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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 OSTI2022

Manning condensation in ion exchange membranes: A review on ion partitioning and diffusion models

Here, the rational design of ion exchange membranes (IEMs) is becoming more pertinent as their usage becomes broader and as their staple applications (i.e., electrodialysis, flow batteries, and fuel cells) improve in commercial viability. Such efforts would be catalyzed by an improved fundamental understanding of ion transport in IEMs. This review discusses recent progress in modeling ion partitioning and diffusion in IEMs in an effort to relate IEM performance metrics to fundamental membrane properties over which researchers and membrane manufacturers possess direct and sometimes precise control. Central focus is given to the Donnan-Manning model for ion partitioning and the Manning-Meares model for ion diffusion in IEMs. These two frameworks, which are derived from Manning's counter-ion condensation theory for polyelectrolyte solutions, have been widely used within the IEM literature since their recent introduction. To explore this topic, the mathematical derivation of both models is revisited, followed by a survey of experimental and computational discussions of counter-ion condensation in IEMs. Alternative models which fulfill similar roles in predicting IEM transport properties are compared. This review concludes by highlighting the uniquely favorable positions of the Donnan-Manning and Manning-Meares models and discussing their prospects as leading predictors of IEM partitioning and diffusive properties.

25 ENERGY STORAGE↗
DOE OSTI2021

Modeling of aqueous species interaction energies prior to nucleation in cement-based gel systems

Arguably the most ubiquitous construction material in modern civilization, concrete is enabling the development of megacities around the globe together with increasing living standards in developing nations. However, the exact formation mechanisms of the strength-giving calcium-rich gels remain a topic of debate. Using density functional modeling, we simulate the fundamental solution-based building blocks of cement hydrates (calcium ions and silicate and aluminate monomers) and their propensity to form pair-wise complexes with bonding environments characteristic of those found in calcium-silicate-hydrate, calcium-alumino-silicate-hydrate and sodium-containing calcium-alumino-silicate-hydrate gels, as assessed from Gibbs free energies of chemical reactions. By accurately simulating the high pH pore solution chemistry in Portland cements and related systems, along with discrete solvation of the species, we hypothesize potential early age formation routes of the gels and discuss limitations and future work associated with this approach.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Prospects for beyond the Standard Model physics searches at the Deep Underground Neutrino Experiment: DUNE Collaboration

Abstract The Deep Underground Neutrino Experiment (DUNE) will be a powerful tool for a variety of physics topics. The high-intensity proton beams provide a large neutrino flux, sampled by a near detector system consisting of a combination of capable precision detectors, and by the massive far detector system located deep underground. This configuration sets up DUNE as a machine for discovery, as it enables opportunities not only to perform precision neutrino measurements that may uncover deviations from the present three-flavor mixing paradigm, but also to discover new particles and unveil new interactions and symmetries beyond those predicted in the Standard Model (SM). Of the many potential beyond the Standard Model (BSM) topics DUNE will probe, this paper presents a selection of studies quantifying DUNE’s sensitivities to sterile neutrino mixing, heavy neutral leptons, non-standard interactions, CPT symmetry violation, Lorentz invariance violation, neutrino trident production, dark matter from both beam induced and cosmogenic sources, baryon number violation, and other new physics topics that complement those at high-energy colliders and significantly extend the present reach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Numerical simulation of compressible fluid-dynamics in the chamber of inertial fusion energy systems

Here, this paper aims to establish new and innovative modeling capabilities for analyzing chambers in Inertial Fusion Energy (IFE) systems. IFE is emerging as a promising method to achieve fusion power production, but several challenges must be overcome to develop an IFE pilot plant or deploy commercial IFE systems. These challenges are both theoretical and technical, encompassing a deeper understanding of the underlying physical phenomena and the development of new technologies and materials. One of the needs is to develop mathematical models to describe IFE systems and numerical tools to simulate them. This paper contributes to this endeavor by presenting a new OpenFOAM solver for IFE systems, focusing on gas dynamics in their chambers. The analysis and development of chamber designs will play a significant role in the transition from single-shot experiments to high-repetition rates, as there is a need to protect the chamber walls from the intense radiation fields produced by fusion reactions. A promising design option, normally referred to as thick wall chamber design, consists in using lithium or molten salt jet arrays within the chamber. A critical phenomenon is the venting of high-pressure gases from the center to the external part of the chamber, passing through the blanket array. This process involves the propagation and attenuation of strong pressure waves, requiring suitable modeling approaches for compressible fluid-dynamics. The solver proposed in this work implements a multi-material hydrodynamics model tailored to accurately describe the non-linear propagation of pressure waves while avoiding numerical oscillation issues typical of high-velocity compressible simulation. This solver is verified against numerical test cases, validated against experimental data, and applied to the analysis of the High-Yield Lithium-Injection Fusion-Energy (HYLIFE-I) concept. The relevance of this paper is threefold. Firstly, it contributes to developing and testing modeling approaches for compressible fluid-dynamics phenomena, with specific focus on the new and unexplored topic of IFE thick-liquid-wall blanket modeling. Secondly, it marks one of the first applications of the OpenFOAM library in the research field of IFE systems. Finally, the investigated problem is of practical interest for IFE developers, as it provides useful indications about relevant phenomena in pressure wave propagation in the chamber of these systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Opportunities and Challenges of Computational Electromagnetics Methods for Superconducting Circuit Quantum Device Modeling: A Practical Review

High-fidelity numerical methods that model the physical layout of a device are essential for the design of many technologies. For methods that characterize electromagnetic effects, these numerical methods are referred to as computational electromagnetics (CEM) methods. Although the CEM research field is mature, emerging applications can still stress the capabilities of the techniques in use today. The design of superconducting circuit quantum devices falls in this category due to the unconventional material properties and important features of the devices covering nanometer to centimeter scales. Such multiscale devices can stress the fundamental properties of CEM tools which can lead to an increase in simulation times, a loss in accuracy, or even cause no solution to be reliably found. While these challenges are being investigated by CEM researchers, knowledge about them is limited in the broader community of users of these CEM tools. This review is meant to serve as a practical introduction to the fundamental aspects of the major CEM techniques that a researcher may need to choose between to model a device, as well as provide insight into what steps they may take to alleviate some of their challenges. Our focus is on highlighting the main concepts without rigorously deriving all the details, which can be found in many textbooks and articles. After covering the fundamentals, we discuss more advanced topics related to the challenges of modeling multiscale devices with specific examples from superconducting circuit quantum devices. We conclude with a discussion on future research directions that will be valuable for improving the ability to successfully design increasingly more sophisticated superconducting circuit quantum devices. Although our focus and examples are taken from this area, researchers from other fields will still benefit from the details discussed here.

Elkin, Samuel T. [Virginia Tech., Blacksburg]↗
DOE OSTI2024

Automating the Analysis of Large Language Models Responses through Zero-Shot Question Answering

Recent advancements in Large Language Models (LLMs) have shown significant potential in various applications, yet their evaluation, particularly in zero-shot question answering scenarios, remains a challenging task. In this study, our objective was to explore precision metrics for Large Language Models (LLM) and design and implement a software pipeline to automatically evaluate LLMs' outputs under zero-shot question answering. Zero-shot question answering involves a model providing answers to questions about topics it hasn't seen during training. It leverages the principles of zero-shot learning by relying on semantic understanding and generalization from related knowledge. The data used was metadata from medical databases on congenital heart disease. We explored eleven LLM metrics and selected three for our evaluation: BLEU, BERTScore, and MoverScore. BLEU calculates a score based on the overlap of n-grams (contiguous sequences of n items, typically words) between the machine-generated translation and the reference translations. Higher BLEU scores indicate better correspondence between the machine-generated and human-generated translations. BERTScore is a metric used to evaluate the quality of machine-generated text by measuring the similarity of token embeddings produced by BERT (Bidirectional Encoder Representations from Transformers) between the generated text and reference text. MoverScore is a metric that quantifies the dissimilarity between the distributions of word embeddings from machine-generated text and reference text, emphasizing semantic similarity over exact token overlap. We also introduced HBKI, a composite metric summarizing these approaches. We tested five models —GPT-3, Llama-2, Gemini 1.5 Pro, Solar 10.7B, and Mixtral-8x7b. Our software pipeline, designed and implemented using Object-Oriented Programming principles, allows users to customize the selection and extraction of features for topics of interest in their own research. Our results show that MoverScore delivered the most precise evaluation of the LLM's outputs, while Mixtral-8x7b achieved the best overall performance in extracting metadata from the databases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Simulation-aided occupant-centric building design: A critical review of tools, methods, and applications

Occupants are active participants in their built environment, affecting its performance while simultaneously being affected by its design and indoor environmental conditions. With recent advances in computer modeling, simulation tools, and analysis techniques, topics such as human-building interactions and occupant behavior have gained significant interest in the literature given their premise of improving building design processes and operating strategies. In practice, the focus of occupant-centric literature has been mostly geared towards the latter (i.e., operation), leaving the implications on building design practices underexplored. This paper fills the gap by providing a critical review of existing studies applying computer-based modeling and simulation to guide occupant-centric building design. The reviewed papers are organized along four main themes, namely occupant-centric: (i) metrics of building performance, (ii) modeling and simulation approaches, (iii) design methods and applications, and (iv) supporting practices and mechanisms. Important barriers are identified for a more effective application of occupant-centric building design practices, including the limited consideration of metrics beyond energy efficiency (e.g., occupant well-being and space planning), the limited implementation and validation of the proposed methods, and the lack of integration of occupant behavior modeling in existing building performance simulation tools. Finally, future research directions are discussed, covering large-scale international data collection efforts to move from generic assumptions about occupant behavior to specific/localized knowledge, improved metrics of measuring building performance, and improved industry practices, such as building codes, to promote an occupant-in-the-loop approach to the building design process.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

A Solar Fuels Nexus: Molecules and Materials for Light-Driven Catalysis

The American Chemical Society (ACS) selects two groups of graduate students each year to plan and host a one-day symposium at each national meeting (both fall and spring).This year our Graduate Student Symposium Planning Committee (GSSPC), composed of seven students from four universities, proposal entitled “A Solar Fuels Nexus: Molecules and Materials for Light-Driven Catalysis” was selected for the “Crossroads in Chemistry” ACS Meeting that will take place March 23-26, 2023 in Indianapolis, IN. All members of our GSSPC are affiliated with the DOE Fuels from Sunlight Energy Innovation Hub, with two from the Liquid Sunlight Alliance (LiSA) and five from the Center for Hybrid Approaches in Solar Energy to Liquid Fuels (CHASE). Here we request funds to support this symposium. This symposium will highlight research progress and perspectives in the solar fuels generation field and seeks to advance the four priority research objectives (PROs) established by the Department of Energy’s Office of Basic Energy Sciences (DOE-BES) Roundtable Report that are also central to many research goals within LiSA and CHASE. The symposium will consist of research presentations from 10 invited senior researcher speakers on topics such as molecular catalyst design, computational modeling of electron transfer systems, microenvironmental effects on CO2 reduction and H2O oxidation catalysis, and intelligent design of semiconductor interfaces with ample time for discussions. These research topics fit very well with the Solar Photochemistry supported research areas of “light-driven electron and energy transfer in condensed phase and interfacial molecular systems,” “electrocatalysis and photocatalysis of solar fuels reactions,” and “semiconductor photoelectrochemistry.” More broadly, this symposium seeks to advance the DOE-BES’s mission to: “support fundamental research to understand, predict, and ultimately control matter and energy at the level of electrons, atoms, and molecules” by providing a diverse atmosphere where such research will be disseminated, discussed, and debated. There will be a strong focus on Diversity, Equity, and Inclusivity (DEI) in our symposium. Of our 10 speakers, 7 will be from underrepresented demographics in STEM, including 5 who identify as women. Furthermore, we have representatives from academia accompanied by one national lab scientist and one officer from the Office of Fossil Energy and Carbon Management at the DOE. All speakers will be holding a short DEI moment ahead of their talks. In order to support the career development of attending early career scientists, we will also be hosting a luncheon specifically for graduate students and postdocs to provide them opportunities to network with the distinguished speakers and other attendees. DOE funds for this symposium will be used to support the attendance and participation of 15 graduate students from US institutions by defraying travel and registration costs. These funds will promote engagement and conversation between early career scientists in the solar fuels field, while disseminating solar fuels research funded by and relevant to the DOE.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2024

Going beyond BEM with BEM: an insight into dynamic inflow effects on floating wind turbines

Blade element momentum (BEM) theory is the backbone of many industry-standard wind turbine aerodynamic models. To be applied to a broader set of engineering problems, BEM models have been extended since their inception and now include several empirical corrections. These models have benefitted from decades of development and refinement and have been extensively used and validated, proving their adequacy in predicting aerodynamic forces of horizontal-axis wind turbine rotors in most scenarios. However, the analysis of floating offshore wind turbines (FOWTs) introduces new sets of challenges, especially if new-generation large and flexible machines are considered. In fact, due to the combined action of wind and waves and their interaction with the turbine structure and control system, these machines are subject to unsteady motion and thus unsteady inflow on the wind turbine's blades, which could put BEM models to the test. Consensus has not been reached on the accuracy limits of BEM in these conditions. This study contributes to the ongoing research on the topic by systematically comparing four different aerodynamic models, ranging from BEM to computational fluid dynamics, in an attempt to shed light on the unsteady aerodynamic phenomena that are at stake in FOWTs and whether BEM is able to model them appropriately. Simulations are performed on the UNAFLOW 1:75 scale rotor during imposed harmonic surge and pitch motion. Experimental results are available for these conditions and are used for baseline validation. The rotor is analyzed in both rated operating conditions and low wind speeds, where unsteady aerodynamic effects are expected to be more pronounced. Results show that BEM, despite its simplicity, can adequately model the aerodynamics of FOWTs in most conditions if augmented with a dynamic inflow model.

17 WIND ENERGY↗
DOE OSTI2023

Editorial: Neuroscience, computing, performance, and benchmarks: Why it matters to neuroscience how fast we can compute

At the turn of the millennium the computational neuroscience community realized that neuroscience was in a software crisis: software development was no longer progressing as expected and reproducibility declined. The International Neuroinformatics Coordinating Facility (INCF) was inaugurated in 2007 as an initiative to improve this situation. The INCF has since pursued its mission to help the development of standards and best practices. In a community paper published this very same year, Brette et al. tried to assess the state of the field and to establish a scientific approach to simulation technology, addressing foundational topics, such as which simulation schemes are best suited for the types of models we see in neuroscience. In 2015, a Frontiers Research Topic “Python in neuroscience” by Muller et al. triggered and documented a revolution in the neuroscience community, namely in the usage of the scripting language Python as a common language for interfacing with simulation codes and connecting between applications. The review by Einevoll et al. documented that simulation tools have since further matured and become reliable research instruments used by many scientific groups for their respective questions. Open source and community standard simulators today allow research groups to focus on their scientific questions and leave the details of the computational work to the community of simulator developers. A parallel development has occurred, which has been barely visible in neuroscientific circles beyond the community of simulator developers: Supercomputers used for large and complex scientific calculations have increased their performance from ~10 TeraFLOPS (10 13 floating point operations per second) in the early 2000s to above 1 ExaFLOPS (10 18 floating point operations per second) in the year 2022. This represents a 100,000-fold increase in our computational capabilities, or almost 17 doublings of computational capability in 22 years. Moore's law (the observation that it is economically viable to double the number of transistors in an integrated circuit every other 18–24 months) explains a part of this; our ability and willingness to build and operate physically larger computers, explains another part. It should be clear, however, that such a technological advancement requires software adaptations and under the hood, simulators had to reinvent themselves and change substantially to embrace this technological opportunity. It actually is quite remarkable that—apart from the change in semantics for the parallelization—this has mostly happened without the users knowing. The current Research Topic was motivated by the wish to assemble an update on the state of neuroscientific software (mostly simulators) in 2022, to assess whether we can see more clearly which scientific questions can (or cannot) be asked due to our increased capability of simulation, and also to anticipate whether and for how long we can expect this increase of computational capabilities to continue.

biophysically detailed models↗
DOE OSTI2022

Spatial Transferability of Machine Learning Based Volume Estimation Models

High-quality traffic volume data is essential for efficient transportation planning and operations. However, such high-quality data is expensive to collect, owing primarily to the high capital cost of installing and maintaining continuous counting stations (CCSs). Recent availability of probe-based vehicle data offers a cost-effective solution for increasing the observability of traffic volumes. However, having ample ground truth traffic data is a prerequisite for developing robust volume estimation models. Though this might not be a big issue in many states, states with scarce CCS data might be able to benefit from robust volume estimation models developed in (adjacent) data-rich states. While there is a reasonable amount of spatial transferability research in the transportation domain, there is a dearth of knowledge on the spatial transferability of probe-based volume estimation models. To address this gap, this paper explores spatial transferability of volume estimation models developed from data in three states (Colorado, North Carolina, and Pennsylvania). Results indicate that it is extremely important to maintain temporal consistency when attempting spatial transferability of volume estimation models. It was also found that models trained on regions with lower peak traffic volumes will limit the performance of models transferred to states with higher peak hourly traffic volumes. Corroborating findings from existing spatial transferability research on other topics, it was found that a meta-model (developed using data from multiple states) performs better than volume estimation models developed within any one of the states.

ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Γ valley transition metal dichalcogenide moiré bands

Significance At small twist angles, moiré patterns form in transition metal dichalcogenide bilayers. Using sophisticated ab initio calculations, we develop a model able to describe the band structure of these systems. We found that the moiré pattern acts as a long-wavelength modulating potential, with a sixfold rotational symmetry not present in the underlying lattice. The modulation potential reduces hole band widths and localizes electrons or holes around honeycomb or kagome lattice sites.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Manufactured solutions for an electromagnetic slot model

The accurate modeling of electromagnetic penetration is an important topic in computational electromagnetics. Electromagnetic penetration occurs through intentional or inadvertent openings in an otherwise closed electromagnetic scatterer, which prevent the contents from being fully shielded from external fields. To efficiently model electromagnetic penetration, aperture or slot models can be used with surface integral equations to solve Maxwell's equations. A necessary step towards establishing the credibility of these models is to assess the correctness of the implementation of the underlying numerical methods through code verification. Surface integral equations and slot models yield multiple interacting sources of numerical error and other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the electric-field integral equation with a slot model. Finally, we demonstrate the effectiveness of these approaches for a variety of cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Developing a Distributed Trust Model for Distributed Energy Resources

Electric power system operators can manage distribution system reliability by coordinating end customer usage of distributed energy resources. The end customers in this regard are Service Provisioning Customers, who provide their energy resources to a Grid Service Provider, which in turn dispatches large aggregations of distributed energy resources to provide reliable service to the power system.The security of this system relies upon information protection mechanisms, as described in IEEE 2030.5. However, in addition to preventive security measures, a monitoring function is required to ensure trustworthiness. Trust models are a method to detect and respond to both expected and unexpected behavior. Different trust models are required for various types and characteristics of each situation. This paper will describe the topics that must be considered when developing a trust model as it applies to distributed energy resources. The major contribution of this paper is the creation and application of a Distributed Trust Model applied to distributed energy resources.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Transport and confinement physics: Chapter 2 of the special issue: on the path to tokamak burning plasma operation

Progress in physics understanding and theoretical model development of plasma transport and confinement (TC) in the ITPA TC Topical Group since the publication of the ITER Physics Basis (IPB) document (Doyle et al 2007 Nucl. Fusion 47 S18) was summarized focusing on the contributions to ITER and burning plasma prediction and control. This paper provides a general and streamlined overview on the advances that were mainly led by the ITPA TC joint experiments and joint activities for the last 15 years (see JEX/JA table in appendix). This paper starts with the scientific strategy and scope of the ITPA TC Topical group and overall picture of the major progress, followed by the progress of each research field: particle transport, impurity transport, ion and electron thermal turbulent transport, momentum transport, impact of 3D magnetic fields on transport, confinement mode transitions, global confinement, and reduced transport modeling. Cross references with other Topical Groups are given in order to highlight overlapped topics, such as the 3D effect on the plasma transport in the edge and L-H transition physics. The increasing overlap between the topical groups is a reflection of the progress on integrating the known physics into comprehensive models that are better and better able to reproduce the plasma transport. In recent years, such integration has become increasingly prevalent when considering transport from the SOL, through the edge pedestal, and into the plasma core. In the near future, increased collaboration also with the magneto-hydrodynamic and energetic particles community will be important as we approach burning plasma conditions in next-step fusion devices. A summary of remaining challenges and next steps for each research field is given in the Summary section.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Modular Growth and Nucleation Formulations in Modular Plasticity Models

Recent investigations like the second and third Sandia Fracture Challenges have characterized and demonstrated the performance of a variety of failure techniques and models. These surveys have considered a wide breadth of models encapsulating both general failure criteria as well as those focusing on pore nucleation and growth. Extensive reviews exist on both topics. The former category generally consists of classic models like the Johnson-Cook or Wilkins criteria. These models were recently added to modular plasticity models in the Library of Advanced Materials for Engineering (LAME) as criteria for use with element death capabilities. The latter category was not treated in that effort. There exists a large class of failure models based on predicting the evolution of pores and failure associated with such microstructures. While the exact mechanisms and corresponding impact on the macroscale behavior remain an active area of research, a large suite of formulations have been proposed combining different features of both pore nucleation and subsequent growth. The most famous of these are based on the popular Gurson model of pore growth derived via micromechanical analysis assuming a plastically incompressible matrix. Numerous other models exist for both growth and nucleation and the Cocks-Ashby growth and Horstemeyer-Gokhale nucleation models have been used successfully in recent Sandia Fracture Challenges. This specific combination is colloquially referred to as the "BCJ-failure model as it has been frequently used with the Bammann-Chisea-Johnson plasticity model.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Co-Simulation of Electric Power Distribution Systems and Buildings including Ultra-Fast HVAC Models and Optimal DER Control

Smart homes and virtual power plant (VPP) controls are growing fields of research with potential for improved electric power grid operation. A novel testbed for the co-simulation of electric power distribution systems and distributed energy resources (DERs) is employed to evaluate VPP scenarios and propose an optimization procedure. DERs of specific interest include behind-the-meter (BTM) solar photovoltaic (PV) systems as well as heating, ventilation, and air-conditioning (HVAC) systems. The simulation of HVAC systems is enabled by a machine learning procedure that produces ultra-fast models for electric power and indoor temperature of associated buildings that are up to 133 times faster than typical white-box implementations. Hundreds of these models, each with different properties, are randomly populated into a modified IEEE 123-bus test system to represent a typical U.S. community. Advanced VPP controls are developed based on the Consumer Technology Association (CTA) 2045 standard to leverage HVAC systems as generalized energy storage (GES) such that BTM solar PV is better utilized locally and occurrences of distribution system power peaks are reduced, while also maintaining occupant thermal comfort. An optimization is performed to determine the best control settings for targeted peak power and total daily energy increase minimization with example peak load reductions of 25+%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Discovering Active Subspaces for High-Dimensional Computer Models

Dimension reduction techniques have long been an important topic in statistics, and active subspaces (AS) have received much attention this past decade in the computer experiments literature. The most common approach towards estimating the AS is to use Monte Carlo with numerical gradient evaluation. While sensible in some settings, this approach has obvious drawbacks. Recent research has demonstrated that active subspace calculations can be obtained in closed form, conditional on a Gaussian process (GP) surrogate, which can be limiting in high-dimensional settings for computational reasons. In this paper, we produce the relevant calculations for a more general case when the model of interest is a linear combination of tensor products. These general equations can be applied to the GP, recovering previous results as a special case, or applied to the models constructed by other regression techniques including multivariate adaptive regression splines (MARS). Furthermore, using a MARS surrogate has many advantages including improved scaling, better estimation of active subspaces in high dimensions and the ability to handle a large number of prior distributions in closed form. In one real-world example, we obtain the active subspace of a radiation-transport code with 240 inputs and 9,372 model runs in under half an hour.

97 MATHEMATICS AND COMPUTING↗