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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 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A database of ultrastable MOFs reassembled from stable fragments with machine learning models

High-throughput screening of hypothetical metal-organic framework (MOF) databases can uncover new materials, but their stability in real-world applications is often unknown. We leverage community knowledge and machine learning (ML) models to identify MOFs that are thermally stable and stable upon activation. We separate these MOFs into their building blocks and recombine them to make a new hypothetical MOF database of over 50,000 structures with orders of magnitude more (1) connectivity nets and (2) inorganic building blocks than were present in prior databases. Further, this database shows a 10-fold enrichment of ultrastable MOF structures that are stable upon activation and more than 1 standard deviation more thermally stable than the average experimentally characterized MOF. For nearly 10,000 ultrastable MOFs, we compute elastic moduli to confirm that these materials have good mechanical stability, and we report methane deliverable capacities. We identify privileged metal nodes in ultrastable MOFs that optimize gas storage and mechanical stability simultaneously.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Interface and Thermophysical Properties of R 32 Refrigerant

Driven by the urgent demand for efficient cooling in microelectronics and advanced thermal management systems, difluoromethane (R32/CH 2 F 2 ) has emerged as a promising candidate owing to its favorable thermophysical properties, including high heat transfer efficiency and low viscosity. While bulk properties such as density, viscosity, and thermal conductivity have been widely studied, interfacial properties, including surface tension and interfacial thickness, remain comparatively underexplored, despite their importance in phase-transition dynamics. Here, we perform molecular dynamics (MD) simulations from 180 to 300 K using an optimized transferable force field for fluoropropenes with enhanced electrostatics to assess both bulk and interfacial behavior of R32. Simulations reproduced density within ±2.1%, viscosity within 3.05%, and thermal conductivity within 7.41% of NIST reference data. Heat capacities (C p and C v ) were predicted within 5%. For interfacial properties, surface tension trends were reproduced within 13.58% deviation, and the vapor–liquid coexistence curve closely matched reference data, yielding a critical temperature of 345.7 K (1.6% deviation) and a critical density of 0.397 g/cm 3 (6.4% deviation). Importantly, the vapor–liquid interface exhibited pronounced temperature-dependent broadening across the 180–290 K range. This behavior correlates with increasing molecular kinetic energy, reduction in intermolecular cohesive interactions, and a progressive loss of preferential dipole alignment, which collectively enhance thermal fluctuation amplitudes at elevated temperatures. These validated results provide predictive molecular-level insights, particularly for interfacial properties that remain less characterized. By reducing property prediction errors in key parameters such as critical temperature, this work provides reliable inputs for heat-exchanger and system models. Such correlations can support optimized component sizing, improved performance, and reduced refrigerant charge. Beyond R32, the methodology offers a transferable framework for blended and next-generation low-GWP refrigerants, contributing to sustainable thermal management aligned with the 2027 EU F-Gas regulation and 2030 Kigali Amendment.

Fluids↗
DOE OSTI2020

Revealing Three-Dimensional Morphology in Nanoporous Gold Using Three-Dimensional X-Ray Fresnel Coherent Diffractive Imaging Tomography

Nanoporous metals fabricated by dealloying have a unique bi-continuous, sponge-like porous structure with ultra-high surface area. The unique properties of these materials, especially nanoporous gold, have numerous potential applications in sensors and actuators and in energy-related applications such as catalytic materials, super-capacitors, and battery supports. The degree of porosity and size of the metal ligaments are critical parameters that determine many properties and thus govern the functionalities of nanoporous metals in many applications including energy storage and conversion. Additionally, we used Fresnel coherent diffractive imaging combined with tomographic reconstruction to quantify the nanoscale three-dimensional spatial distribution and homogeneity of the porosity and ligament size within a bulk sample of nanoporous gold. The average porosity and its standard deviation along the axial direction through the sample were determined, as well as the characteristic feature size and its standard deviation. The result shows that free corrosion is an effective way to create homogeneous nanoporous metals with sample sizes on the order of 1 µm.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A Novel Method for Controlling Crud Deposition in Nuclear Reactors Using Optimization Algorithms and Deep Neural Network Based Surrogate Models

This work presents the use of a high-fidelity neural network surrogate model within a Modular Optimization Framework for treatment of crud deposition as a constraint within light-water reactor core loading pattern optimization. The neural network was utilized for the treatment of crud constraints within the context of an advanced genetic algorithm applied to the core design problem. This proof-of-concept study shows that loading pattern optimization aided by a neural network surrogate model can optimize the manner in which crud distributes within a nuclear reactor without impacting operational parameters such as enrichment or cycle length. Several analysis methods were investigated. Analysis found that the surrogate model and genetic algorithm successfully minimized the deviation from a uniform crud distribution against a population of solutions from a reference optimization in which the crud distribution was not optimized. Strong evidence is presented that shows boron deposition in crud can be optimized through the loading pattern. This proof-of-concept study shows that the methods employed provide a powerful tool for mitigating the effects of crud deposition in nuclear reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Time-Resolved Evolution of the 3D Nanoporous Structure of Sintered Ag by X-Ray Nanotomography: Role of the Interface with a Copper Substrate

Here, the evolution of the nanoporous structure of cylindrical sintered silver samples during high temperature aging, ranging from 200 to 350 °C for 350 min, is studied through in situ computed X-ray tomography. Investigations are carried out for two types of specimens: pure sintered silver and specimens containing a silver-copper interface. It is shown that the overall pore evolution is driven by the evolution of very few large ones. The smaller pores, although being more numerous, do not really evolve before being absorbed by the few bigger ones. In pure silver, pore evolution is driven by diffusion (Ostwald ripening) but the presence of an interface promotes faster growth kinetics until the aging time reaches a threshold value, after which a deviation from Ostwald ripening occurs. The transition is a function of the aging temperature. This behavior is associated with the competition between elastic relaxation and surface energy minimization.

42 ENGINEERING↗
DOE OSTI2025

Magnitude and timescale of liquid water path adjustments to cloud droplet number concentration perturbations for nocturnal non-precipitating marine stratocumulus

Cloud liquid water path (L) adjusts to perturbations in cloud droplet number concentration (N) over time. We explore the magnitude and timescale of this adjustment in nocturnal non-precipitating marine stratocumuli using large eddy simulations of baseline conditions and aerosol seeding experiments for 22 meteorological conditions. The results confirm that the L adjustment (δL) slope (k) is more negative for simulation pairs with relatively low N and less negative for high N. Overall, k is unlikely to be lower than −0.4 within 24 h of seeding start, meaning the L adjustment is unlikely to fully offset the brightening due to the Twomey effect. After seeding, the δL becomes increasingly negative, which can be characterized by an exponential convergence. This evolution is governed by a short timescale around 5 h and lasts for around 8–12 h. It is driven by the feedback between entrainment, L, and boundary layer (BL) turbulence. Other processes, including radiation, surface fluxes, and subsidence, respond to the seeding weakly. This short timescale is insensitive to the amount of seeding, making the evolution of δL and some other deviations similar for different seeding amounts after appropriate scaling. The timescale of k evolution is closely related to the δL timescale and hence also short, while it could also be affected by the δN evolution. The results are most relevant to conditions where seeding is applied to a large area of marine stratocumulus in well-mixed and overcast BL where shear is not a primary source of turbulence.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Measurement of Two-Point Energy Correlators within Jets in 𝑝 + 𝑝 Collisions at $\sqrt{𝑠}$ = 200 GeV

Hard-scattered partons ejected from high-energy proton-proton collisions undergo parton shower and hadronization, resulting in collimated collections of particles that are clustered into jets. A substructure observable that highlights the transition between the perturbative and nonperturbative regimes of jet evolution in terms of the angle between two particles is the two-point energy correlator (EEC). In this Letter, the first measurement of the EEC at RHIC is presented, using data taken from 200 GeV 𝑝 + 𝑝 collisions by the STAR experiment. The EEC is measured both for all the pairs of particles in jets and separately for pairs with like and opposite electric charges. These measurements demonstrate that the transition between perturbative and nonperturbative effects occurs within an angular region that is consistent with expectations of a universal hadronization regime that scales with jet momentum for a given initiator flavor. Additionally, a deviation from Monte Carlo predictions at small angles in the charge-selected sample could result from mechanics of hadronization not fully captured by current models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Origin and effect of film sub-stoichiometry on ultraviolet, ns-laser damage resistance of hafnia single layers

Understanding the origin of laser damage-prone precursors in high index materials such as hafnia holds the key to the development of laser damage-resistant multilayer dielectric coated optics for high power and energy laser systems. In this study, we investigate the source of sub-stoichiometry, a potent laser damage precursor, in hafnia films produced by an ion beam sputtering (IBS) deposition method and the effect of such defects on the film performance upon ns ultraviolet (UV) laser (8 ns, 355 nm) exposure. Chemical analysis of data obtained via Rutherford backscattering spectroscopy (RBS) suggests that hafnia films deposited at two different planetary locations from the same deposition run exhibit anisotropic and location-dependent stoichiometries. While the oxygen-to-hafnium ratio is at the stoichiometric value of 2 for the hafnia film at the edge location, the ratio is significantly deviated and is 1.7 for that deposited at the planetary center. The sub-stoichiometric hafnia films display a much lower 1-on-1 damage onset at 1.6 ± 0.2 J/cm 2 compared to 2.3 ± 0.2 J/cm 2 in a stoichiometric film. The low damage performance films also have an over three times higher damage density at fluences above initiation. Coupled with Monte Carlo simulations, we reveal that sub-stoichiometry is primarily attributed to preferential removal of oxygen during film deposition by the bombardment of energetic reflected argon neutrals. The resulting oxygen deficiencies create the sub-bandgap states which facilitate the strong laser energy coupling and reduce the resistance to laser-induced damage in the hafnia single layer films.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Effects of magnetic fields on HPGe tracking detectors

Here, we present a study of magnetic fields effects on the position resolution and energy response of hyper-pure germanium detectors. Our results provide realistic estimates of the potential impact on the resolving power of tracking-arrays from (fringe) magnetic fields present when operating together with large spectrometers. By solving the equations of motion for the electron and holes in the presence of both electric and magnetic fields, we analyzed the drift trajectories of the charge carriers to determine the deviations in the positions at the end point of the trajectories, as well as changes in drift lengths affecting the energy resolution and peak shift due to trapping. Our results show that the major effect is in the deviation of the transverse (to the electric field direction) position and suggest that, if no corrective action is taken in the pulse-shape and tracking data analysis procedures, a field strength ≳ 0.1 T will start to impact the intrinsic position resolution of 2 mm (RMS). At fields above ~1 T, the degradation of the energy response becomes observable.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Pressure-Dependent Phase Behavior of Chemically Synthesized Ytterbium Hydride Nanoparticles and Confinement in CMK-3

In this work, we developed a chemical synthesis protocol to prepare both spherical and rod shaped YbH x nanoparticles and infiltrate a mesoporous CMK-3 structure with YbH x nanoparticles. The phase evolution of the YbH x nanoparticles was monitored as a function of the pressure in a diamond anvil cell. The cell volume of the Yb atom showed an unexpected positive deviation from the calculated equation of state (EoS) for the α-phase (space group Pnma) of YbH x . Additionally, the β-phase (space group Fm3̅m) YbH x nanoparticles appeared to become amorphous at approximately 27 GPa, although the same behavior was not observed in the Pnma (α-phase). The Pmna phase remained stable (measured up to 59.3 GPa) and showed a significantly higher than expected volume per Yb atom relative to the calculated EoS. This deviation could be attributed to the nanoscale effect on the thermodynamics of ytterbium hydride formation, which could provide a path forward to accessing higher order ytterbium hydrides (YbH x , x > 3) at pressures much lower than in the bulk metal.

diamond anvil cell↗
DOE OSTI2024

Breakthrough Conductivity Enhancement in Deep Eutectic Solvents via Grotthuss–Type Proton Transport

There is an increasing demand for the development of ion-conducting electrolytes for energy storage systems. Much attention is directed toward deep eutectic solvents as potential candidates. In the search for highly conductive systems, the possibility of designing deep eutectic solvents with Grotthuss-type proton transport is widely overlooked. Herein, ethaline, a mixture of choline chloride and ethylene glycol is used in a 1:2 molar ratio, to induce a significant conductivity increase with the addition of water and sulfuric acid (H 2 SO 4 ). The achieved breakthrough conductivity is analyzed experimentally and simulated with ab initio molecular dynamics (AIMD). At sufficient water content, an H-bonding network is formed that leads to a significant breakthrough conductivity based on H 2 SO 4 -derived proton transfer following the long-established Grotthuss proton transport mechanism. This result is substantiated by the positive deviation from the ideal KCl line in the Walden plot. Specifically, the data series positioned above the reference line indicates a Grotthuss mechanism in action. The AIMD simulations demonstrate proton transfer between water and ethylene glycol, supported by simulation frames captured at various times.

36 MATERIALS SCIENCE↗
DOE OSTI2020

An a priori evaluation of a principal component and artificial neural network based combustion model in diesel engine conditions

A principal component analysis (PCA) and artificial neural network (ANN) based chemistry tabulation approach is presented. ANNs are used to map the thermochemical state onto a low-dimensional manifold consisting of five control variables that have been identified using PCA. Three canonical configurations are considered to train the PCA-ANN model: a series of homogeneous reactors, a nonpremixed flamelet, and a two-dimensional lifted flame. The performance of the model in predicting the thermochemical manifold of a spatially-developing turbulent jet flame in diesel engine thermochemical conditions is a priori evaluated using direct numerical simulation (DNS) data. The PCA-ANN approach is compared with a conventional tabulation approach (tabulation using ad hoc defined control variables and linear interpolation). The PCA-ANN model provides higher accuracy and requires several orders of magnitude less memory. Here, these observations indicate that the PCA-ANN model is superior for chemistry tabulation, especially for modelling complex chemistries that present multiple combustion modes as observed in diesel combustion. The performance of the PCA-ANN model is then compared to the optimal estimator, i.e. the conditional mean from the DNS. The results indicate that the PCA-ANN model gives high prediction accuracy, comparable to the optimal estimator, especially for major species and the thermophysical properties. Higher errors are observed for the minor species and reaction rate predictions when compared to the optimal estimator. It is shown that the prediction of minor species and reaction rates can be improved by using training data that exhibits a variation of parameters as observed in the turbulent flame. The output of the ANN is analysed to assess mass conservation. It is observed that the ANN incurs a mean absolute error of 0.05% in mass conservation. Furthermore, it is demonstrated that this error can be reduced by modifying the cost function of the ANN to penalise for deviation from mass conservation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2021

Optimized allocation method of the VSC-MTDC system for frequency regulation reserves considering the cost

In recent years, the interconnection of asynchronous power grids through the VSC-MTDC system has been proposed and extensively studied in light of the potential benefits of economical bulk power exchanges and frequency regulation reserves sharing. This paper proposed an optimized allocation method for sharing frequency regulation reserves among the interconnected power systems and the corresponding frequency regulation control of the VSC-MTDC system under emergency frequency deviation events. Firstly, the frequency regulation reserve classification is proposed. In the classification, the available frequency response capacity reserves of each interconnection are divided into commercial reserves and regular reserves. While the commercial reserves are procured through long-term contracts, the regular reserves are purchased based on market prices of frequency regulation services. Secondly, based on the proposed frequency regulation reserve classification, a novel frequency regulation control is then introduced for the VSC-MTDC system. This control method could minimize the costs of the disturbed power grid for the needed frequency response supports from the other power grids. Simulation verifications are performed on a modified IEEE 39 bus system and a highly reduced power system model representing the North American grids. The simulation verification indicates that the developed frequency regulation control significantly reduced ancillary service costs of the disturbed power grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Biobased Flame Retardants Towards Sustainable Building Materials with Low Embodied Carbon

Incorporation of fire retardants in different types of products is one of the essential steps in the material production process to minimize fire risk and meet fire safety requirements. A variety of commonly used flame retardants based on halogen, mineral, and other compounds has gained popularity due to their efficient flame-retardant behaviors. However, especially in the case of halides, there are numerous toxicity related issues and environmental pollution effects that have urged the building sector to deviate from their use and focus on the development of non-toxic alternatives. Therefore, to enhance the safety of flame retardants, the synthesis of flame retardants from waste feedstocks using phosphorous chemistry with a dual flame-retardant mechanism has been established. A range of waste feedstocks that include cardanol, vanillin, and gallic acids has been converted into a series of flame retardants using a one-step approach by incorporating phosphorous moieties into their structures. The established pathways allow to develop a range of flame-retardant materials by converting waste feedstocks into phosphorous-based materials with inherent flame retardancy. The introduction of abundant aromatic structures from biobased feedstocks enables high charring capabilities in materials in which these biobased flame retardants have been incorporated, increasing their char yields which significantly enhances the flame suppressing properties of the designed materials. Studies show that inclusion of phosphoric moieties into structures allows the displacement of flame enhancing radicals, by releasing non-flammable and non-toxic gases, therefore inhibiting the spread of fire in the gas phase. The resulting biobased flame retardants have been incorporated in wood substrates, foam insulation, and hemp fibers where the results show that only 1-5% of loading of biobased flame retardant suppressed the flame completely. This study represents a novel approach for the development of flame retardants with high performance while utilizing waste feedstocks as a source for their design.

Demchuk, Zoriana [ORNL] (ORCID:0000000326292235)↗
DOE OSTI2021

Status of the Fermilab Muon g - 2 Experiment

The muon anomalous magnetic moment, aµ = ( g - 2 )/2, is a low-energy observable which can be both measured and computed with very high precision, making it an excellent test of the Standard Model (SM) and a sensitive probe of new physics. Recent efforts improved the precision of both the theoretical prediction and the experimental measurement. On the theory side, the Muon g - 2 Theory Initiative, an international team of more than 130 physicists, reached in 2020 a consensus on the SM prediction for aµ. On the experimental side, the E989 Muon g - 2 Collaboration at Fermilab (FNAL) published in April 2021 a new measurement of aµ from the Run-1 dataset (2018) with 0.46 ppm precision, corroborating the previous Brookhaven National Laboratory (BNL) measurement and increasing the discrepancy with the SM value to 4.2 standard deviations. In this paper, I will discuss the experimental setup and report on the current status of the experiment.

Girotti, Paolo↗
DOE OSTI2026

Terrestrial laser scanning data (Levels 0 and 1) from Urban Biogeochemistry Pilot Project sites, Knoxville, Tennessee, Jul 2024 - Jul 2025

This data package contains data from terrestrial laser scanning (TLS) at five urban park sites in Knoxville, Tennessee, USA. All parks include open-grown and/or closed-canopy trees and mixed nearby land use. These study sites were established as part of the Urban Biogeochemistry Pilot Project, which has an overall goal of better understanding how hydrobiogeochemical cycling is altered within the human environment. These five sites represent a gradient of urbanization, and were instrumented to understand hydrological and biogeochemical cycling (e.g., soil moisture, soil physical properties and biogeochemistry, tree transpiration, species type). The TLS data archived here were collected to provide detailed, three-dimensional information about forest structure. Specifically, data were collected to allow tree- and stand-level characterization of woody structure and leaf area. TLS scans were placed to capture the area around trees with sap flow sensors, and as much of a 50 m radius area around the meteorological station as possible given site property limits. Derived products will allow upscaling of water content and transpiration data. This data package contains the following data: - High-level files document further details of the campaign and data package: 1_CampaignSummary.csv provides details about the campaign and study site, 2_ScanAreasDetail.csv provides details about each separate scan area (groups of scans post-processed into a single point cloud), 3_TerrestrialLidarSensor.csv provides further technical details about the Riegl VZ-400i TLS sensor, TLS_CSV_dd.csv is a CSV Data Dictionary providing information about the fields in CSV files following the ESS-DIVE CSV File Formatting Guidelines Reporting Format, TLS_flmd.csv is a File Level Metadata file providing information about each file in the data package following the ESS-DIVE File Level Metadata Reporting Format, and README.txt is a text file describing the overall project and file structure. - Level 0 data are the raw data (.PROJ folders) as recorded by the Riegl VZ-400i TLS instrument before scan co-registration and post-processing with the Riegl's proprietary RiSCAN PRO software, which requires a license. - Level 1 data contain post-processed, co-registered data from each scan area. The "PointClouds" folder for each scan area contains a .las file with 1 cm resolution point cloud data exported from RiSCAN PRO. These are the main files likely to be of interest to most users and can be further processed with any software capable of manipulating .las files (e.g. Python, R CloudCompare). The "Project Information" folder contains log files from post-processing in RiSCAN PRO that may be of interest to users who want to see detailed records of post-processing, including all PDF reports generated by RiSCAN PRO. The "ScanPositions" folder contains information about the final position of all TLS scans, after post-processing, in multiple formats. The file ScanPositions_*.csv provides final geo-referenced scan positions, and the file SOP_backup_*.csv can be used in RiSCAN PRO to restore the co-registered scan positions if users wish to re-process raw data (Level 0 .PROJ folders) with RiSCAN PRO software (e.g., subsample to a different resolution, exclude a certain scan position, or apply different filters on reflectance or deviation values) without redoing time-consuming co-registration steps.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Here, our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto-Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.

Chaotic dynamical systems↗