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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Thermal Radiation Transport with Tensor Trains

We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated by the rank of the decomposition. When the solution is “low rank,” the memory footprint of the specific intensity solution vector may be significantly compressed. The algorithm, following a step-then-truncate approach of a traditional discrete ordinates method, operates directly on the compressed state vector, thereby enabling large speedups for low-rank solutions. To achieve these speedups, we rely on a recently developed rounding approach based on the Gram-SVD. We detail how familiar S N algorithms for (gray) thermal transport can be mapped to this TT framework and present several numerical examples testing both the optically thick and thin regimes. The TT framework finds low-rank structure and supplies up to ≃60× speedups and ≃1000× compressions for problems demanding large angle counts, thereby enabling previously intractable SN calculations and supplying a promising avenue to mitigate ray effects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Machine Learning–Based Condition Monitoring of a Circulating Water System of a Canadian Nuclear Plant

With the need to maintain long-term reliable energy using nuclear power plants, there is an underlying demand to ensure that the maintenance of plant components and systems is also done in an efficient and cost-effective manner. One way to achieve this is by moving from time-based maintenance to condition-based maintenance. The research presented in this paper focuses on applying statistical and machine-learning-based methods to capture anomalies within data for fault detection to further develop into condition monitoring. This paper focuses on system data for a circulating water system (CWS) of a pressurized heavy-water reactor for detecting anomalies. The different methodologies used for detecting and capturing anomalies in the CWS data are matrix profile, density-based spatial clustering of applications with noise (DBSCAN), and support vector machines (SVMs). Matrix profile and DBSCAN are used to distinguish between normal data and anomalous data. This paper presents a hybrid method using DBSCAN and SVM when a portion of the data is used for DBSCAN to generate clusters. This portion of data is then used to train the SVM along with the clusters generated by DBSCAN as output. SVM is then tested on unseen data as a predictive tool, which can work in real time to categorize data points as either normal or anomalous. This paper presents results that show the high accuracies of DBSCAN and SVM in capturing anomalies within the data for a CWS for fault detection. Thus, the maintenance plan would be focused on component condition rather than a time-based schedule by switching to an automated system to identify and predict faults within a CWS.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

A Local Macroscopic Conservative (LoMaC) Low Rank Tensor Method for the Vlasov Dynamics

Abstract In this paper, we propose a novel Local Macroscopic Conservative (LoMaC) low rank tensor method for simulating the Vlasov-Poisson (VP) system. The LoMaC property refers to the exact local conservation of macroscopic mass, momentum and energy at the discrete level. This is a follow-up work of our previous development of a conservative low rank tensor approach for Vlasov dynamics ( arXiv:2201.10397 ). In that work, we applied a low rank tensor method with a conservative singular value decomposition to the high dimensional VP system to mitigate the curse of dimensionality, while maintaining the local conservation of mass and momentum. However, energy conservation is not guaranteed, which is a critical property to avoid unphysical plasma self-heating or cooling. The new ingredient in the LoMaC low rank tensor algorithm is that we simultaneously evolve the macroscopic conservation laws of mass, momentum and energy using a flux-difference form with kinetic flux vector splitting; then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables by a conservative orthogonal projection. The algorithm is extended to the high dimensional problems by hierarchical Tuck decomposition of solution tensors and a corresponding conservative projection algorithm. Extensive numerical tests on the VP system are showcased for the algorithm’s efficacy.

Guo, Wei↗
DOE OSTI2026

Testing thermal-relic dark matter with a dark-photon mediator

In light of recent DAMIC-M results, we present the status of thermal-relic dark matter χ coupled to a kinetically mixed dark photon A ′ . In the predictive “direct annihilation” regime, m A ′ > m χ , the relic abundance depends on the kinetic mixing parameter, and there is a minimum value compatible with thermal freeze-out. Using only electron- and nuclear-recoil direct-detection results, we find that, for complex scalar dark matter, the direct annihilation regime is now excluded for nearly all values of m χ ; the only exception is the resonant annihilation regime where m A ′ ≈ 2 m χ . Direct annihilation relic targets for other representative models, including Majorana and pseudo-Dirac candidates, remain viable across a wide range of model parameters but will be tested with a combination of dedicated accelerator searches in the near future. In the opposite “secluded annihilation” regime, where m χ > m A ′ , this scenario is excluded by cosmic microwave background measurements for all m χ ≲ 30 GeV . Similar conclusions in both the direct and secluded regimes hold for all anomaly-free vector mediators that couple to the first generation of electrically charged Standard Model particles.

Krnjaic, Gordan [Fermilab; Chicago U., KICP] (ORCI↗
DOE OSTI2024

Decentralized Microgrid Protection Through Relative Fault Direction Classification: Preprint

Protection in inverter-based resources (IBRs) dominated microgrids generally face significant challenges due to the low fault current and inconsistent fault behaviors from IBRs. Recently, machine learning-based approaches have attracted considerable attention to address these challenges. This paper introduces a novel decentralized protection strategy for microgrids. The proposed method decomposes the protection challenge into several distributed learning tasks, enabling individual relays to autonomously determine the direction of faults using a binary classification framework based on support vector machine (SVM) algorithms. Following the distributed fault direction estimation, classifier outcomes are shared among neighboring relays, facilitating a local decision-making process to ascertain the presence of faults within the neighborhood. Finally, a tripping signal is generated based on the classifier results of each relay to operate the circuit breaker. To test and validate this approach, a 100% renewable microgrid model is simulated in MATLAB/Simulink. In the numerical analysis, the application of SVM classifiers in our approach yields impressive results: an average relay classification accuracy of 98%, and a 96% accuracy in circuit breaker control. These findings highlight the potential of machine-learning-based approaches in enhancing the efficiency and reliability of microgrid protection systems.

decentralized algorithm↗
DOE OSTI2026

Representativity error scaling of models of the high temperature test facility

Error scaling is a critical step toward the validation of modeling capabilities for high-temperature gas-cooled reactors (HTGRs). Extensive effort is being made to bring HTGRs into the validation basis of numerous thermal-hydraulics codes. Here, this paper demonstrates how systems-level codes can be leveraged to perform error scaling analyses between an experimental facility and a plant-to-be facility. Specifically, we focus on two conduction cooldown experiments from the High Temperature Test Facility (HTTF) and the General Atomics 350 MW th modular high-temperature gas-cooled reactor (MHTGR-350). The error scaling methodology employed in this study is representativity, which in the context of this work was used to quantify how well experiments captured the physics of the plant facility by comparing sensitivity vectors between the two facilities. In addition, two different RELAP5–3D models of the HTTF were included in the comparison to determine if modeling methodologies notably impact the representativity results. The key figures of merit are the maximum block temperature and the coolant outlet temperature. The time-dependent maximum block temperature had a low representativity of below 0.1 for both models across both transients. The coolant outlet temperature had a higher representativity of around 0.6 for both models during the pressurized conduction cooldown, but it was below 0.2 for the depressurized conduction cooldown. Overall, the HTTF experiments were not representative of the transients in the MHTGR-350. However, these results can play a significant role in informing future potential experiments for HTGR systems that iterate on what the HTTF accomplished.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Simulant Development of Potential 200 West Area Waste Feeds

Preliminary planning for retrieval, qualification, and pretreatment of waste in Hanford’s 200 West Area (200W) has begun as part of the West Area Risk Management project. Experimental studies to technically mature pretreatment process operations will likely be needed because of the uniqueness of 200W waste. Pacific Northwest National Laboratory formulated five simulants to represent 200W-qualified feed based on the preliminary flowsheet provided by Washington River Protection Solutions, LLC. The simulant recipes were devised using applicable historical information as a reference point to support the use of the flowsheet waste vectors, which were combined into five distinct groups. These five groups formed the basis for the liquid composition targets that were adapted into recipes using charged-balanced salt species. The liquid phase recipes were batched in 1-L quantities and analyzed at Pacific Northwest National Laboratory. Once confirmed to be stable, the liquid solutions were tested for compatibility with candidate solid components. Specific solid components were recommended based on cross-examining the proposed solid phases in the flowsheet with relevant data from the literature. Mixtures of solid components were added to aliquots of the liquid batches and sub-sampled to measure particle size distribution. The measured distribution was compared to independently created benchmark distributions appropriate for each simulant. This process was iterated until a solid phase composition that resulted in a representative particle size distribution was found. After the final compositions were confirmed, a suite of chemical and physical characterization data was collected. This report describes the simulant basis, formulation methodology, laboratory measurements, and data collected for the recipes recommended to represent 200W waste feeds.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Anomaly Detection for Online Monitoring of Thermocouple Sensors in the Advanced Test Reactor

This study explores data-driven anomaly detection methods to analyze sensor fail- ures in the Advanced Gas Reactor (AGR) nuclear fuel irradiation experiments. Specifically, we examine failures of thermocouples (TCs), which are critical for mon- itoring and controlling in-reactor temperatures during operation. Failures were pri- marily observed during abrupt power transitions and manifested as sensor drop-outs, drifts, or unexplained behavior. We applied three time-series analysis techniques— rolling mean smoothing, matrix profile, and vector auto-regression (VAR)—to de- tect anomalies in TC data prior to failure events. The rolling mean method effec- tively highlighted deviations aligned with reported failures, while the matrix profile provided partial early warning but sometimes flagged normal fluctuations during power-down periods. VAR shows potential in capturing multivariate dependencies but requires further calibration. A rare case of TC drift was also documented, which did not result in failure, underscoring the challenge of building predictive models with sparse positive examples. Our findings demonstrate that traditional statistical tools can aid anomaly detection but have limited predictive power without richer training data. We propose future directions including synthetic data generation, real- time surrogate modeling, and multi-modal feature integration. This work provides a foundation for applying robust anomaly detection frameworks to mission-critical sensor systems in experimental settings.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗
DOE OSTI2024

The 3D Lyman- α forest power spectrum from eBOSS DR16

We measure the three-dimensional power spectrum (P3D) of the transmitted flux in the Lyman-α (Ly α) forest using the complete extended Baryon Oscillation Spectroscopic Survey data release 16 (eBOSS DR16). This sample consists of ~205 000 quasar spectra in the redshift range 2 ≤ z ≤ 4 at an effective redshift z = 2.334. We propose a pair-count spectral estimator in configuration space, weighting each pair by exp( i k ∙ r), for wave vector k and pixel pair separation r, effectively measuring the anisotropic power spectrum without the need for fast Fourier transforms. This accounts for the window matrix in a tractable way, avoiding artefacts found in Fourier-transform based power spectrum estimators due to the sparse sampling transverse to the line of sight of Ly α skewers. We extensively test our pipeline on two sets of mocks: (i) idealized Gaussian random fields with a sparse sampling of Ly α skewers, and (ii) log-normal LyaCoLoRe mocks including realistic noise levels, the eBOSS survey geometry and contaminants. On eBOSS DR16 data, the Kaiser formula with a non-linear correction term obtained from hydrodynamic simulations yields a good fit to the power spectrum data in the range $(0.02 ≤ k ≤ 0.35)$ h Mpc -1 at the 1–2σ level with a covariance matrix derived from LyaCoLoRe mocks. We demonstrate a promising new approach for full-shape cosmological analyses of Ly α forest data from cosmological surveys such as eBOSS, the currently observing Dark Energy Spectroscopic Instrument and future surveys such as the Prime Focus Spectrograph, WEAVE-QSO, and 4MOST.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Test and Validate Distributed Coaxial Cable Sensors for in situ Condition Monitoring of Coal-Fired Boiler Tubes

This project aims to test, validate, and advance the technology readiness level (from TRL5 to TRL7) of a novel low-cost distributed stainless-steel/ceramic coaxial cable sensing (SSC-CCS) technology for in situ monitoring of the boiler tube temperature in existing coal-fired power plants. The novel SSC-CCS sensing technology and associated condition-based monitoring (CBM) software to be demonstrated in this project will lead to an improved understanding of the boiler tube failure mechanisms and a prognostic system to improve the overall performance, reliability, and flexibility of the nation’s coal-fired power plant fleet. A boiler tube monitoring system with distributed coaxial cable temperature sensors and a sensor acquisition system was constructed. The high-temperature coaxial cable sensor with a length of 1.3m was made by using a quartz tube (1mm inner diameter (ID) and 6mm outer diameter (OD)) to concentrically separate a 304 stainless-steel (SS) rod (1mm OD) and SS tube (7.94mm OD and 6.16mm ID). The sensor acquisition system includes a vector network analyzer (VNA), a radio frequency (RF) power amplifier, multiple switches and a USB hub. The distributed stainless-steel quartz coaxial cable sensor (SSQ-CCS) had a linear response to temperature with a resolution uncertainty of σ = 0.77℃. To withstand the harsh conditions of 3,300 steam pressures and 800℃ high temperatures, the sensor was shielded by a protective tube made of the same material as the boiler tube. The protection tube had an OD of 1.5 inches and a thickness of 0.25 inches. In the laboratory tests, the sensor showed good sensitivity and fast response. The drift was bounded between +0.33% and -0.67% during a test at 600℃ for 350 hours, indicating good stability of the sensor. A field test was conducted where four sensors were welded on four superheat tubes (SH-Ts) at a coal-fired power station over 400 days. Conventional thermocouples were welded to the superheater tubes alongside the coaxial cable sensors for the purpose of comparison. Two sensors were capable of distributed sensing, with three multiplexed sensing sections. The other two sensors were single section. During the 400-day test period, the power plant experienced startups and shutdowns. At the steady state operations, the temperature of the boiler tube is about 600℃ (1112°F). The sensors recorded the entire coal-firing processes (start-up, steady state, and shut-down) and the glitch event. A GSM modem and a Watchdog were added to the system to ensure reliable data recording. The GSM modem sent daily messages to plant managers and Clemson team to inform the status of the sensor system. If the system was not normally working, the Watchdog would reboot the system automatically. The new coaxial cable based distributed sensing technology has been proven to be successful in both laboratory and field tests. A comprehensive four-stage multi-physics computational framework has been developed to assist the design, optimization, installation, and operation of SSQ-CCS. With the consideration of various operation conditions, we predict the distributions of flue gas temperatures within coal-fired boilers, the temperature correlation between the boiler tube and SSQ-CCS, and the safety of SSQ-CCS. A conditional-based monitoring system is implemented as well. The computational framework developed in this work can guide the future operation of coal-fired plants and other power plants for the safety prediction of boiler operations.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2024

Scalable learning of potentials to predict time-dependent Hartree–Fock dynamics

We propose a framework to learn the time-dependent Hartree–Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Although the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange–correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to 60 × 60 × 60 × 60. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

New thermal-relic targets for sub-GeV dark matter direct detection

Dark matter direct detection experiments involving electron recoils are beginning to test highly predictive, thermal-relic milestones for sub-GeV dark matter models. Due to the Lee-Weinberg bound, thermal dark matter candidates in this mass range necessarily require comparably light mediator particles to achieve a suitably large annihilation cross section. Here we present new thermal-relic milestones for sub-GeV dark matter candidates that couple to vector mediators. In these models, the mediators are massive gauge bosons of anomaly-free Abelian extensions to the Standard Model, including the dark photon, gauged L i - L j , B - L , and B - 3 L i models, where B is the baryon number, L is the lepton number, and i , j index the lepton families. Since the same interactions that govern cosmological production also govern electron scattering, the targets we present are firmly predictive and allow for these models to be robustly discovered or falsified. Furthermore, since the mediators we study exhaust the minimal anomaly-free U(1) extensions to the Standard Model, our results offer a complete list of predictive milestones for sub-GeV dark matter coupled to vector mediators.

Han, Xu [Chicago U.] (ORCID:0009000821607836)↗
DOE OSTI2025

Real-World Cyber Security Demonstration for Networked Electric Drives

In this article, we present the design and implementation of a cyber-physical security testbed for networked electric drive systems, aimed at conducting real-world security demonstrations. To our knowledge, this is one of the first security testbeds for networked electric drives, seamlessly integrating the domains of power electronics and computer science, and cybersecurity. By doing so, the testbed offers a comprehensive platform to explore and understand the intricate and often complex interactions between cyber and physical systems. The core of our testbed consists of four electric machine drives, meticulously configured to emulate small-scale but realistic information technology (IT) and operational technology (OT) networks. This setup both provides a controlled environment for simulating a wide array of cyber-attacks, and mirrors potential real-world attack scenarios with a high degree of fidelity. The testbed serves as an invaluable resource for the study of cyber-physical security, offering a practical and dynamic platform for testing and validating cybersecurity measures in the context of networked electric drive systems. As a concrete example of the testbed's capabilities, we have developed and implemented a Python-based script designed to execute step-stone attacks over a wireless local area network (WLAN). This script leverages a sequence of target IP addresses, simulating a real-world attack vector that could be exploited by adversaries. To counteract such threats, we demonstrate the efficacy of our developed cyber-attack detection algorithms, which are integral to our testbed's security framework. Furthermore, the testbed incorporates a real-time visualization system using InfluxDB and Grafana, providing a dynamic and interactive representation of networked electric drives and their associated security monitoring mechanisms. This visualization component not only enhances the testbed's usability but also offers insightful, real-time data for researchers and practitioners, thereby facilitating a deeper understanding of cyber-physical security dynamics in networked electric drive systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Quantitative x-ray scattering of free molecules

Advances in x-ray free electron lasers have made ultrafast scattering a powerful method for investigating molecular reaction kinetics and dynamics. Accurate measurement of the ground-state, static scattering signals of the reacting molecules is pivotal for these pump-probe x-ray scattering experiments as they are the cornerstone for interpreting the observed structural dynamics. Here, this article presents a data calibration procedure, designed for gas-phase x-ray scattering experiments conducted at the Linac Coherent Light Source x-ray Free-Electron Laser at SLAC National Accelerator Laboratory, that makes it possible to derive a quantitative dependence of the scattering signal on the scattering vector. A self-calibration algorithm that optimizes the detector position without reference to a computed pattern is introduced. Angle-of-scattering corrections that account for several small experimental non-idealities are reported. Their implementation leads to near quantitative agreement with theoretical scattering patterns calculated with ab-initio methods as illustrated for two x-ray photon energies and several molecular test systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Control Strategies and Validation in the Hybrid Optimization and Performance Platform (HOPP)

The Hybrid Optimization and Performance Platform (HOPP) is a tool that simulates hybrid power plants in various configurations, and also calculates the financial feasibility of these plants. This report outlines an overview of HOPP and the energy storage dispatch strategies available. It then presents three case studies which demonstrate different applications of HOPP. The first case looks at the profitability of hybrid power plants in different locations in the USA. The second case examines the availability of hybrid power plants to provide energy reliability services. The third case presents a plant that produces both hydrogen and electricity, and demonstrates a dispatch strategy that chooses the most profitable energy vector based on price signals. The next section shows the validation of HOPP on operational data, using data from both unit-scale and utility-scale power plants. This validation process demonstrated that HOPP can simulate the power output of both wind and solar PV plants at both scales with comparable fidelity to an existing commercial software tool. Finally, HOPP is applied in a field test which applies an optimal dispatch strategy to a physical battery in a unit-scale hybrid plant at NREL. HOPP's optimal dispatch strategy, applied in a real-world setting, improved this hybrid plant's ability to meet a load signal while minimizing operational costs.

14 SOLAR ENERGY↗
DOE OSTI2024

A three-point velocity estimation method for two-dimensional coarse-grained imaging data

Time delay and velocity estimation methods have been widely studied subjects in the context of signal processing, with applications in many different fields of physics. The velocity of waves or coherent fluctuation structures is commonly estimated as the distance between two measurement points divided by the time lag that maximizes the cross correlation function between the measured signals, but this is demonstrated to result in erroneous estimates for two spatial dimensions. We present an improved method to accurately estimate both components of the velocity vector, relying on three non-aligned measurement points. We introduce a stochastic process describing the fluctuations as a superposition of uncorrelated pulses moving in two dimensions. Using this model, we show that the three-point velocity estimation method, using time delays calculated through cross correlations, yields the exact velocity components when all pulses have the same velocity. The two- and three-point methods are tested on synthetic data generated from realizations of such processes for which the underlying velocity components are known. The results reveal the superiority of the three-point technique. Finally, we demonstrate the applicability of the velocity estimation on gas puff imaging data of strongly intermittent plasma fluctuations due to the radial motion of coherent, blob-like structures at the boundary of the Alcator C-Mod tokamak.

Materials Science↗
DOE OSTI2025

Machine Learned Empirical Numerical Integrator from Simulated Data

Recently, a number of state-of-the-art surrogate machine learning (ML) models have been designed for global weather and climate prediction, which have been trained using reanalysis data products. Reanalysis data products are constructed using numerical model simulations that combine numerical integration of partial differential equations and parameterization schemes. These products are typically only archived and made available using coarsened spatial and temporal resolutions. This study explores the impact of the numerical generation methods used to produce the training datasets and the temporal resolution of those datasets on machine learning surrogate models. Using the nonlinear vector autoregression (NVAR) machine as an explainable ML technique, simple dynamical systems are emulated with ML models trained on data produced by three classical numerical integration schemes. NVAR is validated as a skillful ML method, capable of producing accurate predictions and, more importantly, reconstructing both the underlying dynamics and the numerical integration scheme used to generate the training data. However, the machine fails to generalize predictions on unseen test data generated by different numerical integration schemes, despite the underlying dynamical system being the same. This result provides a word of caution for the growing field of machine learning emulation of weather and climate dynamics. Furthermore, we illustrate using NVAR that training on temporally coarsened data may increase the required complexity of ML models and potentially introduce new numerical challenges. Finally, we discover that empirical integration schemes with arbitrary time-stepping sizes can be constructed directly from the data, which implies a potential for the development of empirical numerical integration schemes.

54 ENVIRONMENTAL SCIENCES↗