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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Laboratory time series moisture manipulative experiment from sediment across the contiguous US: time series aerobic respiration and geochemistry (v2)

This dataset supports a broader study examining the effects of wetting and drying on hyporheic zone respiration across the contiguous United States (CONUS). The dataset provides data generated from a laboratory moisture manipulation experiment. The contents include time series aerobic respiration and moisture; dissolved oxygen; sediment geochemistry data; and field metadata (including qualitative information on instream and river corridor characteristics). Samples were collected as part of the WHONDRS CONUS-Scale Model-Sample Study (CM). This study was designed following ICON (integrated, coordinated, open, and networked) principles to facilitate a model-experiment (ModEx) iteration approach, leveraging crowdsourced sampling across the CONUS. The data package associated with the CM study is available at https://data.ess-dive.lbl.gov/view/doi:10.15485/1923689. CM sampling began in April 2022 and ended in October 2023. This study uses subsamples from a subset of CM samples collected between June 2022 and June 2023. The original field samples were labeled as CM_###. Subsequent subsamples for this study were labeled as EC_###. The labels from the field samples and the EC subsamples can be mapped directly based on the digits following the prefix and underscore (i.e., EC_001 is a subsample from CM_001). See the critical details section below for more details on sample naming. This data package was originally published in August 2024. It was updated in February 2026 (v2; new and modified files). See the change history section in the readme for more details. For details on how to navigate this data package, see this infographic from the River Corridor SFA https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. This dataset is comprised of one folder of raw Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) data and one main data folder containing (1) file-level metadata; (2) data dictionary; (3) field metadata; (4) readme; (5) field protocol; and a (6) a subfolder with sediment sample data from the incubation experiment. The sample data subfolder contains (1) dissolved organic carbon (DOC, measured as non-purgeable organic carbon, NPOC); (2) total nitrogen (TN); (3) adenosine triphosphate (ATP); (4) percent carbon and nitrogen; (5) effect size; (6) iron (II); (7) gravimetric moisture; (8) respiration rates and raw dissolved oxygen values; (9) specific conductance; (10) pH; (11) temperature; (12) a summary containing median values of each data type for each treatment (wet and dry); (13) methods codes; (14) FTICR-MS methods; and (15) a subfolder of 9.4 Tesla FTICR-MS data. This folder contains three subfolders, one containing the sediment .xml data files, one containing the sediment CoreMS output files, the other containing instructions and scripts for processing the files in CoreMS (https://github.com/EMSL-Computing/CoreMS). All files are .csv, .pdf, .R, .ref, or .xml.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Laboratory time series moisture manipulative experiment from sediment across San Antonio, Texas: time series aerobic respiration and geochemistry

This dataset supports a broader study examining the effects of wetting and drying on hyporheic zone respiration. The dataset provides data generated from a laboratory moisture manipulation experiment. The contents include time series aerobic respiration and moisture; dissolved oxygen; sediment geochemistry data; and field metadata (including qualitative information on instream and river corridor characteristics). Samples were collected as part of the WHONDRS Allison Veach collaboration (AV1). The data package associated with the AV1 study is available at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/2529428. AV1 sampling occurred across 7 perennial and 7 intermittent streams in San Antonio, Texas. Each stream/site was visited both in summer during base flow (July-September 2023) and winter during peak flow (January-February 2024). This study uses subsamples from a subset of AV1 samples. The original field samples were labeled as AV1_###. Subsequent subsamples for this study were labeled as EV_###. The labels from the field samples and the EV subsamples can be mapped directly based on the digits following the prefix and underscore (i.e., EV_001 is a subsample from AV1_001). See the critical details section below for more details on sample naming. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. This dataset is comprised of one main data folder containing (1) file-level metadata; (2) data dictionary; (3) field metadata; (4) readme; (5) field protocol; and a (6) a subfolder with sediment sample data from the incubation experiment. The sample data subfolder contains (1) effect size; (2) iron (II); (3) gravimetric moisture; (4) respiration rates; (5) raw dissolved oxygen values and plots; (6) specific conductance; (7) pH; (8) temperature; (9) a summary containing mean, median, and standard deviation values of each data type for each treatment (wet and dry); and (10) methods codes. All files are .csv or.pdf.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

WHONDRS laboratory time series moisture manipulative experiment from soil core layers across eastern contiguous US: time series aerobic respiration, geochemistry, and aggregates

This dataset supports a broader study examining the effects of wetting and drying on soil layers across the eastern contiguous United States (CONUS). The dataset provides data generated from a laboratory moisture manipulation experiment. The contents include time series aerobic respiration and moisture; dissolved oxygen; sediment geochemistry data; and field metadata. Samples were collected as part of a collaboration between WHONDRS (Worldwide Hydrobiogeochemistry Observation Network for Dynamic River Systems; https://whondrs.pnnl.gov) and MONet (Molecular Observation Network; https://www.emsl.pnnl.gov/monet). The field samples (soil cores) were labeled as MEL_##_COR and subsequent subsamples begin with MEL_##. Additional subsamples were taken for the laboratory experiment and were labeled as EL_##. The labels from the MEL field samples and the EL subsamples can be mapped directly based on the digits following the prefix and underscore (i.e., EL_01 is a subsample from MEL_01). See the critical details section below for more details on sample naming and experimental design.For details on how to navigate this data package, see this infographic from the River Corridor SFA https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About.In addition to this readme, this data package also includes a file-level metadata (FLMD) file that describes each file and a data dictionary (DD) that describes all column/row headers and variable definitions.This dataset is comprised of (1) a folder containing environmental context photos; (2) file-level metadata; (3) data dictionary; (4) field metadata; (5) readme; (6) international generic sample number (IGSN) mapping file; and (7) a subfolder with soil sample data from field samples and the incubation experiment. The sample data subfolder contains (1) effect size; (2) gravimetric moisture from field samples and incubation experiment; (3) respiration rates, raw dissolved oxygen values, and plots; (4) specific conductance, pH, and temperature from the incubation; (5) soil aggregates; (6) a summary containing median values of each data type for each treatment (wet and dry) in the incubation; (7) a summary containing averages for each data type of each soil layer; and (8) methods codes. All files are .csv, .pdf, .jpeg, or .jpg.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Assessing methods in fusion and fitting for time series construction in remote sensing-based earth observations

This study evaluates the comparative performance of spatiotemporal fusion and time-series fitting methods for constructing high-spatiotemporal-resolution remote sensing time-series data. Due to in-class similarity of fusion methods and fitting methods, we employ the Fit-FC (Fitting, spatial Filtering, and residual Compensation) model as a representative fusion method and the linear harmonic fitting model as a representative fitting method. Both Fit-FC and the linear harmonic fitting are widely used for high-spatiotemporal-resolution time-series data construction, and we modify the original Fit-FC model to enable automatic time-series fusion. To ensure data representativeness, we use 3 years (2019–2021) of Harmonized Landsat and Sentinel-2 surface reflectance datasets and Terra MCD43A4 products. Eight experimental regions are selected worldwide to guarantee generalization of the comparative performance between fusion and fitting methods, covering diverse land-use types (cropland, developed land, forest, and grassland) and varying climatological conditions. Time-series of NDVI and surface reflectance are analyzed under both actual observations and simulated data-missing scenarios. The constructed time-series data reveals that (1) the modified Fit-FC and linear harmonic fitting model achieve excellent performance in constructing high-resolution time-series images; (2) the fusion method outperforms the fitting method in constructing time-series of NDVI and surface reflectance images in cropland-, forest-, and grassland-dominated regions; (3) both methods achieve comparable performance in developed-dominated regions; (4) the fusion method is more robust to missing data, and better captures abrupt phenological transitions under conditions of continuous missing data; (5) the fitting method is computationally more efficient, making it suitable for large-scale time-series image reconstruction. This study provides valuable insights for selecting optimal strategies to generate high-resolution time-series images across diverse application scenarios and lays a foundation for extensions to other vegetation indices or land surface variables.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Multitaper Magnitude‐Squared Coherence for Time Series With Missing Data: Understanding Oscillatory Processes Traced by Multiple Observables

To explore the hypothesis of a common source of variability in two time series, observers may estimate the magnitude-squared coherence (MSC), which is a frequency-domain view of the cross correlation. For time series that do not have uniform observing cadence, MSC can be estimated using Welch's overlapping segment averaging. However, multitaper has superior statistical properties to Welch's method in terms of the tradeoff between bias, variance, and bandwidth. The classical multitaper technique has recently been extended to accommodate time series with underlying uniform observing cadence from which some observations are missing. This situation is common for solar and geomagnetic data sets, which may have gaps due to breaks in satellite coverage, instrument downtime, or poor observing conditions. We demonstrate the scientific use of missing-data multitaper magnitude-squared coherence by detecting known solar mid-term oscillations in simultaneous, missing-data time series of solar Lyman α flux and geomagnetic Disturbance Storm Time index. Due to their superior statistical properties, we recommend that multitaper methods be used for all heliospheric time series with underlying uniform observing cadence.

Astro-statistics techniques (1886)↗
DOE OSTI2023

A new method for detecting abrupt changes in the dependence among multivariate hydrological series based on moving cut total correlation

Knowledge of how to define and estimate the dependence among multivariate hydrological series is essential for detecting abrupt changes in the dependence. Here, in this paper, a new method (BMCTC) is proposed to detect all possible abrupt change points in the dependence among multivariate hydrological series. The total correlation estimated by the matrix-based Renyi's alpha-order entropy functional is firstly introduced to define and measure the dependence strength among multivariate hydrological series. Then, the moving cut total correlation (MCTC) sequence is built by the moving window technique, which is used to measure changes in the dependence strength among multivariate hydrological series. Finally, the Bernaola-Galvan algorithm is used to detect all change points of the MCTC sequence. Simulations are performed to compare the effectiveness of BMCTC with Pearson correlation (BMCPC) and Spearman correlation (BMCSC), Cramer-von Mises (CvM) and copula-based likelihood-ratio (CLR). The results show that all change points are detected by BMCTC regardless of the samples size, but wrong change points or no change points are detected by other methods in most cases. BMCTC is applied to detect change points in the dependence among annual runoff, precipitation and sediment discharge series in the Xiliugou and the Kuyehe River, China. It is found that the dependence among runoff, precipitation and sediment discharge changed abruptly in 1980 and 1996 in the Kuyehe River and in 1999 in the Xiliugou River. These changes are mainly caused by human activities such as construction of water conservancy projects and coal mining.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

SigTime: Learning and Visually Explaining Time Series Signatures

Understanding and distinguishing temporal patterns in time series data is essential for scientific discovery and decision-making. For example, in biomedical research, uncovering meaningful patterns in physiological signals can improve diagnosis, risk assessment, and patient outcomes. However, existing methods for time series pattern discovery face major challenges, including high computational complexity, limited interpretability, and difficulty in capturing meaningful temporal structures. Here, to address these gaps, we introduce a novel learning framework that jointly trains two Transformer models using complementary time series representations: shapelet-based representations to capture localized temporal structures and traditional feature engineering to encode statistical properties. The learned shapelets serve as interpretable signatures that differentiate time series across classification labels. Additionally, we develop a visual analytics system—SigTime—with coordinated views to facilitate exploration of time series signatures from multiple perspectives, aiding in useful insights generation. We quantitatively evaluate our learning framework on eight publicly available datasets and one proprietary clinical dataset. Additionally, we demonstrate the effectiveness of our system through two usage scenarios along with the domain experts: one involving public ECG data and the other focused on preterm labor analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Accelerating countermeasure candidate discovery for A-series chemical warfare agent exposure

The recent alleged use of A-series chemical warfare agents (CWAs) highlights the urgent need to better understand their inhibition of cholinesterase enzymes and the reported shortcomings of traditional oxime countermeasures. Here, using high-throughput (HT) mass spectrometry (MS) technologies, we characterized the largely unknown inhibition kinetics of A-series CWAs on human acetylcholinesterase (hAChE) and its reactivation by oximes, achieving label-free quantitation at rates of up to 7,000 reactions per hour. Our findings indicate i) A-series agents exhibit inhibitory potencies similar to traditional CWAs like sarin and VX, and ii) bipyridinium-based oximes can reactivate A-series-adducted hAChE in vitro, challenging prior reports on oxime efficacy. These results underscore the need for continued exploration of countermeasure candidates against A-series CWAs and demonstrate the potential of HT-MS for rapidly and safely characterizing emerging toxic chemicals.

acetylcholinesterase↗
DOE OSTI2025

Multiple Changepoint Detection for Non‐Gaussian Time Series

ABSTRACT This article combines methods from existing techniques to identify multiple changepoints in non‐Gaussian autocorrelated time series. A transformation is used to convert a Gaussian series into a non‐Gaussian series, enabling penalized likelihood methods to handle non‐Gaussian scenarios. When the marginal distribution of the data is continuous, the methods essentially reduce to the change of variables formula for probability densities. When the marginal distribution is count‐oriented, Hermite expansions and particle filtering techniques are used to quantify the scenario. Simulations demonstrating the efficacy of the methods are given and two data sets are analyzed: 1) the proportion of home runs hit by Major League Baseball batters from 1920 to 2023 and 2) a six‐dimensional series of tropical cyclone counts from the Earth's basins of generation from 1980 to 2023. In the first series, beta marginal distributions are used to describe the proportions; in the second, Poisson marginal distributions seem appropriate.

Lund, Robert [Department of Statistics University ↗
DOE OSTI2025

The OCEAN ICE mooring compilation: a standardised, pan-Antarctic database of ocean hydrography and current time series

Continuous moored time series of temperature, salinity, pressure and current speed and direction are of great importance for understanding the continental shelf and under-ice-shelf dynamics and thermodynamics that govern water mass transformations and ice melting in and around Antarctic marginal seas. In these regions, icebergs and sea ice make ship-based mooring deployment and recovery challenging. Nevertheless, over decades, expeditions around the fringe of Antarctica sporadically deployed and recovered hundreds of moored instruments, including those facilitated through ice shelves boreholes. These datasets tend to be archived in a wide range of data centres, with, to our knowledge, no clear format standardisation. As a result, systematic analysis of historical mooring time series in the marginal seas is often challenging. Here we present the first version of a standardised pan-Antarctic moored hydrography and current time series compilation, with broad international contributions from data centres, research institutes and individual data owners. The mooring records in this compilation span over five decades, from the 1970s to the 2020s, providing an opportunity for a systematic study of the pan-Antarctic water mass transport and shelf connectivity. As a demonstration of the utility of this compilation, we present spectral analysis of the compiled current velocity time series, which unsurprisingly shows the dominating presence of tidal variability within most records. This component of the variability is fitted using multi-linear regression to tidal frequencies, and the tidal fit is removed from the original time series to leave de-tided variability. Given the limited record durations to months to years, de-tided variability is dominated by synoptic (3–10 d period), intraseasonal (10–80 d) and seasonal (∼6 months–1 year) signals. The spatial distribution of the kinetic energy integrated within frequency bands is presented and discussed within respective regional contexts, and future avenues of research are proposed. This data compilation is assembled under the endorsement of Ocean-Cryosphere Exchanges in ANtarctica: Impacts on Climate and the Earth System (OCEAN ICE) project (https://ocean-ice.eu/, last access: 23 October 2025) funded by the European Commission and UK Research and Innovation. It is available and regularly updated in NetCDF format with the SEANOE database at https://doi.org/10.17882/99922 (Zhou et al., 2024a).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Deep learning for time series forecasting: a survey of recent advances

Time series forecasting plays a critical role in numerous real-world applications, such as finance, healthcare, transportation, and scientific computing. In recent years, deep learning has become a powerful tool for modeling complex temporal patterns and improving forecasting accuracy. This survey provides an overview of recent deep learning approaches for time series forecasting, involving various architectures including RNNs, CNNs, GNNs, transformers, large language models, MLP-based models, and diffusion models. We first identify key challenges in the field, such as temporal dependency, efficiency, and cross-variable dependency, which drive the development of forecasting techniques. Then, the general advantages and limitations of each architecture are discussed to contextualize their adaptation in time series forecasting. Furthermore, we highlight promising design trends like multi-scale modeling, decomposition, and frequency-domain techniques, which are shaping the future of the field. This paper serves as a compact reference for researchers and practitioners seeking to understand the current landscape and future trajectory of deep learning in time series forecasting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

PV-BESS DC-Series Integration for Regulated DC Systems

DC-series integration introduces a novel approach to seamlessly integrate a solar photovoltaic (PV) array and a battery energy storage (BES) in series. This system, referred to as the PV-integrated battery energy storage system—dc series (PVBESS-DCS), simplifies integration and enhances power density by leveraging the inherent voltage-source characteristics of batteries and adopting the concept of partial power processing. However, addressing voltage variations of a PV array and a BES under different operational conditions remains a challenge to apply the PVBESS-DCS to a regulated dc system, where the dc-bus voltage is fixed. This article proposes a PVBESS-DCS solution tailored for regulated dc systems. Within this framework, we present a controllable series voltage source compensating for the voltage differences between the PV and BES sources and the dc bus. Thus, the system can perform PV maximum power point tracking and curtailment control while charging and discharging BES and connected to a regulated dc bus. Additionally, we present a single-stage multiport partial power processing dc–dc converter designed for the proposed PVBESS-DCS. It utilizes a triple active bridge dc–dc converter topology. Finally, this article presents operating principles, control strategies, simulation results, and experimental findings of the proposed PVBESS-DCS for regulated dc systems.

25 ENERGY STORAGE↗
DOE OSTI2025

Oscillation Risks of Grid-Following and Grid-Forming Inverter-Based Resources in Series-Compensated Networks

Here, this paper investigates the dynamic behavior of a grid-connected inverter-based resource (IBR) when connected radially to a series compensated line. Potential interactions between the series compensation and the IBR have been identified for both types: grid-following (GFL) or grid-forming (GFM). The study begins with electromagnetic transient (EMT) simulations to demonstrate stability issues. Subsequently, nonlinear analytical models are formulated in the dq frame, validated against the EMT simulation, and leveraged to assess eigenvalues and participation factors. Influencing factors of the dominant oscillation modes have been identified. The analysis results show that series compensation may make a mode associated with the synchronization unit unstable. Furthermore, customized feedback systems are built for the synchronizing loop. Series compensation can increase the sensitivity of the voltage phase angle towards the synchronizing angle, and introduce phase lag in the real power response towards the synchronizing angle. These factors may cause interactions with the phase-locked loop in GFL-IBR systems and with power-based synchronization in GFM-IBR systems, potentially leading to instability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

A Preferences Corpus and Annotation Scheme for Human-Guided Alignment of Time-Series GPTs

The process of time-series forecasting such as predicting trajectories of silicon content in blast furnaces is a difficult task. Most time-series approaches today focus on scalar-type MSE loss optimization. This optimization approach, while widely common, could benefit from the use of human expert or process-level preferences. In this paper, we introduce a novel alignment and fine-tuning approach that involves learning from a corpus of preferred and dis-preferred time-series prediction trajectories. Our contributions include (1) a preference annotation pipeline for time-series forecasts, (2) the application of Score-based Preference Optimization (SPO) to train decoder-only transformers from preferences, and (3) results showing improvements in forecast quality. The approach is validated on both proprietary blast furnace data and the UCI Appliances Energy dataset. The proposed preference corpus and training strategy offer a new option for fine-tuning sequence models in industrial settings.

DPO↗
DOE OSTI2026

Monitoring of Liquid Metal Reactor Heater Zones with Recurrent Neural Network Learning of Temperature Time Series

Advanced high-temperature fluid reactors (ARs), such as sodium fast reactors (SFRs) and molten salt cooled reactors (MSCRs) utilize high-temperature fluids at ambient pressure. To melt the fluid during reactor startup and prevent fluid freezing during cooldown, the thermal–hydraulic systems of such ARs include heater zones consisting of specific heaters with controllers, temperature sensors, and thermal insulation. The failure of heater zones due to insulation material degradation or improper installation, resulting in parasitic heat losses, can lead to fluid freezing. The detection of faults using a heat-transfer model is difficult because of a lack of knowledge of the experimental details. Data-driven machine learning of heater zone temperature time series offers a viable alternative. In this study, we benchmarked the performance of recurrent neural networks (RNNs) in an analysis of heat-up transient temperature time series of heater zones installed on a liquid sodium vessel. The RNN models include long short-term memory (LSTM) and gated recurrent unit (GRU) networks, as well as their bi-directional variants, BiLSTM and BiGRU. Anomalous temperature points were designated using a percentile-based threshold applied to residual fluctuations in the detrended temperature time series. Additionally, the impact of the exponentially weighted moving average (EWMA) method on detection accuracy was examined. The RNN models’ performance was assessed using precision, recall, and F 1 score metrics. Results demonstrated that RNN models effectively detect anomalies in temperature time series with the best models for each heater zone achieving F 1 scores of over 93%. To explain the variations in RNN model performance across different heater zones, we used Kullback–Leibler (KL) divergence to quantify the relative entropy between training and testing data, and the Detrended Fluctuation Analysis (DFA) to assess long-range temporal correlations. For datasets with strong long-range correlations and minimal relative entropy between training and testing data, GRU is the best-performing model. When the data exhibits weaker long-term correlations and a significant relative entropy between training and testing distributions, BiGRU shows the best performance. For the data sets with intermediate values of both KL divergence and DFA, the best performance is obtained with LSTM and BiLSTM, respectively.

gated recurrent unit↗
DOE OSTI2024

Energy Efficient Streaming Time Series Classification with Attentive Power Iteration

Efficiently processing time series data streams in real-time on resource-constrained devices offers significant advantages in terms of enhanced computational energy efficiency and reduced time-related risks. We introduce an innovative streaming time series classification network that utilizes attentive power iteration, enabling real-time processing on resource-constrained devices. Our model continuously updates a compact representation of the entire time series, enhancing classification accuracy while conserving energy and processing time. Notably, it excels in streaming scenarios without requiring complete time series access, enabling swift decisions. Experimental results show that our approach excels in classification accuracy and energy efficiency, with over 70% less consumption and threefold faster task completion than benchmarks. This work advances real-time responsiveness, energy conservation, and operational effectiveness for constrained devices, contributing to optimizing various applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Parallel hybrid quantum-classical machine learning for kernelized time-series classification

Supervised time-series classification garners widespread interest because of its applicability throughout a broad application domain including finance, astronomy, biosensors, and many others. Here, in this work, we tackle this problem with hybrid quantum-classical machine learning, deducing pairwise temporal relationships between time-series instances using a timeseries Hamiltonian kernel (TSHK). A TSHK is constructed with a sum of inner products generated by quantum states evolved using a parameterized time evolution operator. This sum is then optimally weighted using techniques derived from multiple kernel learning. Because we treat the kernel weighting step as a differentiable convex optimization problem, our method can be regarded as an end-to-end learnable hybrid quantum-classical-convex neural network, or QCC-net, whose output is a data set-generalized kernel function suitable for use in any kernelized machine learning technique such as the support vector machine (SVM). Using our TSHK as input to a SVM, we classify univariate and multivariate time-series using quantum circuit simulators and demonstrate the efficient parallel deployment of the algorithm to 127-qubit superconducting quantum processors using quantum multi-programming.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Machine-learned closure of URANS for stably stratified turbulence: connecting physical timescales & data hyperparameters of deep time-series models

Stably stratified turbulence (SST), a model that is representative of the turbulence found in the oceans and atmosphere, is strongly affected by fine balances between forces and becomes more anisotropic in time for decaying scenarios. Moreover, there is a limited understanding of the physical phenomena described by some of the terms in the Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations—used to numerically simulate approximate solutions for such turbulent flows. Rather than attempting to model each term in URANS separately, it is attractive to explore the capability of machine learning (ML) to model groups of terms, i.e. to directly model the force balances. We develop deep time-series ML for closure modeling of the URANS equations applied to SST. We consider decaying SST which are homogeneous and stably stratified by a uniform density gradient, enabling dimensionality reduction. We consider two time-series ML models: long short-term memory and neural ordinary differential equation. Both models perform accurately and are numerically stable in a posteriori (online) tests. Furthermore, we explore the data requirements of the time-series ML models by extracting physically relevant timescales of the complex system. We find that the ratio of the timescales of the minimum information required by the ML models to accurately capture the dynamics of the SST corresponds to the Reynolds number of the flow. The current framework provides the backbone to explore the capability of such models to capture the dynamics of high-dimensional complex dynamical system like SST flows.

97 MATHEMATICS AND COMPUTING↗