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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 OSTI2020

Platinum and Palladium Monolayer Electrocatalysts for Formic Acid Oxidation

The direct formic acid fuel cell holds great promise as a next generation portable power source. In this paper we report an experimental study on Pt and Pd monolayer (Pt* and Pd*) atop the close-packed facet of transition metal substrates (denoted Pt*/M or Pd*/M, where M = Pt, Pd, Ir, Au, Rh and Ru) model catalysts for formic acid oxidation (FAO) and demonstrate a promotional effect on Pt*/Au(111) and Pd*/Pt(111) surfaces. Contrary to findings on monometallic surfaces, in situ infrared reflection adsorption spectroscopy collected during formic acid oxidation at potentials anodic of 375 mV reveal that the poisoning reaction intermediate CO is not formed on the monolayer surfaces, suggesting a promotion of the direct mechanisms of FAO at the expense of the indirect mechanism through CO. Our density functional theory calculations on model surfaces with 1:1 stoichiometry for overlayer to support metal atoms for the thermochemistry of the elementary steps defined by adsorbed CO, OH, COOH, and HCOO on the (111) facet of Pt, PtML/Au, Pd, and PdML/Pt largely attribute the promotional effect observed for the monolayer catalysts to easier removal of CO brought about by easier activation of water, relative to the monometallic catalysts. This synergy between experiments and theory brings us closer to a fundamental understanding of FAO electrocatalysts under reaction conditions, paving the way to achieving more active electrocatalysts possibly with less Pt or Pd; a pre-requisite for the mass commercialization of this technology.

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

The Application of Differential Scanning Calorimetry to Investigate Precipitation Behavior in Nickel-Base Superalloys Under Continuous Cooling and Heating Conditions

In this study, a suite of experimental tools and fast-acting, numerical-simulation techniques was used to quantify the precipitation behavior of three nickel-base superalloys: IN-100, LSHR, and 718. Experimental methods comprised differential scanning calorimetry (DSC) to establish the specific heat as a function of temperature and selected direct-resistance heating trials (using a Gleeble ® machine) to obtain samples for microstructural analysis. For the DSC experiments, each alloy was cooled at a prescribed constant rate (between 5 and 20 K/min) after an initial soak/equilibration in the high-temperature, single-phase (supersolvus) temperature regime. On-heating DSC trials beginning at ambient temperature were also performed on alloy 718 in three different starting conditions: super- δ -solvus solution treated and water quenched (denoted as ST), solution treated and aged (STA), and solution treated and overaged (STOA). DSC results, revealing the thermal signatures associated with the kinetics of precipitation of γ ' (IN-100, LSHR) or γ ' and γ " (718), were interpreted using a previously-developed fast-acting routine that treats concurrent nucleation, growth, coarsening, and dissolution. For these simulations, special attention was paid to various thermo-kinetic input parameters including equilibrium solvus-approach curves, bulk free energies of transformation, matrix-precipitate interface energies, and effective diffusivities. For the γ - γ ' superalloys (IN-100 and LSHR), estimates of precipitate volume fraction as a function of temperature from the specific-heat data revealed semi-quantitative agreement with simulation predictions. For the γ - γ '- γ " superalloy (718), simulation predictions of precipitate volume fractions were converted to specific heat as a function of temperature and showed semi-quantitative agreement with the direct measurements.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Insight into the Relationship Between Viscosity and Structure of CaO-SiO{sub 2}-MgO-Al{sub 2}O{sub 3} Molten Slags

This article elucidates the quantitative relationship between viscosity and structure in a basic slag system of CaO-SiO{sub 2}-MgO-Al{sub 2}O{sub 3} and focuses on the role of Al{sub 2}O{sub 3}. Slag viscosity was measured by the rotating cylinder method, and structural information was obtained using Fourier transformation infrared, Raman and magic angular spinning nuclear magnetic resonance (MAS-NMR) techniques. The results show that, as the Al{sub 2}O{sub 3} content increased, slag viscosity increased initially and decreased afterwards, directly indicating that Al{sub 2}O{sub 3} had an amphoteric effect on slag viscosity. The Raman spectra verified that with increasing Al{sub 2}O{sub 3} content, the concentrations of Q{sup 0}(Si) and Q{sup 2}(Si) decreased first and then increased, while that of Q{sup 1}(Si) kept increasing and that of Q{sup 3}(Si) increased first and then decreased. The {sup 27}Al MAS-NMR spectra proved that the mole ratios of AlO{sub 5} and AlO{sub 6} to AlO{sub 4} kept increasing with the increase of Al{sub 2}O{sub 3} content, and, overall, Al{sub 2}O{sub 3} changed from a network former to a network modifier. The relationship between the viscosity and structure of the molten slags was further analyzed quantitatively based on the modified (NBO/T), denoted as (NBO/T)′, and we found a fine linear correlation between the logarithm of viscosity and (NBO/T)′. Moreover, the variations of thermodynamic properties of this system also indirectly supported the present experimental results.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Ordering effects on deformation substructures and strain hardening behavior of a CrCoNi based medium entropy alloy

Here, a CrCoNi based medium entropy alloy with small additions of Ti, Al and Nb (denoted as (CrCoNi) 93 Al 4 Ti 2 Nb) in the as-quenched condition, exhibits tensile properties comparable to those of the equiatomic CrCoNi alloy at room temperature. Dark field transmission electron microscopy (TEM), atomic resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) together with atom probe tomography (APT) show that spatially-localized long range ordering (LRO) L1 2 domains exist in this alloy. The evolution of deformation substructure with plastic deformation in this alloy was characterized using electron backscatter diffraction (EBSD), electron channeling contrast imaging (ECCI) and STEM based techniques including the recently developed weak beam dark field STEM imaging. Plastic deformation occurs by the slip of a/2<110>dislocations, which are narrowly dissociated into Shockley partial dislocations on {111} slip planes. Their dissociation distances in the (CrCoNi) 93 Al 4 Ti 2 Nb alloy are much smaller than the widths of the corresponding partials in the equiatomic CrCoNi alloy due to one or more of the minor alloying elements (Al, Ti, Nb). Dislocation slip in this alloy has a pronounced planar character. The leading dislocations in slip bands glide as pairs due to the existence of LRO domains. Multipoles were formed through the slip of dislocations with opposite signs on adjacent {111} slip planes. Those multipoles serve as building blocks for the formation of subgrain structures consisting of fine slip bands. The distances between slip bands were continuously refined during plastic deformation and dynamic refinement of slip bands plays a crucial role in strain hardening. The effects of LRO domains on planar dislocation slip, the deactivation of deformation twinning and strain hardening of this alloy are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Realizing efficient operations of Ni-cermet-based fuel cells on hydrocarbons via an in situ self-assembled metal/oxide nano-heterostructured catalyst

Operating Ni-cermet-based fuel cells on hydrocarbons is charming by largely hindered by poor coking tolerance and severe deterioration. Here, in this study, we report an effective metal/oxide nano-heterostructured catalyst with a nominal composition of Pr 0.95 Ru 0.05 O 2-δ (PRO), which is in situ self-assembled to a Pr 0.95 Ru 0.05-x O 2-δ oxide frame coated with Ru metallic nanoparticles (denoted as Ru/PRO) under the operation condition. When applied to the Ni-cermet (Ni-YSZ) anodes, the cells achieve decent peak power densities of 1.784 and 1.870 W cm -2 on CH 4 and C 3 H 8 with only 3% H 2 O at 750 °C, respectively. Moreover, the cells with Ru/PRO-coated anode demonstrate excellent durability when operated on CH 4 for ~ 220 h and C 3 H 8 for ~115 h. It is demonstrated that the Ru/PRO generates hydroxyl species that react with carbon species, followed by the formation of COH intermediates on Ni anode surfaces for removing the coking, as confirmed by experiments and computations.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2025

Heterostructured nano-catalysts with efficient metal-oxide interfaces unlock high-performance direct methanol protonic ceramic fuel cells

Direct methanol protonic ceramic fuel cells (PCFCs) are attractive due to their low cost, convenient storage, and high volumetric energy density, as well as their suitability for transportation. However, the poor coking tolerance of conventional nickel-based anodes leads to their susceptibility to severe carbon deposition and significant deactivation after long-term exposure to hydrocarbons. Herein, we report a nano-catalyst of Ce 0.6 Ni 0.2 Cu 0.2 O 2 with a heterogeneous structure that is spontaneously reduced into a Ce 0.6 Ni 0.2-x Cu 0.2-x O 2-δ (CeNCO) oxide framework interfaced with a nano NiCu alloy (denoted as NC/CeNCO) under operating conditions, as confirmed by analyses of X-ray diffraction, X-ray photoelectron spectroscopy, scanning electron microscopy, and transmission electron microscopy. A Ni-BaCe 0.7 Y 0.06 Yb 0.06 Zr 0.06 Hf 0.06 Gd 0.06 O 3-δ anode-supported PCFC employing the NC/CeNCO metal-oxide catalyst achieved a peak power density of 1.11 W cm −2 and operational stability of about 100 h at 700 °C when fueled by 35 % CH 3 OH-15 % H 2 O-50 % N 2 . In conclusion, the enhanced performance and coking resistance are attributed to the efficient interfaces of Ni, Cu, and ceria-based oxide in NC/CeNCO for CH 3 OH reforming, as confirmed by analyses of electrochemical performance and Raman spectroscopy with density functional theory calculations, revealing that these interfaces can enhance CH 3 OH activation and promote efficient OH-mediated carbon removal via COH intermediates.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2023

Heterogeneity or illusion? Track the carbon Kuznets curve of global residential building operations

Residential buildings, the “last mile” sector in the global decarbonization, have become the most significant uncertain factor hindering carbon neutrality with increasing household energy demand. To track the operational carbon in buildings, this study investigates the carbon Kuznets curve (CKC) and the corresponding decoupling status of residential building operations at four emission scales by using the data of 30 countries from 2000 to 2019. The results show that (1) the CKC model can fit more than half of the samples. Most curves have an inverted U-shape, with 76% of emission per household and 82% of total emissions. (2) In the presence of the CKC, over four-fifths of global residential buildings peak regardless of any emission scale. The analysis denotes that the carbon emissions of developed countries reach their peaks earlier. In the total emissions, the samples’ peaking proportion is 20% and 25% with income per capita < 20,000 United States dollars (USD) and 20,000–40,000 USD, respectively. (3) The Tapio decoupling analysis and the threshold regression effectively verify the robustness and the heterogeneity of CKCs, respectively. Strong decoupling effects of CKCs in most countries are demonstrated at the scales of emission per floor space and the total emissions, and the heterogeneity proves the classic inverted U-shaped relationship between economy and emissions doesn’t exist in all emitters. Overall, this study tracks the historical carbon emission trajectories of residential building operations at a global scale, providing reference for different economies to simulate the dynamic of building carbon emissions along with the economic booming.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Theoretical assessments of CO 2 activation and hydrogenation pathways on transition-metal surfaces

Carbon dioxide (CO 2 ) hydrogenation on transition-metal active sites offers a promising carbon utilization route toward mitigating greenhouse gas emissions. C 1 products are often formed in parallel during CO 2 hydrogenation, prompting investigations into the intrinsic properties of transition metals that drive activity and product selectivity. Here, in this work, close-packed surfaces of a selection of transition-metal catalysts (Ni, Co, Rh, Ru, Pd, and Pt) were studied with density functional theory (DFT) calculations to understand their fundamental reactivities for CO 2 transformation reactions. Results indicate that CO 2 conversion proceeds through CO* formation and hydrogenation to form C 1 products (* denotes an adsorbed species). Ni, Co, Rh, and Ru favor CO/CH 4 formation, while Pd and Pt favor CO/CH 3 OH formation. The ability of a metal to dissociate C-O bonds drives selectivity between CH 4 and CH 3 OH, while competition between CO* desorption and surface hydrogenation describes CO selectivities. The C-O bond dissociation steps often impose the highest barrier along CH 4 formation reaction profiles, suggesting their kinetic relevance for CH 4 formation rates. The provided DFT-derived data sets detail a comprehensive reaction network of elementary steps relevant to C 1 chemistries, ultimately offering a benchmark for insights into design strategies for materials that exploit transition-metal active sites in carbon capture or utilization processes.

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

Enhanced relaxed physical factorization preconditioner for coupled poromechanics

The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the efficient and robust solution to the block linear systems arising from the three-field displacement-velocity-pressure formulation of coupled poromechanics. For its application, however, it is necessary to invert blocks with the algebraic form C^ = (C + βFF T ), where C is a symmetric positive definite matrix, FF T a rank-deficient term, and β a real non-negative coefficient. The inversion of C^, performed in an inexact way, can become unstable for large values of β, as it usually occurs at some stages of a full poromechanical simulation. In this work, we propose a family of algebraic techniques to stabilize the inexact solve with C^. This strategy can prove useful in other problems as well where such an issue might arise, such as augmented Lagrangian preconditioning techniques for Navier-Stokes or incompressible elasticity. First, we introduce an iterative scheme obtained by a natural splitting of matrix C^. Second, we develop a technique based on the use of a proper projection operator annihilating the near-kernel modes of C^. Both approaches give rise to a novel class of preconditioners denoted as Enhanced RPF (ERPF). Furthermore, effectiveness and robustness of the proposed algorithms are demonstrated in both theoretical benchmarks and real-world large-size applications, outperforming the native RPF preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

ZIF-8 derived carbon materials with multifunctional selective adsorption abilities

We report a family of carbon materials (denoted SFZ8C) prepared from templated carbonization of zeolitic imidazolate framework-8 (ZIF-8) in NaCl-ZnCl 2 eutectic salt. The hard-templating effect of the salt is utilized to sustain the framework and maximize the porosity during carbonization. In addition to rich surface nitrogen and oxygen species, SFZ8Cs have large specific surface area. These combined features give rise to excellent adsorption properties for light hydrocarbon gases. SFZ8Cs have both C 2 H 2 /CO 2 selective and C 3 /C 2 selective adsorption, as well as the ability to selectively remove impurities from methane. Particularly noteworthy is the excellent C 3 /C 2 selective adsorption performance by SFZ8C-900. Its propane/ethane selectivity (7.68) is on par with the best value (7.72) reported so far, yet SFZ8C-900 excels in propane uptake capacity. Here, the multifunctional properties together with the ease for the mass production make SFZ8Cs promising for a number of important applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Synthesis and characterization of UiO-66-NH 2 incorporated graphene aerogel composites and their utilization for absorption of organic liquids

This work details the synthesis, materials characterization and absorption capacity of graphene aerogel (GA) loaded with UiO-66-NH 2 metal organic framework (MOF). Throughout the study, a series of density-tunable MOF/GA composites were synthesized by adjusting the MOF/graphene oxide (GO) mass ratio of the precursors before hydrothermal reduction and subsequent critical point drying to achieve MOF-x%/GA composites, with x, ranging from 0 to 100, denoting the weight percent ratio of MOF to GO in the starting solution. Scanning electron microscopy (SEM) images and Barrett-Joyner-Halenda (BJH) pore size calculations supported that MOF loading enlarged the macroporous (>50 nm) structure of the GA framework but had no influence on the mesoporous (2–50 nm) structure of GA. The degree of MOF loading first decreased and then increased the density of resulting composites, exhibiting a minimum for the 10–30% samples. Such behavior with respect to MOF loading has not been reported previously. MOF-x%/GA samples were further investigated for absorption capacity using various organic liquids. MOF-30%/GA proved to be the best absorbent sample for all solvents tested, achieving the highest capacity for chloroform at 147.0 ± 10.0 mg/mg. The behavior is attributed to the structural changes induced by the MOF incorporation as well as the interactions between the organic molecules and the MOF.

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

Encapsulation of highly viscous CO 2 capture solvents for enhanced capture kinetics: Modeling investigation of mass transfer mechanisms

The encapsulation of highly viscous liquid-like Nanoparticle Organic Hybrid Materials (NOHMs) inside a gas permeable polymer to form SIPs (Solvent Impregnated Polymers) significantly enhanced the CO 2 capture kinetics of NOHMs, leading to a remarkable 50-fold increase in CO 2 flux compared to the neat NOHMs. To understand the mechanism for enhanced CO 2 mass transfer within these hybrid materials, kinetic modeling of CO 2 uptake into SIPs containing polyethylenimine functionalized NOHMs, denoted NPEI-SIP, was conducted. CO 2 mass transfer into NPEI-SIP films was found to conform, both qualitatively and quantitatively, with a diffusion-controlled moving front model. The diffusion-controlled model was also used to simulate CO 2 uptake within a fixed bed containing polydisperse NPEI-SIP particles, and this model accurately predicted experimentally measured breakthrough curves at 25 °C and 50 °C. The 50-fold increase in gas flux was shown to be a consequence of the very large CO 2 permeability within the polymer–solvent composite. Furthermore, the increase in gas flux is also dependent on the diffusion–reaction regime in which the chemical solvent operates, and the largest improvement will occur when immobilizing solvents, such as NOHMs, which operate in the instantaneous-reaction regime. The CO 2 capacity (~3 mol CO 2 /kg) and saturation time (~5 min) of 430 μm SIP particles were comparable to popular CO 2 chemisorption materials such as amine grafted silicates, in spite of the slow kinetics of NOHM-I-PEI in liquid form (CO 2 saturation time ~24 h for a 1 mm thin film).

36 MATERIALS SCIENCE↗
DOE OSTI2026

Interface-engineered (CrMnTiZnCo) 3 O 4 @polypyrrole nano-hybrids for superior lithium storage

High-entropy oxides (HEO) have emerged as promising anode materials for lithium-ion batteries (LIBs) due to their high theoretical specific capacity. However, their practical application is hindered by several challenges, including significant volume expansion, electrode pulverization, and substantial irreversible capacity loss during initial cycles. To address these limitations, this study designed a novel core-shell composite material, denoted as HEO@PPy, which consists of a (CrMnTiZnCo) 3 O 4 -based HEO core and a polypyrrole (PPy) shell. This composite demonstrates remarkable electrochemical performance: it maintains a specific capacity of 1090.1 mAh/g after 100 cycles at 100 mA/g and retains 521.8 mAh/g after 1000 cycles at 1 A/g, highlighting its superior cycling stability. Furthermore, it exhibits excellent rate capability, delivering a capacity of 372.1 mAh/g even at a high current density of 5 A/g. These findings confirm that the strategic compositional and structural design of HEOs, combined with hybridization with conductive polymers like PPy, provides a viable pathway for developing advanced anode materials for next-generation, high-performance lithium-ion batteries.

25 ENERGY STORAGE↗
DOE OSTI2022

Development, characterization, and modeling of a high-performance Ru/B2CA catalyst for ammonia synthesis

This paper documents the development and performance of a nano-phase Ru catalyst on a (BaO) x (CaO) y (Al 2 O 3 ) support. Extensive screening of the support’s ternary composition shows the best stoichiometry is (BaO) 2 (CaO)(Al 2 O 3 ), denoted B2CA. The paper first describes catalyst preparation and characterization. The paper reports a detailed 12-step reaction mechanism that represents ammonia synthesis over wide ranges of temperature, pressure, space velocity, and feed composition. Additionally, the mechanism is developed and validated using results of packed-bed experiments. The elementary reaction pathways consider surface adsorbates, including catalyst-poisoning behaviors. The rate expressions include important coverage-dependent activation barriers. Machine learning models assist interpretation of the catalyst-support interactions. The detailed chemistry is much more predictive than is possible with global representations (N 2 + 3H 2 ⇌ 2NH 3 ). The validated models can be applied to assist optimizing reactor design and operating conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Discovery, characterization, and metabolic engineering of Rieske non-heme iron monooxygenases for guaiacol O-demethylation

Aryl-O-demethylation is a common rate-limiting step in the catabolism of lignin-related compounds, including guaiacol. In this work, we used randomly barcoded transposon insertion sequencing (RB-TnSeq) in the bacterium Novosphingobium aromaticivorans to identify a Rieske-type guaiacol O-demethylase, GdmA. Similarity searches identified GdmA homologs in other bacteria, along with candidate reductase partners, denoted GdmB. GdmAB combinations were biochemically characterized for activity with several lignin-related substrates. Structural and sequence comparisons of vanillate- and guaiacol-specific O-demethylase active sites revealed conserved hallmarks of substrate specificity. GdmAB combinations were also evaluated in Pseudomonas putida KT2440, which does not natively utilize guaiacol. GdmAB from Cupriavidus necator N-1 demonstrated the highest rate of guaiacol turnover in vitro and in engineered P. putida strains and notably higher catalytic efficiency than a cytochrome P450 system (GcoAB) and the vanillate Rieske-type O-demethylase from P. putida (VanAB). The GdmAB O-demethylases described here expand the suite of options for microbial conversion of a model lignin-derived substrate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

The activity of antimicrobial peptoids against multidrug-resistant ocular pathogens

Background: Ocular infections caused by antibiotic-resistant pathogens can result in partial or complete vision loss. The development of pan-resistant microbial strains poses a significant challenge for clinicians as there are limited antimicrobial options available. Synthetic peptoids, which are sequence-specific oligo-N-substituted glycines, offer potential as alternative antimicrobial agents to target multidrug-resistant bacteria. Methods: The antimicrobial activity of synthesised peptoids against multidrug-resistant (MDR) ocular pathogens was evaluated using the microbroth dilution method. Hemolytic propensity was assessed using mammalian erythrocytes. Peptoids were also incubated with proteolytic enzymes, after which their minimum inhibitory activity against bacteria was re-evaluated. Results: Several alkylated and brominated peptoids showed good inhibitory activity against multidrug-resistant Pseudomonas aeruginosa strains at concentrations of ≤15 μg mL -1 (≤12 µM). Similarly, most brominated compounds inhibited the growth of methicillin-resistant Staphylococcus aureus at 1.9 to 15 μg mL -1 (12 µM). The N-terminally alkylated peptoids caused less toxicity to erythrocytes. The peptoid denoted as TM5 had a high therapeutic index, being non-toxic to either erythrocytes or corneal epithelial cells, even at 15 to 22 times its MIC. Additionally, the peptoids were resistant to protease activity. Conclusions: Peptoids studied here demonstrated potent activity against various multidrug-resistant ocular pathogens. Their properties make them promising candidates for controlling vision-related morbidity associated with eye infections by antibiotic-resistant strains.

60 APPLIED LIFE 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↗