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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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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

DIP: Digital Information Platform

The third DIP workshop’s topic is DIP for Flight Operators and Consumers. Participants will receive insight the consumer onboarding process and steps to take to consume from the platform. Showcase demos will be provided covering data integration services, data analytics using ML/AI technologies, and Collaborative Digital Decision Reroute (CDDR) capabilities. More details on service performance metrics will be discussed as well as updates on the technical development plan and schedule. Participants interested in consuming DIP services are highly encouraged to attend this workshop and provide feedback.

ATM-X↗
NASA NTRSDate not supplied

Holey Silicon-based Thermopiles for High-Sensitivity Broadband Thermal Detection in Space

Future planetary missions call for thermal detectors with high sensitivity over a wide range of temperature or wavelength. Conventional approaches based upon photon detectors are limited to a narrow and material-selective range of wavelength, and they often require cryogenic cooling for measurements of far-infrared (FIR) radiation or very low-temperature objects, which result in a significant increase in the system’s size, weight, and power (SWaP). While thermal detectors based upon thermopiles are uncooled and sensitive to a wide range of wavelengths including FIR radiation, their sensitivity, limited by the material’s thermoelectric response and heat losses, is an order of magnitude lower than photon detectors. To address the sensitivity requirements for future planetary science missions that target very cold objects such as ice giant planets, icy regoliths, planetary satellites, and primitive bodies, we introduce a high-sensitive broadband thermopile concept using holey silicon – a thin membrane of silicon with a microfabricated arrangement of pores that can be optimized to minimize heat losses and enable breakthrough thermoelectric performance. In this paper, we present our analytical model for the holey silicon-based thermopile, its performance expectations, and its performance comparisons with the state-of-the-art thermopile technology. We will investigate the roles of thermal conductance in holey silicon-based thermopile performance, the impact of thermal conduction and thermal radiation at different temperature limits, and the performance trade-off between the responsivity and noises.

thermopiles↗
NASA NTRSDate not supplied

Soluble Organic Matter (SOM) analysis of the Hayabusa2 samples: The first results

The Hayabusa2 spacecraft successfully collected the surface and possible sub-surface materials of the asteroid 162173 Ryugu. Ryugu is a C-type asteroid characterized by a low-albedo surface probably consisting of hydrous minerals and carbonaceous materials. [1] The direct optical and spectral analysis of the returned samples indicates that Ryugu material is dominated by hydrous carbonaceous chondrite-like matter (similar to CI chondrites) [2]. Since carbonaceous chondrites have generally yielded various types of organic matter, the collected Ryugu grains are expected to contain diverse types of organic compounds including bio-related molecules. The occurrence of organic compounds in the Ryugu surface will provide clues to the evolution of prebiotic molecules and their preservations associated with aqueous alteration of the primitive asteroid. The initial analysis of soluble organic matter (SOM) of the Hayabusa2-returned samples has been performed by an international team consisting of 32 members. Because the sample amount available for comprehensive SOM analyses is limited, and because the SOM is expected to be present as a complex mixture of various types of organic compounds with very small concentrations of each compound, high-sensitivity and high-resolution analytical techniques have been developed using carbonaceous meteorites [e.g. 3]. Two aggregate samples of the Ryugu grains (A106 and C107) were allocated for the solvent extractions and bulk carbon (C), hydrogen (H), nitrogen (N), sulfur (S) and oxygen (O) measurements. The A106 sample was collected during the 1st sampling in February 2019 and the C107 sample was collected during the 2nd sampling in July 2019 after the Small Carry Impactor (SCI) operation. They consist mainly of particles smaller than 1 mm in diameter, and each sample mass was 38-39 mg. They were firstly investigated spectroscopically in the near infrared wavelength range by the Stone Team prior to the solvent extractions. Other small grains (A0080 and C0057) were also allocated for this study to investigate the spatial distribution of organic compounds on the sample surface. The extraction and analytical measurements implemented by the SOM Team are summarized in Figure 1. Each powder sample was extracted sequentially with non-polar to polar solvents, i.e., hexane, dichloromethane (DCM), methanol (MeOH) and H2O, for non-targeted analysis to reveal the compound composition. Each solvent extract was analyzed by solution state nuclear magnetic resonance (NMR) spectroscopy [4], Fourier transform- ion cyclotron resonance/mass spectrometry (FT-ICR/MS) with ESI and APPI ionization [5] and by high-resolution mass spectroscopy using Orbitrap MS coupled with nano-liquid chromatography (nanoLC/Orbitrap MS) [6], and using two dimensional gas chromatography/mass spectrometry (GC×GC/MS). The extracted residues were passed to the Chemistry Team for further inorganic element analysis. The other powder sample was subjected to the hot water extraction for amino acid analyses including chiral isomer separation, which was performed by three-dimensional (3D) high-performance liquid chromatography (HPLC) with high-sensitivity fluorescence detection (FD) [7] and by HPLC/FD coupled with quadrupole-time of flight/mass spectrometry (QToF/MS) [8]. After the hot water extraction, the residue was split into two halves. One half was further extracted with hydrochloric acid (HCl) to analyze for amino acids in bound-form. The other half was sequentially extracted with DCM/MeOH (1/1) to analyze semi-polar compounds such as polycyclic aromatic hydrocarbons (PAHs) by GC/MS, followed by further extraction with formic acid to analyze polar heterocyclic compounds, and subsequent extraction with HCl to detect bound-form polar compounds. The extracted residues were passed to the IOM Team for the analysis of insoluble organic matter (IOM). Compound-specific stable isotope analyses will be performed using GC/combustion/isotope ratio mass spectrometry (GC/C/IRMS) if the compound concentration is high enough to enable such an isotopic measurement. All extraction procedures were performed on an ISO 6 (Class 100) clean bench inside an ISO 5 (Class 1000) clean room. Baked serpentine powder was also analyzed as a procedural blank. In situ organic compound analysis with the molecular imaging was performed using desorption electrospray ionization (DESI) equipped with Orbitrap MS [9, 10], followed by spatial imaging of organic compounds using ToF/secondary ion mass spectrometry (ToF/SIMS) [11]. The bulk chemical and isotopic compositions of CNS and HO were determined using nano-elemental analysis/isotope ratio mass spectrometry (nanoEA/IRMS) [12] and EA/pyrolysis/IRMS, respectively. We have identified a variety of indigenous organic compounds in the extracts of both A106 and C107 samples. The Ryugu grains host organic molecules under the high-vacuum and cosmic-ray irradiation environment of the asteroid surface. The analysis of extracted molecules is in progress, and the first results will be presented at the symposium.

Hiroshi Naraoka↗
NASA NTRS1980

Exploratory studies of the cruise performance of upper surface blown configurations. Experimental program: Test facilities, model design instrumentation, and lowspeed, high-lift tests

The model hardware, test facilities and instrumentation utilized in an experimental study of upper surface blown configurations at cruise is described. The high speed (subsonic) experimental work, studying the aerodynamic effects of wing nacelle geometric variations, was conducted around semispan model configurations composed of diversified, interchangeable components. Power simulation was provided by high pressure air ducted through closed forebody nacelles. Nozzle geometry was varied across size, exit aspect ratio, exit position and boattail angle. Three dimensional force and two dimensional pressure measurements were obtained at cruise Mach numbers from 0.5 to 0.8 and at nozzle pressure ratios up to about 3.0. The experimental investigation was supported by an analytical synthesis of the system using a vortex lattice representation with first order power effects. Results are also presented from a compatibility study in which a short haul transport is designed on the basis of the aerodynamic findings in the experimental study as well as acoustical data obtained in a concurrent program. High lift test data are used to substantiate the projected performance of the selected transport design.

Braden, J. A.↗
DOE OSTI2025

High-precision monitoring of outgassing species in model extreme ultraviolet photoresists with a cavity ring-down spectrometer

Background Extreme ultraviolet (EUV) photoresists play a pivotal role in advancing nanopatterning technologies by balancing image quality and sensitivity. The outgassing behavior of photoresist thin films under EUV and deep ultraviolet (DUV) exposure reveals chemical details relevant to their performance. Aim Here, we focus on utilizing an analytical technique not previously used in photolithography, the tabletop cavity ring-down spectrometer, to investigate outgassing dynamics in EUV photoresists, enabling precise chemical identification and deeper insights into resist processing. Approach The spectrometer’s enhanced laser path length (∼ 20 km) and broadband absorption capabilities in the C–H overtone region allow for sensitive and temporally resolved detection of mixtures of outgassed species. Using a model resist comprising a polymer matrix with a photoacid generator and quencher, we analyzed the influence of time delays between exposure and post-exposure bake (PEB) as well as storage under varying environmental conditions. Results Suppression of isobutylene outgassing and thickness loss was observed with extended delays between exposure and PEB, potentially linked to water absorption and acid deactivation. The technique proved highly effective in distinguishing subtle chemical differences between processing stages. Conclusions Delay times and their environmental conditions, particularly humidity, reduce outgassing and thickness loss of photoresists during PEB, suggesting decreased acid-driven deprotection. This can potentially impact sensitivity, defectivity, and roughness of resist patterns, necessitating precise monitoring and control.

Extreme ultraviolet photoresists↗
DOE OSTI2021

A Miniature Multilevel Structures for Lossless Ion Manipulations Ion Mobility Spectrometer with Wide Mobility Range Separation Capabilities

Here, ion mobility spectrometry employing structures for lossless ion manipulations (SLIM-IMS) is an attractive gas-phase separation technique due to its ability to achieve unprecedented effective ion path lengths (>1 km) and IMS resolving powers in a small footprint. The emergence of multilevel SLIM technology, where ions are transferred between vertically stacked SLIM electrode surfaces, has subsequently allowed for ultralong single pass path lengths (>40 m) to be achieved, enabling ultrahigh resolution IMS measurements to be performed over the entire mobility range in a single experiment. The implementation of multiple SLIM levels requires very little additional space for the SLIM system, and we developed a miniature SLIM module (miniSLIM) based on multilevel SLIM technology and report the performance here. The module is 11.1 cm x 6.7 cm x 1.4 cm (L x W x H) and consists of three SLIM levels totaling 1-meter path length. Ion trajectory simulations were used to optimize the SLIM board spacings and SLIM board thicknesses of the miniSLIM IMS system. Methods of efficiently transferring ions between SLIM levels were examined and a new approach using asymmetric traveling waves (TWs) was developed and implemented in the miniSLIM. We experimentally characterized the performance of the --meter multilevel miniSLIM IMS-MS relative to a drift tube IM--MS using an Agilent tuning mixture and tetraalkylammonium cations. The 1-meter miniSLIM achieved a resolving power of up to 131 (CCS/ΔCCS), ~1.5x higher than achievable with a 78 cm path length drift tube IMS, and successfully transmitted the entire ion mobility range in a single separation. We also demonstrated the miniSLIM’s performance as a standalone IMS system (i.e., without MS), showing baseline separation between Agilent tuning mixture cations with the full mobility range observed, and a standard peptide mixture with different charge states readily differentiated. Overall the miniSLIM provides a compact alternative to high performance IMS instruments possessing similar path lengths.

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

Activation of N 2 on Manganese Nitride-Supported Ni 3 and Fe 3 Clusters and Relevance to Ammonia Formation

Dual-site models were constructed to represent manganese nitride (Mn 4 N)-supported Ni 3 and Fe 3 clusters for NH 3 synthesis. Density functional theory calculations produced an energy barrier of approximately 0.55 eV for N–N bond activation at the interfacial nitrogen vacancy sites (N v ); also, the hydrogenation and removal of interfacial N is promoted by earth-abundant Ni and Fe metals. Steady-state microkinetic modeling revealed that the turnover frequencies of NH 3 production follow an order of Fe 3 @Mn 4 N ≈ Ni 3 @Mn 4 N > Mn 4 N > Fe >> Ni. Moreover, we present clear evidence that, before NH 3 formation, NH migrates from N v onto the metallic sites. Using N binding energy (BE N ) and the transition-state energy of N 2 activation (E TS ) as descriptors, we concluded that the beneficial effects owing to interfacial N v sites are the most pronounced when BE N is either too strong or too weak while E TS is high; otherwise, excessive N v sites may hinder catalyst performance.

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

Engineering donor–acceptor conjugated polymers for high-performance and fast-response organic electrochemical transistors

To date, high-performance organic electrochemical transistors (OECTs) have mostly been based on polythiophene systems. Donor–acceptor (D–A) conjugated polymers are expected to be promising materials for OECTs owing to their high mobility and comparatively low crystallinity (good for ion diffusion). However, the OECT performance of D–A polymers lags far behind that of the polythiophenes. Here we synergistically engineered the backbone and side chain of a series of diketopyrrolopyrrole (DPP)-based D–A polymers and found that redox potential, molecular weight, solution processability, and film microstructures all have a severe impact on their performance. After systematic engineering, P(bgDPP-MeOT2) exhibited the best figure-of-merit (μC*) of 225 F cm -1 V -1 s -1 , amongst the highest performance of the reported D–A polymers. Besides, the DPP polymers exhibited high hole mobility of over 1.6 cm 2 V -1 s -1 , leading to fast response OECTs with a record low turn-off response time of 30 μs. The polymer also exhibited good operation stability with a current retention of 98.8% over 700 electrochemical switching cycles. This work reveals the complexity and systematicness in the development of D–A polymer based high-performance OECTs.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Sustainable Functional Epoxies through Boric Acid Templating

Thermoset polymers (e.g. epoxies, vulcanizable rubbers, polyurethanes, etc.) are crosslinked materials with excellent thermal, chemical, and mechanical stability; these properties make thermoset materials attractive for use in harsh applications and environments. Unfortunately, material robustness means that these materials persist in the environment with very slow degradation over long periods of time. Balancing the benefits of material performance with sustainability is a challenge in need of novel solutions. Here, we aimed to address this challenge by incorporating boronic acid-amine complexes into epoxy thermoset chemistries, facilitating degradation of the material under pH neutral to alkaline conditions; in this scenario, water acts as an initiator to remove boron species, creating a porous structure with an enhanced surface area that makes the material more amenable to environmental degradation. Furthermore, the expulsion of the boron leaves the residual pores rich in amines which can be exploited for CO 2 absorption or other functionalization. We demonstrated the formation of novel boron species from neat mixing of amine compounds with boric acid, including one complex that appears highly stable under nitrogen atmosphere up to 600 °C. While degradation of the materials under static, alkaline conditions (our “trigger”) was inconclusive at the time of this writing, dynamic conditions appeared more promising. Additionally, we showed that increasing boronic acid content created materials more resistant to thermal degradation, thus improving performance under typical high temperature use conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Dynamic Binary Complexes (DBC) as Super-Adjustable Viscosity Modifiers for Hydraulic Fracturing Fluids

In the preceding project year two, we refined three DBC formulations from a selection of over 50 different chemistries. The optimization study primarily encompassed testing for (i) reversibility extent, (ii) performance in the presence of chemical additives, (iii) adhesion and friction behavior during displacement in wellbores and pipelines, (iv) corrosion protection performance, and (v) injection performance with model fracture systems at the laboratory scale. Highly promising results obtained from all these tests signify the significant potential of DBCs in enhancing hydrocarbon recovery from unconventional reservoirs. The primary activities in the third project year included publishing experimental findings across multiple articles and conducting outreach initiatives. Throughout the year, we undertook tasks such as replicating experimental results, further optimizing various formulations and their associated experimental sets, and conducting additional tests to address missing components based on reviewer feedback and suggestions. We also explored the surfactant and friction-reduction aspects of selected formulations through drag reduction tests. In addition, we constructed an improved fracturing performance setup and performed flow injection tests. The specific DBC formulations focused on during this project period were A8/B1, A12/B5, and A10/B12. We also obtained results for additional DBC formulations and a select few commercial fracturing fluids for the purpose of comparison. Within the project's scope, we aim to enhance the experimental findings with the development of various models. The first two years focused on two key aspects: (i) the creation of a high-fidelity hydraulic fracturing model for non-Newtonian fluids to gain insights into the implementation of DBC fluids in fracking environments, and (ii) the development of a multiphase flow simulator for estimating total production, fluid saturation in the reservoir, and the creation of a fracture propagation model and kinetic Monte Carlo (kMC) models for diverse applications. In the third year, we delved into the fundamental nanostructural properties of DBCs, exploring aspects such as material chemistry, pH tunability, and control of DBC formation and stability. Subsequently, in the extension year, we conducted a systematic investigation of various building blocks containing primary, secondary, and tertiary amine functional groups to understand their impact on rheological and viscoelastic properties. Furthermore, we explored a Dissipative Particle Dynamics (DPD) model to simulate self-assembly processes with precision, creating a high-fidelity representation of relevant nanostructures. The tasks performed this year with the significant results obtained have been discussed in Section 2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Towards a Deeper Fundamental Understanding of (Al,Sc)N Ferroelectric Nitrides

Density functional theory (DFT) calculations, within the virtual crystal alloy approximation, are performed, along with the development of a Landau-type model employing a symmetry-allowed analytical expression of the internal energy and having parameters determined from first principles, to investigate properties and energetics of Al1-xScxN ferroelectric nitrides in their hexagonal forms. These DFT computations and this model predict the existence of two different types of minima, namely, the fourfold-coordinated wurtzite (WZ) polar structure and a five-fold coordinated paraelectric hexagonal phase (denoted as H5), for any Sc composition up to 40%. The H5 minimum progressively becomes the lowest-energy state within hexagonal symmetry as the Sc concentration increases from 0 to 0.4. Furthermore, the model points to several key findings. Examples include the crucial role of the coupling between polarization and strains to create the WZ minimum, in addition to polar and elastic energies, and that the origin of the H5 state overcoming the WZ phase as the global minimum within hexagonal symmetry when increasing the Sc composition mostly lies in the compositional dependency of only two parameters-one linked to the polarization and another one being purely elastic in nature. Other examples are that forcing Al1-xScxN systems to have no or a weak change in lattice parameters when heating them allows us to reproduce their finite-temperature polar properties well and that a value of the axial ratio close to that of the ideal WZ structure implies a large polarization at low temperatures but not necessarily at high temperatures because of the ordered-disordered character of the temperature-induced formation of the WZ state. Such findings should allow for a better fundamental understanding of (Al,Sc)N ferroelectric nitrides, which may be used to design efficient devices having, e.g., low operating voltages.

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

Rugged WBG Devices and Advanced Electric Machines for High Power Density Automotive Electric Vehicles

This work explored two very important approaches for supporting transportation electrification and reducing dependence on imports of critical materials. In the first task, several novel electric machine architectures with low rare earth metal content were compared analytically, then experimentally to verify their performance. Rare earth metals are imported largely from China and are widely used in many clean energy systems such as wind turbines and EV motors. Reducing our dependence on this critical material is an important objective for ensuring our independence and continued economic prosperity. In the second task, a GaN based inverter for EV inverters was developed to demonstrate the suitability of that wide bandgap semiconductor device in this important application.

42 ENGINEERING↗
NASA NTRS1990

A revised parametrization of the dispersion constants for high dispersion IUE images

An economical system of parameterizing dispersion constants spectra is derived and applied to International Ultraviolet Explorer (IUE) spectra by equating specific terms to geometric coordinates of an echellogram. Because of the virtual property of the IUE camera pixels, several geometrical rectifications can be performed analytically before the dispersion relations are solved for line and sample position. This permits the relations to be decoupled and reduced to two terms apiece, the simplest representation possible. A generalization of these principles allows the dispersion relations to be determined neatly in other echelle systems having certain well understood distortions. Prismatic cross dispersion, S wave distortion, and optical aberrations are some areas in which this system can be used.

Smith, Myron A.↗
NASA NTRSDate not supplied

NASA’s Prototype Spectral Water Inversion Processor and Emulator (SWIPE): Towards Global Coastal and Inland Water Quality and Algal Biodiversity Monitoring

Degradation of Earth’s inland water resources due to anthropogenic perturbations and climate anomalies at both local and global scales continues to place human health at substantial risk. There is now a growing necessity to develop pragmatic approaches that allow timely and effective extrapolation of local processes, to spatially resolved global products, and to promote operational and sustainable resource policy management. This presentation will provide updates on NASA’s prototype open-source aquatic modeling platform, Spectral Water Inversion Processor and Emulator (SWIPE), which is a comprehensive, multi-faceted modeling platform for both forward and inverse modeling of diverse aquatic ecosystems from the benthos to top-of-atmosphere (TOA). SWIPE provides a cohesive application which leverages recent advancements in particle modeling, Big Data analytics, and machine learning to develop a high-fidelity synthetic training ground for sensitivity studies and algorithm development for multispectral or upcoming hyperspectral missions. Some of the prominent features of SWIPE to be discussed include: 1. Advanced hyperspectral modeling of globally diverse algal and non-algal particles using a novel two-layer coated sphere scattering model and radiative transfer modeling, 2. Massive, highly detailed synthetic spectral libraries of Analysis-Ready-Data (ARD) which include spectral libraries of particle microphysics, water biogeophysical and optical properties, as well as surface and TOA reflectances at 1 nm resolution, 3. An ensemble of pre-built analytic, machine learning, and deep learning inversion algorithms for various water quality and biodiversity related retrieval parameters and uncertainty quantification, 4. Sensor-agnostic water quality inversion at wide ranging spatial and spectral resolutions including a codebase for seamless application in the Google Earth Engine and NASA Earth Exchange (NEX) for planetary scale analysis. SWIPE will be a fully open-source platform based in python with comprehensive documentation, tutorials, and options for distributed computing on high performance computing clusters or on single, local machines. Further, we will discuss how we envision SWIPE contributing towards a global analysis of coastal and inland water quality dynamics.

top-of-atmosphere (TOA)↗
NASA NTRS1991

Heavy hydrocarbon main injector technology program

The Heavy Hydrocarbon Main Injector Program was an analytical, design, and test program to demonstrate an injection concept applicable to an Isolated Combustion Compartment of a full-scale, high pressure, LOX/RP-1 engine. Several injector patterns were tested in a 3.4-in. combustor. Based on these results, features of the most promising injector design were incorporated into a 5.7-in. injector which was then hot-fire tested. In turn, a preliminary design of a 5-compartment 2D combustor was based on this pattern. Also the additional subscale injector testing and analysis was performed with an emphasis on improving analytical techniques and acoustic cavity design methodology. Several of the existing 3.5-in. diameter injectors were hot-fire tested with and without acoustic cavities for spontaneous and dynamic stability characteristics.

Arbit, H. A.↗
NASA NTRS1979

Exploratory studies of the cruise performance of upper surface blown configurations: Experimental program, high-speed pressure tests

Basic pressure data are presented which was obtained from an experimental study of upper-surface blown configurations at cruise. The high-speed (subsonic) experimental work, studying the aerodynamic effects of wing-nacelle geometric variations, was conducted around semi-span model configurations composed of diversified, interchangeable components. Power simulation was provided by high-pressure air ducted through closed forebody nacelles. Nozzle geometry was varied across size, exit aspect ratio, exit position and boattail angle. Both 3-D force and 2-D pressure measurements were obtained at cruise Mach numbers from 0.5 to 0.8 and at nozzle pressure ratios up to about 3.0. The experimental investigation was supported by an analytical synthesis of the system using a vortex lattice representation with first-order power effects. Results are also presented from a compatibility study in which a short-haul transport is designed on the basis of the aerodynamic findings in the experimental study as well as acoustical data obtained in a concurrent program. High-lift test data are used to substantiate the projected performance of the selected transport design.

Braden, J. A.↗
DOE OSTI2023

An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, in stead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves tremendous amount of time spent on training neural networks. Another essential aspect of EnSF is its analytical update step, gradually incorporating data information into the score function, which is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. High-dimensional Lorenz systems are used to demonstrate the performance of our method. EnSF provides surprisingly impressive performance in reliably tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimension) with highly nonlinear observation processes, which is a well-known challenging problem for existing filtering methods.

97 MATHEMATICS AND COMPUTING↗