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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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Metamodeling Time-Temperature Creep Parameters

Abstract There exist many time-temperature parameter (TTP) models for creep rupture prediction of components including the Larson–Miller (LM), Manson–Haferd (MH), Manson–Brown (MB), Orr–Sherby–Dorn (OSD), Manson–Succop (MS), Graham–Walles (GW), Chitty–Duval (CD), Goldhoff–Sherby (GS) models. It remains a challenge to determine which model is “best”, capable of accurate interpolation and physically realistic extrapolation of creep rupture data for a given material. In this study, metamodeling is applied to create a unified TTP metamodel that combines and regresses into twelve TTP models (eight existing and four newly derived). An analysis of the mathematical problems that exist in TTP models is provided. A matlab code is written that can: (1) calibrate the material constants of any of the twelve TTP models (using the metamodel); (2) determine the most suitable stress-parameter function; (3) and report the normalized mean square error (NMSE) of rupture predictions for a given material database. Using the metamodel, and code, a design engineer can make an intelligent selection of the “best” TTP model for creep resistant design. This process is demonstrated using four isotherms of alloy P91 creep rupture data. To assess the influence of material, further validation is performed on alloys Hastelloy X, 304SS, and 316SS. It is determined that the “best” model is dependent on material type and the quality and quantity of available data.

Engineering↗
DOE OSTI2020

Ordovician-Cambrian Units: Hierarchical Evaluation of Geologic Carbon Storage Resource Estimates

The Indiana Geological and Water Survey (IGWS) led subtask 1.1 to assess the regional distribution and estimate the storage capacity of Ordovician-Cambrian stratigraphic units located within the partnership region. A comprehensive data set of wireline logs and petrophysical information was used to generate these interpretations. These data include core analysis for porosity and permeability, mercury injection capillary pressure (MICP), and existing well data including location and stratigraphic information. This report includes storage resource estimates (SREs) for three potential storage reservoirs(limestone and dolostone from the Upper Ordovician Trenton Limestone/Black River Group and equivalent units, the Middle Ordovician St. Peter Sandstone, and primary target reservoir rocks of the Lower Ordovician and Upper Cambrian Knox Supergroup and equivalent units) calculated using six methodologies: (1) a fixed value of porosity of 10 percent in all units evaluated; (2) a unique average porosity (per well) from wireline-derived porosity (neutron, sonic, and/or density porosity for each unit); (3) porosity values from core analysis; (4) a depth-dependent porosity model (Knox Supergroup only); (5) porosity based on a model based on petrophysical facies; and (6) SREs using National Energy Technology Laboratory’s CO2 Storage prospeCtive Resource Estimation Excel aNalysis (CO2-SCREEN beta V2). All methods used the same values for thickness for each unit. However, the areal extent of each assessment was limited by the data available for each method. Estimated volumes were calculated in 1-by-1 kilometer grid cells and summarized as county and total stratigraphic unit volumes. The resultant SREs mass are displayed using boxplots, which allow for comparing data statistics (mean values and variability) between methods. Differences observed in SRE results from the six methods are mainly attributable to differences in the data and conceptual models used to interpret or estimate porosity in each method. Based on this systematic variability between methods, it is inferred that methods 1, 4, and 6 are best used for regional-scale reconnaissance estimates of storage capacity while methods 2, 3, and 5 are more appropriate for local scales where more data is required. All estimates are data-density dependent and different methods require different amounts of data for reasonable assessments. ArcMap 10.5.1 software was used to portray SREs to help visualize spatial variance of estimates for each methodology, and more importantly, to highlight those areas having the greatest total storage potential estimates.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2026

Merged Aerosol Value-Added Product Report

The Merged Aerosol Value-Added Product (VAP) simplifies scientists’ use of Atmospheric Radiation Measurement (ARM) User Facility aerosol data by performing several tedious, time-consuming tasks for the users. First, the VAP identifies the best data available when multiple datastreams exist for a single geophysical quantity so that ARM users do not have to research this for themselves. Second, the VAP consolidates multiple ARM aerosol datastreams into a single file for ARM data users so that they do not have to download, open, and read multiple files for their analysis. Next, the VAP transforms all measurements onto a common one-hour timestamp. The one-hour resolution matches the time resolution of the slowest instrument. Instruments with faster sampling rates than one measurement per hour are averaged over the time interval. Finally, the VAP reads the QA/QC variables and marks data with known issues as missing, so that users do not have to spend excessive time cleaning data. This includes incorporating Data Quality Reports (DQRs) that exist at the time when the VAP data is generated. DQRs are reports filed by instrument mentors or data users that indicate a problem with the output data of individual instruments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Well Stimulation Treatment in California: Evaluation of Disclosure Data, May 2015 – October 2019

In this document, disclosure data from 1,228 well stimulations occurring May 2015 to October 2019 in California are evaluated. This evaluation updates a previous study that was based on 618 well stimulations occurring May 2015 to June 2016 (Stringfellow, W.T., Camarillo, M.K., and Jordan, P. 2017, Status of Well Stimulation in California Since Implementation of SB-4 Regulations, Berkeley National Laboratory, Berkeley, CA). While the goal of the previous study was to provide a summary of information obtained since passage of California Senate Bill No. 4—Oil and Gas, the goal of the current evaluation is to provide a basis for studying chemical indicators that could potentially be used to detect aquifer contamination. We evaluate chemical indicators is a separate document using the data contained herein as well as data from monitoring wells located within oil fields. Compared with the data used by Stringfellow et al. 2017, the current evaluation is based on a more diverse data set. While the previous study contained data for only two oil fields with more than 30 well stimulations, the current data set contains four oil fields with more than 30 well stimulations, making these data more ideal for comparisons using statistical tests. More producers and a new oil field, Buena Vista Nose, are represented in the current data set. Some well stimulation practices remain relatively unchanged since the previous study. Well stimulation is mostly occurring in Kern County with the exception of a single well stimulation in Orange County. Almost all well stimulations are hydraulic fracturing. The current data set contains two acid fracturing treatments and one matrix acidizing treatment. The median number of chemicals added per well stimulation—excluding water and proppant—was previously 21; the number in the expanded data set is 20. Median water added per well stimulation was previously 89,000 gallons and is now 98,000 gallons. While this water use represents a 10% increase, water use for hydraulic fracturing in California is still lower than water use in other oil and gas fields. Chemical formulations appear to have shifted since the previous study. This shift may be related to a change in the predominant service company. We identified 26 chemicals for which the frequency of use has changed by more than 30%. The total number of chemicals used has also expanded. Previously, 178 unique chemicals were identified as being added to well stimulation fluids. The total number of unique chemicals is now 205. Analytical data available for base and recovered fluids has expanded. The number of base fluid samples has increased from 12 to 35 and the number of recovered fluid samples has increased from 1,078 to 2,166. The expanded data set is more ideal for an evaluation of indicator chemicals and comparisons across different formations. The analytical data for recovered fluid samples indicates that many ions, radioactive constituents, and organics are consistently observed, making these chemicals ideal for consideration as potential indicators of aquifer contamination.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Bifacial PV test-bed irradiance measurements

Data for 2 front-facing and 4 rear-facing IMT irradiance sensors placed on a scaled-down setup that replicate a PV array in a highly-reflective rooftop. The test-bed consist of 3 rows of 20x2ft aluminum sheets (the “panels”), supported by a Unistrut structure, with 6 irradiance sensors (IMT) measuring front and rear irradiance in the center module of the center row. High quality weather-station data available

14 SOLAR ENERGY↗
DOE OSTI2023

Nuclear Structure and Decay Data for A=44 Isobars

Experimental nuclear spectroscopic data are evaluated for 12 known nuclides of mass number A=44 (Si, P, S, Cl, Ar, K, Ca, Sc, Ti, V, Cr, Mn). Detailed evaluated information are presented for each reaction and decay. Recommended values combining all available data are provided for all spectroscopic properties of each level, γ-ray, and decay radiation. No excited states have yet been identified in 44 Si, 44 P, 44 Cr, and 44 Mn. Information for excited states in 44 Cl and 44 V are limited. Nuclides of 44 S, 44 Ar and 44 K have been studied via only a few reactions and decays, while 44 Ca, 44 Sc and 44 Ti are the most investigated nuclides through various reactions and decays. Evaluators note that the half-life of the g.s. of 44 S has been measured independently, with fairly good statistics, in three references, most precise being 100 ms 1 by 2004Gr20, but this value is in disagreement with the values of 125.5 ms 25 and 119 ms 6 by 2022Tr03, and 123 ms 10 by 1995So03. We adopted the unweighted average of this discrepant dataset. Another outstanding issue is that of the β + -delayed proton decay of 44 Cr g.s. to 44 V, where the T=2, 0 + IAS state in 44 V is expected to be strongly populated by a superallowed β transition, but has not been definitely identified as discussed in detail by 2020Fu05. A detailed study of 44 Cr decay is required to unravel the status of the T=2, 0 + IAS state in 44 V. Furthermore, this work supersedes earlier ENSDF evaluations of A=44 by 2011Ch39 and 1999Ca45.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Uranium Mononitride (UN) Handbook

Uranium Mononitride (UN) is being reexamined as a high temperature advanced nuclear fuel in many reactor applications due to its high thermal conductivity, high melting point, and high fissionable uranium density, among other desirable properties. A thorough review of the experimental data for the material and irradiation properties has been collected and is presented in this handbook. As an outcome of this review, in many cases, it is apparent that additional experimental verification must be conducted to verify the available data and to verify the suggested empirical correlations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Temperature Dependence of Band Gap Renormalization in High-T Sensor Materials via First-Principles and Experimental Corroboration

Understanding the temperature dependence of functional properties of high-T gas sensing materials is vital for their applications in combustion environments. The electron-phonon coupling that derives the electronic structure change with temperatures is a key property of interest as it affects other sensing responses. Herein, we assess the temperature dependence of band gap renormalization in metal oxides and perovskites by employing Allen-Heine-Cardona theory with first-principles simulations and corroborate with experimental observation. The calculated temperature-dependent band gap changes of these materials studied are in good agreement with in-house experimental data, proving that the theory can adequately predict renormalization on the band gap in the system of interest. The predicted and measured band gap variations are characterized using an analytical model, which can provide useful insights on the simulated zero-temperature band gaps. Based on the available data, a set of 53 metal oxides and perovskites were identified as potential high-T gas sensors. A machine learning model has been developed to predict the band-gap change by capturing the overall trend of the empirical parameters with respect to a reduced feature obtained by transforming the set of available physical features.

Park, Jongwoo↗
DOE OSTI2021

The Simons Observatory: gain, bandpass and polarization-angle calibration requirements for B-mode searches

We quantify the calibration requirements for systematic uncertainties for next-generation ground-based observatories targeting the large-angle B-mode polarization of the Cosmic Microwave Background, with a focus on the Simons Observatory (SO). We explore uncertainties on gain calibration, bandpass center frequencies, and polarization angles, including the frequency variation of the latter across the bandpass. We find that gain calibration and bandpass center frequencies must be known to percent levels or less to avoid biases on the tensor-to-scalar ratio r on the order of Δ r∼10-3, in line with previous findings. Polarization angles must be calibrated to the level of a few tenths of a degree, while their frequency variation between the edges of the band must be known to O(10) degrees. Given the tightness of these calibration requirements, we explore the level to which residual uncertainties on these systematics would affect the final constraints on r if included in the data model and marginalized over. We find that the additional parameter freedom does not degrade the final constraints on r significantly, broadening the error bar by O(10%) at most. We validate these results by reanalyzing the latest publicly available data from the collaboration within an extended parameter space covering both cosmological, foreground and systematic parameters. Finally, our results are discussed in light of the instrument design and calibration studies carried out within SO.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Correcting for reporting delay: an example using dengue fever data

One complication to infectious disease forecasting efforts is delay in reporting of cases, where real-time data often under-report the true disease burden. This pair of R scripts (1) provides example code demonstrating several strategies to account for the reporting delay and improve disease forecasts and (2) applies these methods using publicly-available data on dengue fever case reporting in Puerto Rico from 1990 to 2009.

Joann VanDervort, Lauren↗
DOE OSTI2025

Data from a multi-year targeted proteomics study of a longitudinal birth cohort of type 1 diabetes

The deployment of liquid chromatography-mass spectrometry-based plasma proteomics experiments in a large cohort is sparse, leading to a lack of data available for benchmarking, method development or validation. Comprised of 6,426 plasma analyses, The Environmental Determinants of Diabetes in the Young (TEDDY) proteomics validation study constitutes one of the largest targeted proteomics experiments in the literature to date. The proteomics data from this study were generated over the course of 2.5 years from over 900 study subjects, each providing up to 29 longitudinal samples. The data also includes 916 quality control samples. The targeted mass spectrometry assay was comprised of 694 peptides mapping to 167 proteins and the panel was measured in each subject and QC sample. The targeted proteomic dataset presented here can be used as a resource for new computational method development, such as for batch correction, as well as for benchmarking and comparing the performance of different methods/tools.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Bayesian inference of the dense-matter equation of state encapsulating a first-order hadron-quark phase transition from observables of canonical neutron stars

The remarkable progress in recent multimessenger observations of both isolated neutron stars (NSs) and their mergers has provided some of the much needed data to improve our understanding about the equation of state (EOS) of dense neutron-rich matter. Various EOSs with or without some kinds of phase transitions from hadronic to quark matter (QM) have been widely used in many forward modelings of NS properties. Direct comparisons of these predictions with observational data sometimes also using χ 2 minimizations have provided very useful constraints on the model EOSs. Furthermore, it is normally difficult to perform uncertain quantifications and analyze correlations of the EOS model parameters involved in forward modelings especially when the available data are still very limited.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Packages of Distributed Energy Technologies Demonstrating Demand Flexibility at Community Scale

The combination of increased electric load growth across all sectors, deferred electrical infrastructure investment, and other factors resulting in variable electric power supply, has created technical challenges to maintaining a resilient and reliable grid. Many federal, regional, and local efforts are in play to modernize the electric grid, including advancing building technologies and distributed energy resources (DERs) that are utilizing smarter controls to become responsive to both occupant and grid needs. This report reviews ten pilot projects demonstrating how groups of buildings combined with behind-the-meter (BTM) DERs such as electric vehicle (EV) charging, battery storage, flexible HVAC and domestic hot water systems, and photovoltaic systems can reliably and cost effectively provide grid services. Each of the ten pilot projects aim to deliver both energy efficiency and demand flexibility (DF) while supporting load growth. The ten demonstration teams are piloting flexible DER packages across diverse communities of residential and commercial buildings to address a variety of regional grid needs. The outcomes of these pilot projects will be used to inform future scaling through utility program development. This paper characterizes the ten teams, showcasing the decision-making process used by each group to develop their packages (Section 2), the grid services they plan to deliver (Section 3), the types of DER packages selected for deployment within building sectors (Section 4) and trends between building sector, DER types, and grid services In order to achieve community scale benefits, the pilot projects must utilize aggregated control mechanisms for coordinating buildings and DERs together. Several types of coordinated control architectures have evolved amongst the teams, influenced by use type, existing market conditions, and integration type. Three coordinated controls architectures have been characterized, highlighting their use cases, benefits, challenges, and tradeoffs in their design. These insights can aid utilities, control vendors, and developers in scaling community-level energy systems (Paul, 2024). Ultimately, the technology packages selected by the ten teams will be coordinated to provide power system services, also known as grid services. Insights from these demonstrations will be useful for grid operators, regulators, aggregators and other stakeholders as they look to deploy demand flexible resources as grid services in the future. The grid services that each team is targeting for demonstration are described in Section 3 and Section 4. Methods for evaluating the grid services have been described in the paper Metrics for Evaluating Grid Service Provision from Communities of Grid-interactive and Efficient Buildings and other DER (MacDonald, 2023). To identify technology packages for demonstration, Section 2 shows that project teams used a range of analysis approaches, including building energy modeling, AMI data analysis, cost-benefit frameworks, and utility pilot data. Some teams emphasized technical modeling to quantify grid impacts and demand reduction potential, while others prioritized economic evaluations, stakeholder input, or exploratory pilots to inform deployment decisions. This diversity reflects the need to tailor selection methods to project goals, available data, and organizational context. Section 5 discusses trends between the DER technologies deployed and the grid service provisions from each team. Residential buildings (multifamily and single family) lean towards technologies that enhance energy efficiency (e.g. weatherization upgrades, smart thermostats) and onsite power generation integration (e.g. solar PV). Commercial building demonstrations prioritize technologies that ensure operational reliability (e.g. battery storage) and centralized energy management systems and optimization solutions. Teams that are deploying controllable storage-based technologies are more likely to provide grid services that require a near real-time response. Teams incorporating load shifting technologies like smart thermostats with HEMs are likely to include energy markets participation and customer bill management offerings. Campus demonstrations are adopting diverse sets of DERs to emphasize renewable generation, paired with centralized control. This section also describes technologies that were considered during project planning but ultimately excluded from final deployment. These demonstrations reveal that effective DER package design should be tailored to building type, customer segment, and construction vintage. Multifamily buildings benefit from centralized HVAC upgrades and supervisory controls, while single-family homes are well-suited for individualized technologies like solar, storage, and smart home energy monitors. Commercial and campus settings prioritize EMIS integration and load optimization. New construction enables cost-effective integration of DER-ready infrastructure, whereas retrofits require deployments aligned with owner and tenant value streams. For utility program planners, early coordination with developers and building owners, paired with segmented and modular program offerings, can improve adoption, scalability, and grid impact.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Bioinformatic teaching resources - for educators, by educators - using KBase, a free, user-friendly, open source platform

Over the past year, biology educators and staff at the Department of Energy Systems Biology Knowledgebase (KBase) initiated a collaborative effort to develop a curriculum for bioinformatics education. KBase is a free and easily accessible data science platform that integrates many bioinformatics resources into a graphical user interface built upon reproducible analysis notebooks. KBase held conversations with college and high school instructors to understand how KBase could potentially support their educational goals. These conversations morphed into a working group of biological and data science instructors that adapted the KBase platform to their curriculum needs, specifically around concepts in Genomics, Metagenomics, Pangenomics, and Phylogenetics. The KBase Educators Working Group developed modular, adaptable, and customizable instructional units. Each instructional module contains teaching resources, publicly available data, analysis tools, and markdown capability to tailor instructions and learning goals for each class. The online user interface enables students to conduct hands-on data science research and analyses without requiring programming skills or their own computational resources (these are provided by KBase). Alongside these resources, KBase continues to work with instructors, supporting the development of additional curriculum modules. For anyone new to the platform, KBase, and the growing KBase Educators Organization, provides a community network, accompanied by community-sourced guidelines, instructional templates, and peer support to use KBase within a classroom whether virtual or in-person.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

New insights into the pole parameters of the Λ(1380), the Λ(1405) and the Σ(1385)

A coupled-channel S- and P-wave next-to-leading order chiral-unitary approach for strangeness S = –1 meson-baryon scattering is extended to include the new data from the KLOE and AMADEUS experiments as well as the Λπ mass distribution of the Σ(1385). The positions of the poles on the second Riemann sheet corresponding to the Σ(1385) pole and the Λ(1380) and Λ(1405) poles as well as the couplings of these states to various channels are calculated. We find that the resonance positions and branching ratios are on average determined with about 20% higher precision when including the KLOE and AMADEUS data. Additionally, for the first time, the correlations between the parameters of the poles are investigated and shown to be relevant. We also find that the Σ(1385) has negligible influence on the properties of the Λ states given the available data. Still, we identify isospin-1 cusp structures in the present solution in light of new measurements of π ± Λ line-shapes by the Belle collaboration.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Toward equitable environmental exposure modeling through convergence of data, open, and citizen sciences: an example of air pollution exposure modeling amidst increasing wildfire smoke

Exposure modeling is critical in environmental epidemiology and human health but may face challenges (e.g., skewed data, unequal error, context-insensitive validation, and computational demands). Modeling decisions reflect the intended use of the models and the values that modelers prioritize. We aimed to provide a conceptual framework and machine learning (ML) modeling protocols that address these issues. With 500m-gridded hourly PM 2.5 and O 3 levels in Illinois before, during, and after the 2023 Canadian wildfire season as a motivating example, we conducted modeling experiments to evaluate modeling methods, guided by three domains we propose based on theories of science: 1) Data Diversity, leveraging open and citizen science data to enhance inclusivity, parsimony, and representativeness; 2) Equitable Accuracy, ensuring fairly distributed uncertainties across subpopulations; and 3) Sustainable Modeling, balancing accuracy with reducing computational demands to promote accessibility for under-resourced researchers. Here, we found that ML with publicly available data can achieve high accuracy. Depending on methods, performance may vary substantially, even with identical input data. Large but skewed data may reduce performance. Misuse of cross-validation protocols can underestimate prediction error; although we observed R 2 s of ∼98 %, the modeled estimates varied significantly, indicating the need for careful model validation. By using new modeling protocols including representativeness-considered training and validation data and a new loss function, we achieved high agreement between estimates and ground-based measurements (e.g., R 2 = ∼90 % for PM 2.5 ; ∼80 % for O 3 ), equally distributed errors across sociodemographic strata and urban–rural divides, and reduction in computation time—from several weeks or months to a few days.

Exposure assessment↗
DOE OSTI2025

Subspace-Driven Learning for Anomaly Detection in Process Transients

Nuclear power plant (NPP) monitoring and diagnostic centers are actively investigating and implementing automated anomaly detection algorithms to help plants catch anomalies sooner, thereby preventing or reducing the duration of unexpected shutdowns. Current machine learning-based anomaly detection methods are expected to be highly effective during stable, full-power operations because NPPs typically operate as baseload power generators, meaning there are extensive operating data available from plant equipment. However, it is expected that anomaly detection methods will face significant challenges during transient conditions (i.e., when power output falls below full power) because plants only occasionally operate at these lower power levels, generating sparse transient operational data, and resulting in false alarms or missed detections. Here, to address this issue, transfer learning is used, which for this problem leverages knowledge (in the form of learned features) from stable, full-power operations to improve detection accuracy during transient conditions, even with limited data. In this effort, a novel subspace approach is developed to transfer a subset of the data features from full power operation to transients. This approach is validated through experiments using synthetic data and was found to outperform two baseline transfer learning approaches in anomaly detection performance across a range of amounts of transient data used in the training process.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗
DOE OSTI2021

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks

The Fokker--Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines, but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants and hence require the development of a data-driven modeling approach. When the data available is directly on the PDF, there exist methods for inverse problems that can be employed to infer the coefficients and thus determine the FP equation and subsequently obtain its solution. Herein, we address a more realistic scenario, where only sparse data are given on the particles' positions at a few time instants, which are not sufficient to accurately construct directly the PDF even at those times from existing methods, e.g., kernel estimation algorithms. To this end, we develop a general framework based on physics-informed neural networks (PINNs) that introduces a new loss function using the Kullback--Leibler divergence to connect the stochastic samples with the FP equation to simultaneously learn the equation and infer the multidimensional PDF at all times. In particular, we consider two types of inverse problems, type I, where the FP equation is known but the initial PDF is unknown, and type II, in which, in addition to the unknown initial PDF, the drift and diffusion terms are also unknown. In both cases, we investigate problems with either Brownian or Lévy noise or a combination of both. Here, we demonstrate the new PINN framework in detail in the one-dimensional (1D) case, but we also provide results for up to five dimensions demonstrating that we can infer both the FP equation and dynamics simultaneously at all times with high accuracy using only very few discrete observations of the particles.

97 MATHEMATICS AND COMPUTING↗