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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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NASA NTRS2022

Data-driven Expectations for Electromagnetic Counterpart Searches Based on LIGO/Virgo Public Alerts

Searches for electromagnetic counterparts of gravitational-wave signals have redoubled since the first detection in2017 of a binary neutron star merger with a gamma-ray burst, optical/infrared kilonova, and panchromatic after glow. Yet, one LIGO/Virgo observing run later, there has not yet been a second, secure identification of an electromagnetic counterpart. This is not surprising given that the localization uncertainties of events in LIGO and Virgo’s third observing run, O3, were much larger than predicted. We explain this by showing that improvements in data analysis that now allow LIGO/Virgo to detect weaker and hence more poorly localized events have increased the overall number of detections, of which well-localized, gold-plated events make up a smaller proportion overall. We present simulations of the next two LIGO/Virgo/KAGRA observing runs, O4 and O5, that are grounded in the statistics ofO3 public alerts. To illustrate the significant impact that the updated predictions can have, we study the follow-up strategy for the Zwicky Transient Facility. Realistic and timely forecasting of gravitational-wave localization accuracy is paramount given the large commitments of telescope time and the need to prioritize which events are followed up. We include a data release of our simulated localizations as a public proposal planning resource for astronomers

Polina Petrov↗

DOE OSTI2022

An Automated Scanning Transmission Electron Microscope Guided by Sparse Data Analytics

Abstract Artificial intelligence (AI) promises to reshape scientific inquiry and enable breakthrough discoveries in areas such as energy storage, quantum computing, and biomedicine. Scanning transmission electron microscopy (STEM), a cornerstone of the study of chemical and materials systems, stands to benefit greatly from AI-driven automation. However, present barriers to low-level instrument control, as well as generalizable and interpretable feature detection, make truly automated microscopy impractical. Here, we discuss the design of a closed-loop instrument control platform guided by emerging sparse data analytics. We hypothesize that a centralized controller, informed by machine learning combining limited a priori knowledge and task-based discrimination, could drive on-the-fly experimental decision-making. This platform may unlock practical, automated analysis of a variety of material features, enabling new high-throughput and statistical studies.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

Data-Driven Learning of Nonautonomous Systems

In this work, we present a numerical framework for recovering unknown nonautonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the nonautonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Knowledge-informed deep learning for hydrological model calibration: an application to Coal Creek Watershed in Colorado

Abstract. Deep learning (DL)-assisted inverse mapping has shown promise in hydrological model calibration by directly estimating parameters from observations. However, the increasing computational demand for running the state-of-the-art hydrological model limits sufficient ensemble runs for its calibration. In this work, we present a novel knowledge-informed deep learning method that can efficiently conduct the calibration using a few hundred realizations. The method involves two steps. First, we determine decisive model parameters from a complete parameter set based on the mutual information (MI) between model responses and each parameter computed by a limited number of realizations (∼50). Second, we perform more ensemble runs (e.g., several hundred) to generate the training sets for the inverse mapping, which selects informative model responses for estimating each parameter using MI-based parameter sensitivity. We applied this new DL-based method to calibrate a process-based integrated hydrological model, the Advanced Terrestrial Simulator (ATS), at Coal Creek Watershed, CO. The calibration is performed against observed stream discharge (Q) and remotely sensed evapotranspiration (ET) from the water year 2017 to 2019. Preliminary MI analysis on 50 realizations resulted in a down-selection of 7 out of 14 ATS model parameters. Then, we performed a complete MI analysis on 396 realizations and constructed the inverse mapping from informative responses to each of the selected parameters using a deep neural network. Compared with calibration using observations covering all time steps, the new inverse mapping improves parameter estimations, thus enhancing the performance of ATS forward model runs. The Nash–Sutcliffe efficiency (NSE) of streamflow predictions increases from 0.53 to 0.8 when calibrating against Q alone. Using ET observations, on the other hand, does not show much improvement on the performance of ATS modeling mainly due to both the uncertainty of the remotely sensed product and the insufficient coverage of the model ET ensemble in capturing the observation. By using observed Q only, we further performed a multiyear analysis and show that Q is best simulated (NSE > 0.8) by including in the calibration the dry-year flow dynamics that show more sensitivity to subsurface characteristics than the other wet years. Moreover, when continuing the forward runs till the end of 2021, the calibrated models show similar simulation performances during this evaluation period as the calibration period, demonstrating the ability of the estimated parameters in capturing climate sensitivity. Our success highlights the importance of leveraging data-driven knowledge in DL-assisted hydrological model calibration.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1998

Hydrostar Thermal and Structural Deformation Analyses of Antenna Array Concept

The proposed Hydrostar mission used a large orbiting antenna array to demonstrate synthetic aperture technology in space while obtaining global soil moisture data. In order to produce accurate data, the array was required to remain as close as possible to its perfectly aligned placement while undergoing the mechanical and thermal stresses induced by orbital changes. Thermal and structural analyses for a design concept of this antenna array were performed. The thermal analysis included orbital radiation calculations, as well as parametric studies of orbit altitude, material properties and coating types. The thermal results included predicted thermal distributions over the array for several cases. The structural analysis provided thermally-driven deflections based on these cases, as well as based on a 1-g inertial load. In order to minimize the deflections of the array in orbit, the use of XN70, a carbon-reinforced polycyanate composite, was recommended.

Amundsen, Ruth M.↗

NASA NTRS2021

The Scientific Legacy of NASA’s Operation IceBridge

The National Aeronautics and Space Administration (NASA)’s Operation IceBridge (OIB) was a 13-year (2009–2021) airborne mission to survey land and sea ice across the Arctic, Antarctic, and Alaska. Here, we review OIB’s goals, instruments, campaigns, key scientific results, and implications for future investigations of the cryosphere. OIB’s primary goal was to use airborne laser altimetry to bridge the gap in fine-resolution elevation measurements of ice from space between the conclusion of NASA’s Ice, Cloud, and land Elevation Satellite (ICESat; 2003–2009) and its follow-on, ICESat-2 (launched 2018). Additional scientific requirements were intended to contextualize observed elevation changes using a multisensor suite of radar sounders, gravimeters, magnetometers, and cameras. Using 15 different aircraft, OIB conducted 968 science flights, of which 42% were repeat surveys of land ice, 42% were surveys of previously unmapped terrain across the Greenland and Antarctic ice sheets, Arctic ice caps, and Alaskan glaciers, and 16% were surveys of sea ice. The combination of an expansive instrument suite and breadth of surveys enabled numerous fundamental advances in our understanding of the Earth’s cryosphere. For land ice, OIB dramatically improved knowledge of interannual outlet-glacier variability, ice-sheet, and outlet-glacier thicknesses, snowfall rates on ice sheets, fjord and sub-ice-shelf bathymetry, and ice-sheet hydrology. Unanticipated discoveries included a reliable method for constraining the thickness within difficult-to-sound incised troughs beneath ice sheets, the extent of the firn aquifer within the Greenland Ice Sheet, the vulnerability of many Greenland and Antarctic outlet glaciers to ocean-driven melting at their grounding zones, and the dominance of surface-melt-driven mass loss of Alaskan glaciers. For sea ice, OIB significantly advanced our understanding of spatiotemporal variability in sea ice freeboard and its snow cover, especially through combined analysis of fine-resolution altimetry, visible imagery, and snow radar measurements of the overlying snow thickness. Such analyses led to the unanticipated discovery of an interdecadal decrease in snow thickness on Arctic sea ice and numerous opportunities to validate sea ice freeboards from satellite radar altimetry. While many of its data sets have yet to be fully explored, OIB’s scientific legacy has already demonstrated the value of sustained investment in reliable airborne platforms, airborne instrument development, interagency and international collaboration, and open and rapid data access to advance our understanding of Earth’s remote polar regions and their role in the Earth system.

Joseph A. MacGregor↗

DOE OSTI2026

Operando Spectroscopic Analysis of Photovoltage Generation in Hematite Photoanodes

Solar-driven water splitting requires sufficient photovoltage to drive both water oxidation and proton reduction. Understanding the factors driving and limiting photovoltage generation is therefore crucial to optimizing photoelectrode design but has proven challenging to determine under operando conditions for photoanodes driving slow multiredox reactions such as water oxidation. In this work, operando optical spectroscopy is employed to measure the hole quasi-Fermi level (E F,p ) position in model hematite photoanodes as a function of applied bias and light intensity. The quasi-Fermi level splitting determined from these data are shown be in excellent agreement with the directly measured photovoltages, demonstrating the primarily electrochemical rather than primarily electrostatic origin of photovoltage in these photoelectrodes. E F,p pinning is observed at low light intensities and biases, indicative of hole trap states lying ∼0.2 eV above the valence band edge with a density of ∼1 nm −2 . Hole accumulation in these trap states is correlated with first order water oxidation. At higher light intensities and/or more anodic bias, E F,p becomes unpinned, assigned to saturation of these trap states, and correlated with the onset of third order water oxidation to molecular oxygen. Comparison with rate law analyses for other photoanodes indicates that such hole trap states may be a ubiquitous feature of metal oxides and suggests that materials processing strategies to suppress the density of such states would be a promising strategy to enhance photoanode performance.

Hematite↗

NASA NTRSDate not supplied

Ice Shape Analysis of an eVTOL Propeller in Forward Flight at the NASA Glenn Icing Research Tunnel

Advanced Air Mobility (AAM) introduces many novel electric vertical takeoff and landing (eVTOL) aircraft configurations for which the effect of icing is not well understood. While icing computational tools have often aided in the design and certification of conventional aircraft, experimental data is needed to support the development and validation of such tools for eVTOL applications. To investigate the icing phenomenon relevant to eVTOL aircraft, NASA Glenn Research Center developed a general-purpose propeller test stand for conducting fundamental icing research on electrically driven propellers in the Icing Research Tunnel (IRT). A 10-day test entry in the IRT was completed in March, 2023, with the goal of generating ice accretions on a non-proprietary propeller geometry under well-characterized conditions. Three carbon fiber propellers of diameters 0.610, 0.711, and 0.914 m (24, 28, and 36 in) were used during the test. Various parametric sweeps of cloud and operating conditions were performed to evaluate the sensitivity of the parameters on the resulting ice accretion characteristics such as ice thickness, mass, location (impingement limits), and type (glaze vs rime). Ice shapes were reviewed for their repeatability, correctness of trends, and sensitivity to parameter variations. The data from the test is being used to support the development of the ice accretion solver, GlennICE.

Icing↗

NASA NTRS2024

Ice Shape Analysis of an eVTOL Propeller in Forward Flight at the NASA Glenn Icing Research Tunnel

Icing↗

DOE OSTI2023

Multiscale Temporal Variability of the Global Air‐Sea CO 2 Flux Anomaly

Abstract The global air‐sea CO 2 flux (F) impacts and is impacted by a plethora of climate‐related processes operating at multiple time scales. In bulk mass transfer formulations, F is driven by physico‐ and bio‐chemical factors such as the air‐sea partial pressure difference (∆pCO 2 ), gas transfer velocity, sea surface temperature, and salinity–all varying at multiple time scales. To de‐convolve the impact of these factors on variability in F at different time scales, time‐resolved estimates of F were computed using a global data set assembled between 1988 and 2015. The F anomalies were defined as temporal deviations from the 28‐year time‐averaged value. Spectral analysis revealed four dominant timescales of variability in F–subseasonal, seasonal, interannual, and decadal with relative amplitude differences varying across regions. A second‐order Taylor series expansion was then conducted along these four timescales to separate drivers across differing regions. The analysis showed that on subseasonal timescales, wind speed variability explains some 66% of the global F anomaly and is the dominant driver. On seasonal, interannual, and decadal timescales, the ∆pCO 2 effect controlled by the ∆pCO 2 anomaly, explained much of the F anomaly. On decadal timescales, the F anomaly was almost entirely governed by the ∆pCO 2 effect with large contributions from high latitudes. The main drivers across timescales also dominate the regional F anomaly, particularly in the mid‐high latitude regions. Finally, the driver of the ∆pCO 2 effect was closely connected with the relative strength of atmospheric pCO 2 and the nonthermal component of oceanic pCO 2 anomaly associated with dissolved inorganic carbon and alkalinity.

Environmental Sciences & Ecology↗

DOE OSTI2019

Evolution of Induced Fracture Networks Using Machine Learning Correlation Image Analysis

Enhanced geothermal systems (EGS) can enrich the Nation’s energy portfolio by increasing the amount of renewable baseload power available to the electrical grid. Microseismic activity, due to fluid resource injection and production, provides critical insight into the processes that occur within EGS subsurface fracture networks. To more precisely characterize these fracture networks, we leverage recent advances in deep neural network (DNN) image analysis techniques. Using seismic spectrogram data collected during a meso scale EGS field experiment as image inputs, we developed a new approach to correlate microseismic events. Our results indicate that our chosen DNN is able to estimate the correlation value between highly correlated events (i.e., cross-correlation coefficients greater than approximately 0.7), but has difficulty estimating correlation values between poorly correlated events. In physical systems however, the highly correlated microseismic events are the events of interest. Therefore, this data-driven method has shown potential for improving domestic Energy and Resource Security, advancing the current methods available to image subsurface EGS thermal reservoirs to enhance the availability of clean and reliable energy to the national electric grid.

58 GEOSCIENCES↗

DOE OSTI2021

Wind Plant Performance Prediction Benchmark Phase 1 (Technical Report)

Financial risk resulting from the uncertainty associated with developing, owning, and operating wind power plants remains a barrier to reducing the levelized cost of energy (LCOE). On average, modern wind power plants in the U.S. underperform their expected annual energy output by 3.5-4.5% , with many underperforming by over 10%. To compensate for this uncertainty, investors require a larger return on investment (ROI) and apply "knock-down" factors that mask much of the underlying sources of uncertainty. Wind energy projects thus have reduced access to low-cost capital. Furthermore, operating wind plants often take a simple approach to estimating operations & maintenance (O&M) costs (e.g. straight-line estimates based on similar plants), which can eat into profits. To overcome these issues, the wind industry must improve the models they use for estimating wind plant performance and operations. An industry consortium (IC) requested that the National Renewable Energy Laboratory (NREL) lead a Department of Energy (DOE) working group to benchmark the accuracy of wind power plant energy predictions against real operational data. The IC was also motivated by DOE and NREL's potential to characterize systematic energy underperformance, identify sources of uncertainty, and explore root causes. The Wind Plant Performance Prediction (WP3) project was created out of this request, and this report represents the successful completion of Phase 1 of the WP3 project. During the project, wind plant owners provided both pre-construction and operational data to NREL. The pre-construction data was provided to wind resource assessment (WRA) consultants so they could conduct energy yield assessments (EYA). NREL took all of the completed EYAs, along with the operational data, and conducted an operational assessment to benchmark the EYA results against actual operational data. Given the large amounts of sensitive data required for this effort, as well as historical opposition to sharing data within industry, successful completion of Phase 1 represents an unprecedented milestone for industry data sharing. To improve the accuracy and confidence of pre-construction EYAs, wind plant owners and investors need better, more certain, energy yield predictions. The WP3 Benchmark Project is an industry-driven response to this reality. For the first time, industry has taken the important step of working together at scale, sharing valuable operational data with DOE and NREL in order to investigate the sources of bias and uncertainty in these energy estimates. This IC provides wind plant preconstruction and operational data to NREL in an organized and documented fashion and provides guidance and feedback as needed. The IC also provides introspection of the design of experiment, key metrics of success, data challenges, analysis best practices, and quality of results.

17 WIND ENERGY↗

DOE OSTI2022

Discovery of Signatures, Anomalies, and Precursors in Synchrophasor Data with Matrix Profile and Deep Recurrent Neural Networks (Final Project Report)

The widespread deployment of phasor measurement unit (PMU) across the U.S. together with the burgeoning machine learning technology made it possible to develop data-driven PMU data analytics to improve grid security and reliability in a more insightful and effective manner. Although PMU applications have been explored for over a decade, the representative PMU usage is limited to the bulk power system monitoring mainly due to the data integrity issues associated with PMUs (typically missing, fragmented, and wrongly amplified data). To forge a breakthrough on this stalemate and embrace PMUs for power system control and protection as well, we applied various advanced machine learning and big data analysis technology to the power system event detection and classification as the first step toward the power system control and protection pertaining to grid security enhancement.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2012

NASA's Carbon Monitoring System Flux-Pilot Project: A Multi-Component Analysis System for Carbon-Cycle Research and Monitoring

The importance of greenhouse gas increases for climate motivates NASA s observing strategy for CO2 from space, including the forthcoming Orbiting Carbon Observatory (OCO-2) mission. Carbon cycle monitoring, including attribution of atmospheric concentrations to regional emissions and uptake, requires a robust modeling and analysis infrastructure to optimally extract information from the observations. NASA's Carbon-Monitoring System Flux-Pilot Project (FPP) is a prototype for such analysis, combining a set of unique tools to facilitate analysis of atmospheric CO2 along with fluxes between the atmosphere and the terrestrial biosphere or ocean. NASA's analysis system is unique, in that it combines information and expertise from the land, oceanic, and atmospheric branches of the carbon cycle and includes some estimates of uncertainty. Numerous existing space-based missions provide information of relevance to the carbon cycle. This study describes the components of the FPP framework, assessing the realism of computed fluxes, thus providing the basis for research and monitoring applications. Fluxes are computed using data-constrained terrestrial biosphere models and physical ocean models, driven by atmospheric observations and assimilating ocean-color information. Use of two estimates provides a measure of uncertainty in the fluxes. Along with inventories of other emissions, these data-derived fluxes are used in transport models to assess their consistency with atmospheric CO2 observations. Closure is achieved by using a four-dimensional data assimilation (inverse) approach that adjusts the terrestrial biosphere fluxes to make them consistent with the atmospheric CO2 observations. Results will be shown, illustrating the year-to-year variations in land biospheric and oceanic fluxes computed in the FPP. The signals of these surface-flux variations on atmospheric CO2 will be isolated using forward modeling tools, which also incorporate estimates of transport error. The results will be discussed in the context of interannual variability of observed atmospheric CO2 distributions.

Pawson, S.↗

DOE OSTI2025

Observation of kinetic mix enhancement in thin-shell OMEGA implosions

Recent separated reactant experiments for thin-shell (6 µ⁢m) shock-driven implosions on OMEGA have demonstrated significant mix from a buried deuterated layer of the shell into the hot spot. Time resolved D 3 He-p reaction history data demonstrate a (50 ± 20)⁢ ps shift earlier in peak nuclear emission for separated reactant experiments relative to control, in contrast to past experimental data for thicker, 20 µ⁢m shells with no laser burn through that show a 75 ps delay due to the time required for hydrodynamic instabilities to develop. This contrast suggests that the mix mechanism was not hydrodynamic. Ion kinetic simulations utilizing fall line analyses show much closer agreement with mix yield and temperature than diffusion models, predicting a D 3 He-p mix yield of 1.7 × 10 9 as compared to the experimental value of 9.3⁢ (±2.1) × 10 8 . This is three orders of magnitude closer than the fall line analysis from a hydrodynamic simulation with an inline diffusive mix model, which suggests minimal mix and D 3 He-p yields of 5×10 5 . This makes kinetic mechanisms the only feasible explanation for the mix seen, demonstrating impact of a non-standard mix mechanism. An analytical model of this kinetic mix mechanism suggests that it can remain significant in situations when the shell expands significantly to low densities, and diffusive models predict negligible mix. Finally, kinetic mix will impact multiple types of high energy density, laser-driven fusion experiments including high-adiabat direct drive cryoexperiments, nuclear cross section experiments, and thin-shell polar direct drive experiments used to tune heat conduction models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Dynamics and drivers of land use and land cover changes in Bangladesh

Abstract Bangladesh has undergone dramatic land use and land cover changes (LULCC) in recent years, but no quantitative analysis of LULCC drivers at the national scale exists so far. Here, we quantified the drivers of major LULCC in combination with biophysical and socioeconomic observations at the sub-district level. We used Landsat satellite data to interpret LULCC from 2000 to 2010 and employed a Global Surface Water Dataset to account for the influences of water seasonality. The results suggest that major LULCC in Bangladesh occur between agricultural land and waterbodies and between forest and shrubland. Exclusion of seasonal waterbodies can improve the accuracy of our LULCC results and driver analysis. Although the gross gain and loss of agricultural land are large on the local scale, the net change (gross gain minus gross loss) at a country scale is almost negligible. Climate dynamics and extreme events and changes in urban and rural households were driving the changes from forest to shrubland in the southeast region. The conversion from agricultural land to standing waterbodies in the southwest region was mainly driven by urban household dynamics, population growth, distance to cities and major roads, and precipitation dynamics. This study, which is the first effort accounting for water seasonality and quantifying biophysical and socioeconomic drivers of LULCC at the national scale, provides a perspective on overall LULCC and underlying drivers over a decadal time scale and national spatial scale and can serve as a scientific basis for developing land policies in Bangladesh.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Data-Driven Discovery of Linear Molecular Probes with Optimal Selective Affinity for PFAS in Water

Approaches to tackle the wide and growing variety of highly persistent per- and polyfluoroalkyl substances (PFAS) are of pressing global need because of their detrimental human health effects, such as cancer, birth defects, and hormone imbalance. Sensitive, selective, and easy-to-use real-time sensors to monitor and detect PFAS and sorbents to extract them are critical to meeting government-mandated environmental concentrations. In this work, we combine all-atom molecular dynamics simulations, enhanced sampling, deep representational learning, and Bayesian optimization to perform high-throughput virtual screening for highly sensitive and selective molecular probes. Our molecular design space consists of 3850 linear hydrocarbon chains with varying degrees of halogenation with and without amine- and phosphine-based headgroups. By employing a data-driven search process, we efficiently explore the molecular design space to optimize the sensitivity to perfluorooctanesulfonic acid (PFOS) as a prototypical PFAS analyte and selectivity relative to a sodium dodecyl sulfate (SDS) interferent. We calculate 504 Gibbs free energies of probe-analyte and probe-interferent interactions and identify probes with PFOS association free energies of up to (-ΔG PFOS ) = 9.8 ± 0.2 kJ/mol and selectivities relative to SDS of (-ΔΔG PFOS–SDS ) = 3.1 ± 1.5 kJ/mol. A C 11 Br 23 P(CH 3 ) 2 probe containing 11 backbone brominated carbons and a tertiary phosphine headgroup possesses the most sensitive binding constant to PFOS within the defined search space of K b PFOS = 177.4 ± 12.7, and a semibrominated probe C 5 H 11 C 7 Br 14 N(CH 3 ) 2 containing 12 backbone carbons and a tertiary amine headgroup possesses the highest selectivity relative to SDS of K b PFOS /K b SDS = 4.6 ± 1.7. A retrospective analysis of our data to extract interpretable design rules reveals that the sensitivity of linear hydrogenated probes increases by approximately 1 kJ/mol per C–C bond. The addition or removal of halogen atoms and amine or phosphine headgroups produces nonmonotonic changes in both sensitivity and selectivity with changes to the sensitivity of up to 2.5 kJ/mol. Finally, this work places empirical limitations on the performance of a wide range of linear probes for PFOS detection and offers a generic strategy for high-throughput computational screening to promote selective and sensitive binding.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Data-Driven Learning of Non-Autonomous Systems

We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances. The time-dependent inputs are then locally parameterized by using a proper model, for example, polynomial regression, in the pieces determined by the time instances. This transforms the original system into a piecewise parametric system that is locally time invariant. We then design a deep neural network structure to learn the local models. Once the network model is constructed, it can be iteratively used over time to conduct global system prediction. We provide theoretical analysis of our algorithm and present a number of numerical examples to demonstrate the effectiveness of the method.

97 MATHEMATICS AND COMPUTING↗