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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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179 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Glancing Angle Deposition in Gas Sensing: Bridging Morphological Innovations and Sensor Performances

Glancing Angle Deposition (GLAD) has emerged as a versatile and powerful nanofabrication technique for developing next-generation gas sensors by enabling precise control over nanostructure geometry, porosity, and material composition. Through dynamic substrate tilting and rotation, GLAD facilitates the fabrication of highly porous, anisotropic nanostructures, such as aligned, tilted, zigzag, helical, and multilayered nanorods, with tunable surface area and diffusion pathways optimized for gas detection. This review provides a comprehensive synthesis of recent advances in GLAD-based gas sensor design, focusing on how structural engineering and material integration converge to enhance sensor performance. Key materials strategies include the construction of heterojunctions and core–shell architectures, controlled doping, and nanoparticle decoration using noble metals or metal oxides to amplify charge transfer, catalytic activity, and redox responsiveness. GLAD-fabricated nanostructures have been effectively deployed across multiple gas sensing modalities, including resistive, capacitive, piezoelectric, and optical platforms, where their high aspect ratios, tailored porosity, and defect-rich surfaces facilitate enhanced gas adsorption kinetics and efficient signal transduction. These devices exhibit high sensitivity and selectivity toward a range of analytes, including NO2, CO, H2S, and volatile organic compounds (VOCs), with detection limits often reaching the parts-per-billion level. Emerging innovations, such as photo-assisted sensing and integration with artificial intelligence for data analysis and pattern recognition, further extend the capabilities of GLAD-based systems for multifunctional, real-time, and adaptive sensing. Finally, current challenges and future research directions are discussed, emphasizing the promise of GLAD as a scalable platform for next-generation gas sensing technologies.

Chemistry↗
NASA NTRS1999

On Multi-Dimensional Unstructured Mesh Adaption

Anisotropic unstructured mesh adaption is developed for a truly multi-dimensional upwind fluctuation splitting scheme, as applied to scalar advection-diffusion. The adaption is performed locally using edge swapping, point insertion/deletion, and nodal displacements. Comparisons are made versus the current state of the art for aggressive anisotropic unstructured adaption, which is based on a posteriori error estimates. Demonstration of both schemes to model problems, with features representative of compressible gas dynamics, show the present method to be superior to the a posteriori adaption for linear advection. The performance of the two methods is more similar when applied to nonlinear advection, with a difference in the treatment of shocks. The a posteriori adaption can excessively cluster points to a shock, while the present multi-dimensional scheme tends to merely align with a shock, using fewer nodes. As a consequence of this alignment tendency, an implementation of eigenvalue limiting for the suppression of expansion shocks is developed for the multi-dimensional distribution scheme. The differences in the treatment of shocks by the adaption schemes, along with the inherently low levels of artificial dissipation in the fluctuation splitting solver, suggest the present method is a strong candidate for applications to compressible gas dynamics.

Wood, William A.↗
DOE OSTI2025

Towards universal unfolding of detector effects in high-energy physics using denoising diffusion probabilistic models

Correcting for detector effects in experimental data, particularly through unfolding, is critical for enabling precision measurements in high-energy physics. However, traditional unfolding methods face challenges in scalability, flexibility, and dependence on simulations. We introduce a novel approach to multidimensional object-wise unfolding using conditional Denoising Diffusion Probabilistic Models (cDDPM). Our method utilizes the cDDPM for a non-iterative, flexible posterior sampling approach, incorporating distribution moments as conditioning information, which exhibits a strong inductive bias that allows it to generalize to unseen physics processes without explicitly assuming the underlying distribution. Our results highlight the potential of this method as a step towards a "universal" unfolding tool that reduces dependence on truth-level assumptions, while enabling the unfolding of a wide range of measured distributions with improved adaptability and accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2008

Spiking Neurons for Analysis of Patterns

Artificial neural networks comprising spiking neurons of a novel type have been conceived as improved pattern-analysis and pattern-recognition computational systems. These neurons are represented by a mathematical model denoted the state-variable model (SVM), which among other things, exploits a computational parallelism inherent in spiking-neuron geometry. Networks of SVM neurons offer advantages of speed and computational efficiency, relative to traditional artificial neural networks. The SVM also overcomes some of the limitations of prior spiking-neuron models. There are numerous potential pattern-recognition, tracking, and data-reduction (data preprocessing) applications for these SVM neural networks on Earth and in exploration of remote planets. Spiking neurons imitate biological neurons more closely than do the neurons of traditional artificial neural networks. A spiking neuron includes a central cell body (soma) surrounded by a tree-like interconnection network (dendrites). Spiking neurons are so named because they generate trains of output pulses (spikes) in response to inputs received from sensors or from other neurons. They gain their speed advantage over traditional neural networks by using the timing of individual spikes for computation, whereas traditional artificial neurons use averages of activity levels over time. Moreover, spiking neurons use the delays inherent in dendritic processing in order to efficiently encode the information content of incoming signals. Because traditional artificial neurons fail to capture this encoding, they have less processing capability, and so it is necessary to use more gates when implementing traditional artificial neurons in electronic circuitry. Such higher-order functions as dynamic tasking are effected by use of pools (collections) of spiking neurons interconnected by spike-transmitting fibers. The SVM includes adaptive thresholds and submodels of transport of ions (in imitation of such transport in biological neurons). These features enable the neurons to adapt their responses to high-rate inputs from sensors, and to adapt their firing thresholds to mitigate noise or effects of potential sensor failure. The mathematical derivation of the SVM starts from a prior model, known in the art as the point soma model, which captures all of the salient properties of neuronal response while keeping the computational cost low. The point-soma latency time is modified to be an exponentially decaying function of the strength of the applied potential. Choosing computational efficiency over biological fidelity, the dendrites surrounding a neuron are represented by simplified compartmental submodels and there are no dendritic spines. Updates to the dendritic potential, calcium-ion concentrations and conductances, and potassium-ion conductances are done by use of equations similar to those of the point soma. Diffusion processes in dendrites are modeled by averaging among nearest-neighbor compartments. Inputs to each of the dendritic compartments come from sensors. Alternatively or in addition, when an affected neuron is part of a pool, inputs can come from other spiking neurons. At present, SVM neural networks are implemented by computational simulation, using algorithms that encode the SVM and its submodels. However, it should be possible to implement these neural networks in hardware: The differential equations for the dendritic and cellular processes in the SVM model of spiking neurons map to equivalent circuits that can be implemented directly in analog very-large-scale integrated (VLSI) circuits.

Huntsberger, Terrance↗
NASA NTRS1989

Report of the 1988 2-D Intercomparison Workshop, chapter 3

Several factors contribute to the errors encountered. With the exception of the line-by-line model, all of the models employ simplifying assumptions that place fundamental limits on their accuracy and range of validity. For example, all 2-D modeling groups use the diffusivity factor approximation. This approximation produces little error in tropospheric H2O and CO2 cooling rates, but can produce significant errors in CO2 and O3 cooling rates at the stratopause. All models suffer from fundamental uncertainties in shapes and strengths of spectral lines. Thermal flux algorithms being used in 2-D tracer tranport models produce cooling rates that differ by as much as 40 percent for the same input model atmosphere. Disagreements of this magnitude are important since the thermal cooling rates must be subtracted from the almost-equal solar heating rates to derive the net radiative heating rates and the 2-D model diabatic circulation. For much of the annual cycle, the net radiative heating rates are comparable in magnitude to the cooling rate differences described. Many of the models underestimate the cooling rates in the middle and lower stratosphere. The consequences of these errors for the net heating rates and the diabatic circulation will depend on their meridional structure, which was not tested here. Other models underestimate the cooling near 1 mbar. Suchs errors pose potential problems for future interactive ozone assessment studies, since they could produce artificially-high temperatures and increased O3 destruction at these levels. These concerns suggest that a great deal of work is needed to improve the performance of thermal cooling rate algorithms used in the 2-D tracer transport models.

Jackman, Charles H.↗
NASA NTRS2008

Hyperspectral Fluorescence and Reflectance Imaging Instrument

The system is a single hyperspectral imaging instrument that has the unique capability to acquire both fluorescence and reflectance high-spatial-resolution data that is inherently spatially and spectrally registered. Potential uses of this instrument include plant stress monitoring, counterfeit document detection, biomedical imaging, forensic imaging, and general materials identification. Until now, reflectance and fluorescence spectral imaging have been performed by separate instruments. Neither a reflectance spectral image nor a fluorescence spectral image alone yields as much information about a target surface as does a combination of the two modalities. Before this system was developed, to benefit from this combination, analysts needed to perform time-consuming post-processing efforts to co-register the reflective and fluorescence information. With this instrument, the inherent spatial and spectral registration of the reflectance and fluorescence images minimizes the need for this post-processing step. The main challenge for this technology is to detect the fluorescence signal in the presence of a much stronger reflectance signal. To meet this challenge, the instrument modulates artificial light sources from ultraviolet through the visible to the near-infrared part of the spectrum; in this way, both the reflective and fluorescence signals can be measured through differencing processes to optimize fluorescence and reflectance spectra as needed. The main functional components of the instrument are a hyperspectral imager, an illumination system, and an image-plane scanner. The hyperspectral imager is a one-dimensional (line) imaging spectrometer that includes a spectrally dispersive element and a two-dimensional focal plane detector array. The spectral range of the current imaging spectrometer is between 400 to 1,000 nm, and the wavelength resolution is approximately 3 nm. The illumination system consists of narrowband blue, ultraviolet, and other discrete wavelength light-emitting-diode (LED) sources and white-light LED sources designed to produce consistently spatially stable light. White LEDs provide illumination for the measurement of reflectance spectra, while narrowband blue and UV LEDs are used to excite fluorescence. Each spectral type of LED can be turned on or off depending on the specific remote-sensing process being performed. Uniformity of illumination is achieved by using an array of LEDs and/or an integrating sphere or other diffusing surface. The image plane scanner uses a fore optic with a field of view large enough to provide an entire scan line on the image plane. It builds up a two-dimensional image in pushbroom fashion as the target is scanned across the image plane either by moving the object or moving the fore optic. For fluorescence detection, spectral filtering of a narrowband light illumination source is sometimes necessary to minimize the interference of the source spectrum wings with the fluorescence signal. Spectral filtering is achieved with optical interference filters and absorption glasses. This dual spectral imaging capability will enable the optimization of reflective, fluorescence, and fused datasets as well as a cost-effective design for multispectral imaging solutions. This system has been used in plant stress detection studies and in currency analysis.

Ryan, Robert E.↗
NASA NTRS1993

Novel use of positively charged nylon transfer membranes for trapping indoleacetic acid or other small anions during efflux from plant tissues

Positively charged nylon blotting membranes were used as an anion binding medium to trap [14C]indoleactic acid (IAA) as it exited cells at the basal ends of Coleus blumei L. stem and Zea mays L. coleoptile segments. Autoradiography was used to visualize where the [14C] that moved out of the cut ends was localized on the nylon membrane. Diffusion of [14C]IAA from the initial point of contact with the nylon membrane was minimal. Comparison of the autoradiograms with anatomical tissue prints of the cut ends of the segments was used to determine what tissues participate in IAA movement. The results of these initial studies were consistent with other reports suggesting that [14C]IAA movement was primarily associated with vascular tissues in both C. blumei stems and corn coleoptiles, but the resolution was not sufficient to identify which vascular tissues were involved in IAA transport. With further refinements, this technique could also be used for studying the movement of other small charged molecules through plant tissues.

NASA Discipline Plant Biology↗
NASA NTRS1998

"Reagentless" flow injection determination of ammonia and urea using membrane separation and solid phase basification

Flow injection analysis instrumentation and methodology for the determination of ammonia and ammonium ions in an aqueous solution are described. Using in-line solid phase basification beds containing crystalline media. the speciation of ammoniacal nitrogen is shifted toward the un-ionized form. which diffuses in the gas phase across a hydrophobic microporous hollow fiber membrane into a pure-water-containing analytical stream. The two streams flow in a countercurrent configuration on opposite sides of the membrane. The neutral pH of the analytical stream promotes the formation of ammonium cations, which are detected using specific conductance. The methodology provides a lower limit of detection of 10 microgram/L and a dynamic concentration range spanning three orders of magnitude using a 315-microliters sample injection volume. Using immobilized urease to enzymatically promote the hydrolysis of urea to produce ammonia and carbon dioxide, the technique has been extended to the determination of urea.

NASA Center JSC↗
DOE OSTI2024

DiffESM: Conditional Emulation of Temperature and Precipitation in Earth System Models With 3D Diffusion Models

Earth system models (ESMs) are essential for understanding the interaction between human activities and the Earth's climate. However, the computational demands of ESMs often limit the number of simulations that can be run, hindering the robust analysis of risks associated with extreme weather events. While low-cost climate emulators have emerged as an alternative to emulate ESMs and enable rapid analysis of future climate, many of these emulators only provide output on at most a monthly frequency. This temporal resolution is insufficient for analyzing events that require daily characterization, such as heat waves or heavy precipitation. We propose using diffusion models, a class of generative deep learning models, to effectively downscale ESM output from a monthly to a daily frequency. Trained on a handful of ESM realizations, reflecting a wide range of radiative forcings, our DiffESM model takes monthly mean precipitation or temperature as input, and is capable of producing daily values with statistical characteristics close to ESM output. Combined with a low-cost emulator providing monthly means, this approach requires only a small fraction of the computational resources needed to run a large ensemble. We evaluate model behavior using a number of extreme metrics, showing that DiffESM closely matches the spatio-temporal behavior of the ESM output it emulates in terms of the frequency and spatial characteristics of phenomena such as heat waves, dry spells, or rainfall intensity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Investigating shock-induced chemical reactions in Ni+Al multilayers: A continuum-based mesoscale approach with Arrhenius kinetics and artificial thermal conduction

A new continuum-based mesoscale modeling approach for shock-induced chemical reactions (SICRs) in Ni+Al multilayers is demonstrated in Sandia’s shock physics hydrocode, CTH. The approach utilizes Arrhenius-type kinetics and artificial thermal conduction. Our work builds upon previous efforts to parameterize equations of state for Ni x Al y [J. Appl. Phys. 137, 075102 (2025)], as well as simulations of inert shocks in realistic 2D microstructures [J. Appl. Phys. 137, 225301 (2025)]. To calibrate the reaction kinetics, pairs of the reaction coordinate, R′, vs time are extracted from the molecular dynamics (MD) literature. Here, the MD-informed kinetics are used to simulate the dynamic evolution of pressure and temperature in 2D mesoscale simulations. Overall, the MD-informed kinetics obtained for planar interfaces are too slow, as initial reaction is not observed on a nanosecond time scale. Even with quasi-periodic shock focusing leading to the formation of so-called “hot-spots,” the hot spots are unable to grow and coalesce using the fitted Arrhenius rate constants. However, by increasing the rate constants by two orders of magnitude, SICRs are observed at a shock pressure near 30 GPa, which is supported by experiments. Consequently, these mesoscale simulations suggest that unresolved shear-based mechanical mixing might possibly account for the discrepancies in kinetic rates, with shock-generated intense perturbations, interfacial vortical flows, and elevated temperatures serving as favorable reaction conditions. Future work will calibrate a shear-dependent reaction rate from the MD simulations with realistic interfaces that are wavy, diffuse, and disordered.

Kittell, David E. [Sandia National Laboratories (S↗
DOE OSTI2024

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Quantifying local and global mass balance errors in physics-informed neural networks

Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced softly in PINN. This paper investigates how mass balance constraints are satisfied when PINN is used to solve the resulting PDEs. We investigate PINN’s ability to solve the 1D saturated groundwater flow equations (diffusion equations) for homogeneous and heterogeneous media and evaluate the local and global mass balance errors. We compare the obtained PINN’s solution and associated mass balance errors against a two-point finite volume numerical method and the corresponding analytical solution. We also evaluate the accuracy of PINN in solving the 1D saturated groundwater flow equation with and without incorporating hydraulic heads as training data. We demonstrate that PINN’s local and global mass balance errors are significant compared to the finite volume approach. Tuning the PINN’s hyperparameters, such as the number of collocation points, training data, hidden layers, nodes, epochs, and learning rate, did not improve the solution accuracy or the mass balance errors compared to the finite volume solution. Mass balance errors could considerably challenge the utility of PINN in applications where ensuring compliance with physical and mathematical properties is crucial.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2001

Modeling of two-phase flow in membranes and porous media in microgravity as applied to plant irrigation in space

In traditional applications in soil physics it is convention to scale porous media properties, such as hydraulic conductivity, soil water diffusivity, and capillary head, with the gravitational acceleration. In addition, the Richards equation for water flux in partially saturated porous media also contains a gravity term. With the plans to develop plant habitats in space, such as in the International Space Station, it becomes necessary to evaluate these properties and this equation under conditions of microgravitational acceleration. This article develops models for microgravity steady state two-phase flow, as found in irrigation systems, that addresses critical design issues. Conventional dimensionless groups in two-phase mathematical models are scaled with gravity, which must be assigned a value of zero for microgravity modeling. The use of these conventional solutions in microgravity, therefore, is not possible. This article therefore introduces new dimensionless groups for two-phase models. The microgravity models introduced here determined that in addition to porous media properties, important design factors for microgravity systems include applied water potential and the ratio of inner to outer radii for cylindrical and spherical porous media systems.

Plant Roots/growth & development↗
DOE OSTI2024

GraMeR: Gra ph Me ta R einforcement learning for multi-objective influence maximization

Influence maximization (IM) is a combinatorial problem of identifying a subset of seed nodes in a network (graph), which when activated, provide a maximal spread of influence in the network for a given diffusion model and a budget for seed set size. IM has numerous applications such as viral marketing, epidemic control, sensor placement and other network-related tasks. However, its practical uses are limited due to the computational complexity of current algorithms. Recently, deep reinforcement learning has been leveraged to solve IM in order to ease the computational burden. However, there are serious limitations in current approaches, including narrow IM formulation that only consider influence via spread and ignore self-activation, low scalability to large graphs, and lack of generalizability across graph families leading to a large running time for every test network. In this work, we address these limitations through a unique approach that involves: (1) Formulating a generic IM problem as a Markov decision process that handles both intrinsic and influence activations; (2)incorporating generalizability via meta-learning across graph families. There are previous works that combine deep reinforcement learning with graph neural network, but this work solves a more realistic IM problem and incorporates generalizability across graphs via meta reinforcement learning. Extensive experiments are carried out in various standard networks to validate performance of the proposed Graph Meta Reinforcement learning (GraMeR) framework. Finally, the results indicate that GraMeR is multiple orders faster and generic than conventional approaches when applied on small to medium scale graphs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Generative modeling enables molecular structure retrieval from Coulomb explosion imaging

Capturing the structural changes that molecules undergo during chemical reactions in real space and time is a long-standing dream and an essential prerequisite for understanding and ultimately controlling femtochemistry. A key approach to tackle this challenging task is Coulomb explosion imaging, which benefited decisively from recently emerging high-repetition-rate X-ray free-electron laser sources. With this technique, information on the molecular structure is inferred from the momentum distributions of the ions produced by the rapid Coulomb explosion of molecules. Retrieving molecular structures from these distributions poses a highly non-linear inverse problem that remains unsolved for molecules consisting of more than a few atoms. Here, we address this challenge using a diffusion-based Transformer neural network. We show that the network reconstructs unknown molecular geometries from ion-momentum distributions with a mean absolute error below one Bohr radius, which is half the length of a typical chemical bond.

Artificial Intelligence (cs.AI)↗
DOE OSTI2026

Constraining Hamiltonians from chiral effective field theory with neutron-star data

Multi-messenger observations of neutron stars (NSs) and their mergers have placed strong constraints on the dense-matter equation of state (EOS). The EOS, in turn, depends on microscopic nuclear interactions that are described by nuclear Hamiltonians. These Hamiltonians are commonly derived within chiral effective field theory (EFT). Ideally, multi-messenger observations of NSs could be used to directly inform our understanding of EFT interactions, but such a direct inference necessitates millions of model evaluations. This is computationally prohibitive because each evaluation requires us to calculate the EOS from a Hamiltonian by solving the quantum many-body problem with methods such as auxiliary-field diffusion Monte Carlo (AFDMC), which provides very accurate and precise solutions but at a significant computational cost. Additionally, we need to solve the stellar structure equations for each EOS which further slows down each model evaluation by a few seconds. In this work, we combine emulators for AFDMC calculations of neutron matter, built using parametric matrix models, and for the stellar structure equations, built using multilayer perceptron neural networks, with the PyCBC data-analysis framework to enable a direct inference of coupling constants in an EFT Hamiltonian using multi-messenger observations of NSs. We find that astrophysical data can provide informative constraints on two-nucleon couplings despite the high densities probed in NS interiors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Nonlinear Ensemble Filtering with Diffusion Models: Application to the Surface Quasigeostrophic Dynamics

The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here, we explore another promising solution in which diffusion models are used to formulate a robust nonlinear ensemble filter for sequential data assimilation. Unlike standard machine learning methods, the proposed ensemble score filter (EnSF) is completely training free and can efficiently generate a set of analysis ensemble members. Here, in this study, we apply the EnSF to a surface quasigeostrophic model and compare its performance against the popular local ensemble transform Kalman filter (LETKF), which makes Gaussian assumptions in the analysis step. Numerical tests demonstrate that EnSF maintains stable performance in the absence of localization and for a variety of experimental settings. We find that while LETKF maintains optimal performance in the case of linear observations of the entire state and a perfect model, EnSF shows improvements over LETKF when nonlinear observations are assimilated and the system is subject to unexpected model errors. A spectral decomposition of the analysis results in this nonlinear observation regime shows that the largest improvements over LETKF occur at large scales (small wavenumbers), where LETKF lacks sufficient ensemble spread. Overall, this initial application of EnSF to a geophysical model of intermediate complexity motivates further development of the algorithm for more realistic problems.

Artificial intelligence↗