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At least 1,765 records · Page 98

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Predicting Initial Trans-Membrane Pressure for Optimized Operations in UF Unit Using Random Forest

With the growing scarcity of freshwater, innovative process design mechanisms like Reverse Osmosis (RO) are increasingly gaining attention among water treatment utilities to address the rising demand. Ensuring reliable water production necessitates efficient resource utilization, minimizing downtime in (ultra-filtration) UF systems. Recent advancements in machine learning (ML) have enabled the development of accurate data-driven models for Model Predictive Control (MPC), often requiring minimal prior knowledge of underlying physical processes. In this study, we present predictive regression models based on Random Forest (RF) and Auto-Regressive (AR) approaches to forecast the initial Trans-Membrane Pressure (TMP) for each filtration cycle in data generated by Direct Potable Reuse (DPR) systems. The proposed RF-based model demonstrates superior performance compared to baseline methods, including historical mean, Last Observation Carried Forward (LOCF), and naïve AR models, across various forecasting horizons in terms of root mean square error (RMSE) metric. To evaluate how different classes of process variables contribute to TMP dynamics over time, we examine the feature importance of independent covariates across multiple forecast horizons. This analysis provides insight into the temporal relevance of operational and sensor-derived features, guiding control and monitoring strategies. Additionally, the impact of hyperparameter tuning on TMP prediction performance is studied for both direct and recursive RF modelling approaches across increasing forecast horizons. Accurate prediction of initial TMP is critical for optimizing RO operations, as it enables the development of robust modelling frameworks by accurately estimating membrane fouling trends, thereby enhancing process efficiency and long-term reliability. The demonstrated efficacy of the RF-based approach highlights its potential as a tool for real-time decision-making in water treatment systems, paving the way for advanced process optimization and sustainable water resource management.

Mukherjee, Subrata [ORNL] (ORCID:0000000309930338)↗

DOE OSTI2025

AUTOMATIC GENERATION OF EVENT TREES AND FAULT TREES: A MODEL-BASED APPROACH

In the past few decades, increasing complexity in modern engineering systems has been driven by the integration of a large number of components and by the fact that the system operations involve many disciplines (e.g., thermal-hydraulics, plant operations, cyber-security). Current safety/reliability modeling approaches to such systems are labor intensive, difficult to learn, and rely heavily on simplistic Boolean logic to depict failure propagation and accident progression. While these methods serve well for simple systems (i.e., linear causal systems with limited small inter- and intra-system interactions), their results are difficult to verify when modeling complex systems (typically performed through the extensive use of modeling assumptions). The development of new methods is addressed to meet these challenges through a model-based system engineering (MBSE) lens. Under MBSE philosophy, every aspect of the system (form or function) is represented by a model that completely characterizes its architecture or behavior. MBSE approach greatly improves the management of design, analysis and verification of complex systems. An integration of Dynamic Probabilistic Risk Assessment (DPRA) methods with MBSE models is proposed to perform safety/reliability analyses of engineering systems. In particular, MBSE representation of the system (performed using Systems Modeling Language [SysML]) is coupled with DPRA methods to automatically generate event trees and fault trees.

97 - MATHEMATICS AND COMPUTING↗

NASA NTRS2016

What Was Learned in Predicting Slender Airframe Aerodynamics with the F-16XL Aircraft

The second Cranked-Arrow Wing Aerodynamics Project, International, coordinated project has been underway to improve high-fidelity computational-fluid-dynamics predictions of slender airframe aerodynamics. The work is focused on two flow conditions and leverages a unique flight data set obtained with the F-16XL aircraft for comparison and validation. These conditions, a low-speed high-angle-of-attack case and a transonic low-angle-of-attack case, were selected from a prior prediction campaign wherein the computational fluid dynamics failed to provide acceptable results. In revisiting these two cases, approaches for improved results include better, denser grids using more grid adaptation to local flow features as well as unsteady higher-fidelity physical modeling like hybrid Reynolds-averaged Navier-Stokes/unsteady Reynolds-averaged Navier-Stokes/large-eddy simulation methods. The work embodies predictions from multiple numerical formulations that are contributed from multiple organizations where some authors investigate other possible factors that could explain the discrepancies in agreement (e.g., effects due to deflected control surfaces during the flight tests as well as static aeroelastic deflection of the outer wing). This paper presents the synthesis of all the results and findings and draws some conclusions that lead to an improved understanding of the underlying flow physics, finally making the connections between the physics and aircraft features.

Rizzi, Arthur↗

DOE OSTI2022

Modeling the Solvation and Acidity of Carboxylic Acids Using an Ab Initio Deep Neural Network Potential

Formic and acetic acid constitute the simplest of carboxylic acids, yet they exhibit fascinating chemistry in the condensed phase such as proton transfer and dimerization. The go-to method of choice for modeling these rare events have been accurate but expensive ab-initio molecular dynamics simulations. Here, we present a deep neural network potential trained using accurate ab-initio data that can be used in tandem with enhanced-sampling methods to perform an efficient exploration of the free-energy surface of aqueous solutions of weak carboxylic acids. In particular, we show that our model captures proton dissociation and provides a good estimate of the pK a , as well as the dimerization of formic and acetic acid. This provides a suitable starting point for applications in different research areas where computational efficiency coupled with the accuracy of ab-initio methods is required.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Homogeneous ice nucleation in an ab initio machine-learning model of water

Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine-learning model trained on density-functional theory energies and forces. We compute nucleation rates at atmospheric pressure, over a broad range of supercoolings, using the seeding technique and systems of up to hundreds of thousands of atoms simulated with ab initio accuracy. The key quantity provided by the seeding technique is the size of the critical cluster (i.e., a size such that the cluster has equal probabilities of growing or melting at the given supersaturation), which is used together with the equations of classical nucleation theory to compute nucleation rates. We find that nucleation rates for our model at moderate supercoolings are in good agreement with experimental measurements within the error of our calculation. We also study the impact of properties such as the thermodynamic driving force, interfacial free energy, and stacking disorder on the calculated rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Atomic understanding of structural deformations upon ablation of graphene

We investigate the atomic rearrangement in graphene under femtosecond pulse illumination with reactive molecular dynamics simulations and compare with ultra-fast laser ablation experiments. To model the impact of the laser pulse irradiation, heat is locally applied to a selected area of the graphene layer and the resulting structural deformation is simulated as a function of time, providing a detailed understanding of the bond breaking process under laser illumination and subsequent re-equilibration afterAQ3 the pulse is turned off. Analysis of the atomic dynamics indicates that the types of defects formed depend on the pulse energy and exposure duration. By varying the exposed area, we determine that the shape of the ablated area is not only a function of the pulse energy, but also of the beam spot size and pulse repetition. Furthermore, we apply a machine learning approach to extrapolate our simulated data to experimental length scales and reproduce the trends in ablated area as a function of temperature. Furthermore, our study provides a first step towards understanding the design parameters for graphene nano-patterning.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

High fidelity multiphysics tightly coupled model for a lead cooled fast reactor concept and application to statistical calculation of hot channel factors

A tightly coupled multiphysics code system is established using the MOOSE framework for hot channel factor (HCF) evaluation on a Lead Fast Reactor (LFR) concept. The coupled system is driven by the Griffin multiphysics coupling capability under which the MOOSE Heat Transfer module and NekRS computational fluid dynamics solver are coupled for conjugate heat transfer using the Cardinal application. The coupled capability is demonstrated on an LFR assembly model based on materials and geometry of a prototypical lead-cooled fast reactor design by Westinghouse Electric Company, LLC. Moreover, the work integrates the Multiphysics Object Oriented Simulation Environment (MOOSE) Stochastic Tools Module (STM) to perform calculations for statistical analysis of HCF. Furthermore, the coupling strategy and workflow demonstrated in this paper is not only useful for predicting accurate hot channel factors for different kinds of advanced reactors but also for other engineering applications such as control rod worth assessment, generation of high-fidelity database for Artificial intelligence (AI)/machine learning (ML) training, design optimization and multi-resolution modeling.

Cardinal↗

DOE OSTI2023

Estimation of Arrivals on Green at Signalized Intersections Using Stop-Bar Video Detection

Across the world, traffic congestion is increasing with alarming rapidity. Traffic signal control effectiveness, in coordinated networks, is often investigated in relation to the type of vehicle arrivals at the signalized intersections. Recently, several transportation agencies have switched from traditional loop detectors to video detection. When video cameras are accompanied by computer vision, one can extract more information about traffic “dynamics” than by using traditional inductive loop detectors. Collecting arrival times of multiple vehicles after the first arrival at the stop-bar detector might be challenging when using inductive loop detectors (since after the first arrival, detector status is always occupied). However, emerging video detection systems allow tracking of each vehicle’s entrance time in the detection zone, departure time from the detection zone, and the type of vehicle. This information can be used to estimate vehicular arrival and departure times, which then can be fed into machine learning algorithms to estimate arrivals on green (AOG). However, such research ideas have not been documented so far. Thus, this paper presents an estimation model for AOG, which was developed using multigene genetic programming. A robust experimental dataset was collected from a highly calibrated and validated microsimulation model of an 11-intersection corridor in Chattanooga, TN. The results of the model’s performance analysis showed the high accuracy of the training-, testing-, and validation datasets. The practical benefit of this model is that it can be applied to estimate arrival types at intersections where only stop-bar video detection exists.

Engineering↗

DOE OSTI2022

Data used in “Enguehard et al. 2022, Machine-Learning Functional Zonation Approach for Characterizing Terrestrial–Aquatic Interfaces: Application to Lake Erie”

The package contains the data layers used in “Enguehard et al. 2022, Machine-Learning Functional Zonation Approach for Characterizing Terrestrial–Aquatic Interfaces: Application to Lake Erie”. Spatial data layers include: topography, wetland vegetation cover, time series of Landsat’s enhanced vegetation index (EVI) between 1990 and 2020. The study aims to characterize coastal wetlands with particular focus on the co-variability between plant dynamics, topography, soil, and other environmental factors. We proposed a functional zonation approach based on machine learning clustering to identify the spatial regions, i.e., zones that capture these co-varied properties. This approach was applied to publicly available datasets along Lake Erie, in the Great Lakes Region

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Atomic Diffusivities of Yttrium, Titanium and Oxygen Calculated by Ab Initio Molecular Dynamics in Molten 316L Oxide-Dispersion-Strengthened Steel Fabricated via Additive Manufacturing

Oxide-dispersion-strengthened (ODS) steels have long been viewed as a prime solution for harsh environments. However, conventional manufacturing of ODS steels limits the final product geometry, is difficult to scale up to large components, and is expensive due to multiple highly involved, solid-state processing steps required. Additive manufacturing (AM) can directly incorporate dispersion elements (e.g., Y, Ti and O) during component fabrication, thus bypassing the need for an ODS steel supply chain, the scale-up challenges of powder processing routes, the buoyancy challenges associated with casting ODS steels, and the joining issues for net-shape component fabrication. In the AM process, the diffusion of the dispersion elements in the molten steel plays a key role in the precipitation of the oxide particles, thereby influencing the microstructure, thermal stability and high-temperature mechanical properties of the resulting ODS steels. In this work, the atomic diffusivities of Y, Ti, and O in molten 316L stainless steel (SS) as functions of temperature are determined by ab initio molecular dynamics simulations. The latest Vienna Ab initio Simulation Package (VASP) package that incorporates an on-the-fly machine learning force field for accelerated computation is used. At a constant temperature, the time-dependent coordinates of the target atoms in the molten 316L SS were analyzed in the form of mean square displacement in order to obtain diffusivity. The values of the diffusivity at multiple temperatures are then fitted to the Arrhenius form to determine the activation energy and the pre-exponential factor. Given the challenges in experimental measurement of atomic diffusivity at such high temperatures and correspondingly the lack of experimental data, this study provides important physical parameters for future modeling of the oxide precipitation kinetics during AM process.

Chemistry↗

DOE OSTI2022

Robotic Planning under Uncertainty in Spatiotemporal Environments in Expeditionary Science

In the expeditionary sciences, spatiotemporally varying environments -- hydrothermal plumes, algal blooms, lava flows, or animal migrations -- are ubiquitous. Mobile robots are uniquely well-suited to study these dynamic, mesoscale natural environments. We formalize expeditionary science as a sequential decision-making problem, modeled using the language of partially-observable Markov decision processes (POMDPs). Solving the expeditionary science POMDP under real-world constraints requires efficient probabilistic modeling and decision-making in problems with complex dynamics and observational models. Previous work in informative path planning, adaptive sampling, and experimental design have shown compelling results, largely in static environments, using data-driven models and information-based rewards. However, these methodologies do not trivially extend to expeditionary science in spatiotemporal environments: they generally do not make use of scientific knowledge such as equations of state dynamics, they focus on information gathering as opposed to scientific task execution, and they make use of decision-making approaches that scale poorly to large, continuous problems with long planning horizons and real-time operational constraints. In this work, we discuss these and other challenges related to probabilistic modeling and decision-making in expeditionary science, and present some of our preliminary work that addresses these gaps. We ground our results in a real expeditionary science deployment of an autonomous underwater vehicle (AUV) in the deep ocean for hydrothermal vent discovery and characterization. Our concluding thoughts highlight remaining work to be done, and the challenges that merit consideration by the reinforcement learning and decision-making community.

Preston, Victoria↗

DOE OSTI2021

Elucidating and predicting the dynamic evolution of water and land systems due to natural and energy-related forcings

Focal Area(s): 3. Insight gleaned from complex data (both observed and simulated) using AI, big data analytics, and other advanced methods, including explainable AI and physics- or knowledge-guided AI; & 1. Data acquisition and assimilation enabled by machine learning, AI, and advanced methods including experimental/network design/optimization, unsupervised learning (including deep learning), and hardware-related efforts involving AI (e.g., edge computing). Science Challenge: Interactions between water, land, and energy systems are complex and occur on a variety of scales, ranging from local to basinal to regional. Accurately predicting the behavior of ground water and surface water systems for 5-10 years and beyond requires an understanding of the current system and the ability to model both the natural system at scale and human-induced forcings related to energy and other activities. Artificial intelligence and machine learning (AI/ML) combined with modern compilation and integration efforts for U.S. groundwater and surface water systems present potential solutions to bolstering detailed physics-based models of these systems. Big data tied with ML and physics-based modeling can drive breakthroughs in understanding the earth system, but research is often impeded by data access (e.g., privacy issues), quality, formats, gaps, multi-source, multi-scale, integration, and spatiotemporal challenges. Effective integration of real data and simulated (synthetic) data that fill gaps is critical. Overcoming these complex data and model integration challenges will enable a transformational approach to acquiring enhanced understanding of environmental systems.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Spatiotemporal Dynamics of the Relative Abundance of Soil Nutrient‐Degrading Enzyme‐Encoding Genes Across Continental US Ecoregions

Understanding the spatiotemporal patterns in the relative abundance of soil extracellular enzyme‐encoding genes is critical for predicting microbial responses to environmental change and their potential role in nutrient cycling. Yet, integrating novel metagenomic observations with spatiotemporal environmental gradients to infer regional patterns and future trajectories has remained unclear. To address this gap, we applied a machine learning (ML) approach, integrating soil metagenomic data with environmental variables—soil properties, topography, vegetation, and climate—to predict the relative abundance of enzyme‐encoding genes for soil carbon (C), nitrogen (N), and phosphorus (P) across surface soils of the continental United States. We assessed potential responses under future emission scenarios (SSP2‐4.5 and SSP5‐8.5) by comparing a baseline (1985–2014) to a future period (2071–2100). The ML model explained 57%–63% of baseline variation. Precipitation was identified as the most influential factor for the relative abundance of C‐ and N‐degrading enzyme‐encoding genes, while slope length, representing horizontal distance that water can travel downslope, was the primary driver for P‐degrading enzyme‐encoding genes abundance. Projections revealed spatially heterogeneous shifts across continental US ecoregions: the relative abundance of C‐ and N‐degrading enzyme‐encoding genes decreased in wetter ecoregions and increased in drier ecoregions under future climate, while P‐degrading enzyme‐encoding genes abundance decreased significantly in semiarid and Mediterranean ecoregions. This study demonstrates the utility of metagenomic data for mapping soil genetic potential and predicting its regional response to environmental change, to inform ecosystem management strategies.

extracellular enzyme-encoding genes↗

DOE OSTI2023

Machine learning methods for particle stress development in suspension Poiseuille flows

Numerical simulations are used to study the dynamics of a developing suspension Poiseuille flow with monodispersed and bidispersed neutrally buoyant particles in a planar channel, and machine learning is applied to learn the evolving stresses of the developing suspension. The particle stresses and pressure develop on a slower time scale than the volume fraction, indicating that once the particles reach a steady volume fraction profile, they rearrange to minimize the contact pressure on each particle. Here we consider how the stress development leads to particle migration, time scales for stress development, and present a new physics-informed Galerkin neural network that allows for learning the particle stresses when direct measurements are not possible. The particle fluxes are compared with the Suspension Balance Model with good agreement. We show that when stress measurements are possible, the MOR-physics operator learning method can also capture the particle stresses.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

High-Throughput Microfluidics Platform for Intracellular Delivery and Sampling of Biomolecules from Live Cells

Nondestructive cell membrane permeabilization systems enable the intracellular delivery of exogenous biomolecules for cell engineering tasks as well as the temporal sampling of cytosolic contents from live cells for the analysis of dynamic processes. Here, in this paper, we report a microwell array format live-cell analysis device (LCAD) that can perform localized-electroporation induced membrane permeabilization, for cellular delivery or sampling, and directly interfaces with surface-based biosensors for analyzing the extracted contents. We demonstrate the capabilities of the LCAD via an automated high-throughput workflow for multimodal analysis of live-cell dynamics, consisting of quantitative measurements of enzyme activity using self-assembled monolayers for MALDI mass spectrometry (SAMDI) and deep-learning enhanced imaging and analysis. By combining a fabrication protocol that enables robust assembly and operation of multilayer devices with embedded gold electrodes and an automated imaging workflow, we successfully deliver functional molecules (plasmid and siRNA) into live cells at multiple time-points and track their effect on gene expression and cell morphology temporally. Furthermore, we report sampling performance enhancements, achieving saturation levels of protein tyrosine phosphatase activity measured from as few as 60 cells, and demonstrate control over the amount of sampled contents by optimization of electroporation parameters using a lumped model. Lastly, we investigate the implications of cell morphology on electroporation-induced sampling of fluorescent molecules using a deep-learning enhanced image analysis workflow.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Phasor-Measurement-Unit-Based Data Analytics Using Digital Twin and PhasorAnalytics Software

A major objective of this project was to apply GE’s commercial machine learning and data analytics toolsets to large-scale, real-world, anonymized Phasor Measurement Unit (PMU) datasets in order to extract signatures, correlated and/or causal factors, and precursor patterns associated with significant power system phenomena. The project had a particular emphasis on extraction of insights relevant to asset health monitoring, real-time load modeling and cybersecurity monitoring. Additionally, the team was directed to undertake a comprehensive data quality analysis for the provided datasets and encouraged to estimate the ‘machine-learning readiness’ of the datasets by documenting any major obstacles to the application of commercial machine learning algorithms. To accomplish the aforementioned objectives, the project team’s work centered around the identification of key event signatures and application of the identified event signatures for event detection and event classification. The industry-validated, semi-supervised machine learning strategy employed for event signature identification involved several major tasks, including data-preprocessing, generation of an overabundance of features, normal data identification, normality modeling, and event signature identification through a methodical, quantitative ranking of features in order of relevance to each studied event type. Throughout the project, data quality issues and mitigation techniques were investigated. In this report, insights are provided regarding the readiness of the provided synchrophasor datasets for application of machine learning and data analytics. The methodologies employed for this technical strategy are summarized in this report. With regards to data preprocessing and feature generation, the provided Training and Test Datasets were ingested into GE’s big data environment. Subsequently, the team applied bad data cleansing and data imputation scripts, event detection scripts, and application programming interfaces (APIs) to the datasets for convenient data access. The project team completed development and validation of dozens of physics-based, statistics-based and transformation-based feature functions used for the extraction of over 60 synchrophasor features. Using a new parallel feature generation technology developed on this project, over 60 features have been rapidly generated for the full two years’ worth of Training and Test Dataset data associated with both the Eastern and Western interconnects. Even accommodating for temporal down-sampling inherent to the feature extraction procedure, this parallel feature generation activity resulted in a massive feature set with a storage requirement approximately equal to that of the raw training dataset itself. With regards to normal data identification and normality modeling, a normality model was built using the feature data extracted from the Training Dataset and iteratively refined subsequent to incremental adjustments and expansions of the Training Dataset feature data. With respect to event characterization and signature identification, an event signature identification pipeline was developed and used in conjunction with the normality model to identify over 15 event signatures for key event categories within the Training Dataset. The identified event signatures were used to characterize hundreds of key events in terms of relative severity, duration, and location of the event. An investigation was undertaken to identify correlated and causal factors involved in transformer events. A separate investigation into temporal trends in ring-down analysis results was undertaken to determine possible associations between system dynamics and various other factors such as loading, season or year. To validate the identified event signatures, additional work was undertaken to develop signature-based anomaly detection and classification tools suitable for convenient application to the synchrophasor datasets. The anomaly detection and classification tools, suitable for online application, were then applied to the entirety of the Eastern Interconnect Training and Test Datasets. Performance of the event detection and classification tools was evaluated upon receipt of the Test Dataset event logs (i.e., the labels for events contained in the Test Dataset), and promising results were obtained despite several challenges (documented herein) associated with application of supervised or semi-supervised machine learning methods to large-scale, anonymized datasets. Finally, the detection and classification tools were used to detect, classify, and characterize thousands of new events not included in the original event logs provided by the DOE within both the Training and Test Datasets.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Accelerating discrete dislocation dynamics simulations with graph neural networks

Discrete dislocation dynamics (DDD) is a widely employed computational method to study plasticity at the mesoscale that connects the motion of dislocation lines to the macroscopic response of crystalline materials. However, the computational cost of DDD simulations remains a bottleneck that limits its range of applicability. Here, we introduce a new DDD-GNN framework in which the expensive time-integration of dislocation motion is entirely substituted by a graph neural network (GNN) model trained on DDD trajectories. As a first application, we demonstrate the feasibility and potential of our method on a simple yet relevant model of a dislocation line gliding through an array of obstacles. We show that the DDD-GNN model is stable and reproduces very well unseen ground-truth DDD simulation responses for a range of straining rates and obstacle densities, without the need to explicitly compute nodal forces or dislocation mobilities during time-integration. Our approach opens new promising avenues to accelerate DDD simulations and to incorporate more complex dislocation motion behaviors.

36 MATERIALS SCIENCE↗

DOE OSTI2023

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗