13% of the cross scan average at the 0.05 significance level. Artifact presence for both clinical and oversampling methods was significantly correlated with breathing period (ρ=0.407, p-value<0.032 clinical, ρ=0.296, p-value<0.041 oversampling). Artifact presence in the oversampling method was significantly correlated with amount of data acquired, (ρ=-0.335, p-value<0.02) indicating decreased artifact presence with increased breathing cycles per scan location. Conclusion: The 4D CT oversampling acquisition with optimized sorting reduced artifact presence significantly and reproducibly compared to the phase-sorted clinical acquisition.

60 APPLIED LIFE SCIENCES↗

SU-G-JeP1-10: Feasibility of CyberKnife Tracking Using the Previously-Implanted Permanent Brachytherapy Seed Cloud

Purpose: Robotic radiosurgery is a salvage treatment option for patients with recurrent prostate cancer. We explored the feasibility of tracking the bolus of permanent prostate implants (PPI) using image recognition software optimized to track spinal anatomy. Methods: Forty-five inert iodine seeds were implanted into a gelatin-based prostate phantom. Four superficial gold seeds were inserted to provide ground-truth alignment. A CT scan of the phantom (120 kVp, 1 mm slice thickness) was acquired and a single-energy iterative metal artifact reduction (MAR) algorithm was used to enhance the quality of the DRR used for tracking. CyberKnife treatment plans were generated from the MAR CT and regular CT (no-MAR) using spine tracking. The spine-tracking grid was centered on the bolus of seeds and resized to encompass the full seed cloud. A third plan was created from the regular CT scan, using fiducial tracking based on the 4 superficial gold seeds with identical align-center coordinates. The phantom was initially aligned using the fiducial-tracking plan. Then the MAR and no-MAR spine-tracking plans were loaded without moving the phantom. Differences in couch correction parameters were recorded in the case of perfect alignment and after the application of known rotations and translations (roll/pitch of 2 degrees; translations XYZ of 2 cm). Results: The spine tracking software was able to lock on to the bolus of seeds and provide couch corrections both in the MAR and no-MAR plans. In all cases, differences in the couch correction parameters from fiducial alignment were <0.5 mm in translations and <1 degree in rotations. Conclusion: We were able to successfully track the bolus of seeds with the spine-tracking grid in phantom experiments. For clinical applications, further investigation and developments to adapt the spine-tracking algorithm to optimize for PPI seed cloud tracking is needed to provide reliable tracking in patients. One of the authors (MD) has received research support and speaker honoraria from Accuray.

60 APPLIED LIFE SCIENCES↗

Critical Analysis of Replacements for R-410A in Heat Pump Applications

Using low-GWP refrigerants can reduce the Green House Gas (GHG) emission of HVAC systems. Research has shown that using heat exchangers with small diameter tubes is a promising solution to meet the performance goals of heat pump using low-GWP refrigerants due to reduced refrigerant charge, reduced flammable impact and environmental impact. However, application of small diameter tube requires in-depth component design optimization to make the new system adapt to low-GWP refrigerants.In this paper, multi-objective optimizations using Particle Swarm Optimization (PSO) algorithm on a R-410A residential 5-ton air source heat pump is performed for improved system performance and reduced material cost. Five R-410A alternatives, i.e., R-32, R-454A, R-454B, R-454C and R-455A are investigated. R-455A and R-454C have GWP lower than 150. As a result of optimization, 12.4%-19.1% Energy Efficiency Ratio (EER) improvement and up to 71% HXs material cost saving is achieved. Life Cycle Climate Performance (LCCP) analysis shows that optimized systems reduce total CO2 emission by 13%-33% depending on the choice of refrigerant and climate zone.The optimal heat exchangers resulting from this research can fit into the original R-410A fan-coil units. The proposed heat pump design method establishes a production and installation path to produce cost-effective low-GWP heat pumps easily accepted by end users.

Li, Zhenning↗

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗