Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Data processing and standardization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An SU(5) × U(1)' SUSY GUT with a “vector-like chiral” fourth family to fit all low energy data, including the muon g – 2

An additional generation of quarks and leptons and their SUSY counterparts, which are vector-like under the Standard Model gauge group but are chiral with respect to the new U(1) 3–4 gauge symmetry, are added to the Minimal Supersymmetric Standard Model (MSSM). We show that this model is a GUT and unifies the three SM gauge couplings and also the additional U(1) 3–4 coupling at a GUT scale of ≈ 5 × 10 16 GeV and explains the experimentally observed deviation of the muon g – 2. We also fit the quark flavor changing processes consistent with the latest experimental data and look at the effect of the new particles on the W boson mass without obviously conflicting with the observed masses of particles, CKM matrix elements, neutrino mixing angles, their mass differences, and the lepton-flavor violating bounds. This model predicts sparticle masses less than 25 TeV, with a gluino mass ≈ 2.3 – 3 TeV consistent with constraints, and one of the neutralinos as the LSP with a mass of ≈ 480 – 580 GeV, which is a potential dark matter candidate. The model is string theory motivated and predicts the VL quarks, leptons, a massive Z' and two Dirac neutrinos at the TeV scale and the branching ratios of μ → eγ, τ → μγ and τ → 3μ with BR(μ → eγ) within reach of future experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Commercial, industrial, and institutional discount rate estimation for efficiency standards analysis: Sector-level data 1998–2023

Underlying each of the U.S. Department of Energy’s (DOE’s) federal appliance and equipment energy conservation standards are a set of complex analyses of the projected costs and benefits of regulation. Any new or amended standard must be designed to achieve significant additional energy conservation, provided that it is technologically feasible and economically justified (42 U.S.C. 6295(o)(2)(A)). DOE determines economic justification based on whether the benefits exceed the burdens, considering a variety of factors, including the economic impact of the standard on consumers of the product and the savings in lifetime operating cost compared to any increase in price or maintenance expenses (42 U.S.C. 6295(o)(2)(B)). As part of this determination, DOE conducts a life-cycle cost (LCC) analysis, which models the combined impact of appliance first cost and operating cost changes on a representative commercial building sample to identify the fraction of customers achieving LCC savings or incurring net cost at the considered efficiency levels. Thus, the commercial discount rate value(s) used to calculate the present value of energy cost savings within the LCC model implicitly plays a role in estimating the economic impact of potential standard levels. This report provides an in-depth discussion of the commercial discount rate estimation process relying on the Capital Asset Pricing Model (CAPM) to estimate a business’ cost of equity, and by adding a risk adjustment factor to the risk-free rate associated with long-term U.S. Treasury bonds to estimate their cost of debt. It is an update to previous reports on estimating commercial discount rates from firm-level and sector-level financial data (e.g., Fujita, 2021, 2016). Major topics covered in this report include the following: • Discount rate estimation methods and rationale • Data sources used and data limitations • Discount rate distributions for use in standards analysis • Discount rate estimation methods and distributions specific to the small business subgroup analysis.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2016

Towards improved and more routine Earth system model evaluation in CMIP

The Coupled Model Intercomparison Project (CMIP) has successfully provided the climate community with a rich collection of simulation output from Earth system models (ESMs) that can be used to understand past climate changes and make projections and uncertainty estimates of the future. Confidence in ESMs can be gained because the models are based on physical principles and reproduce many important aspects of observed climate. More research is required to identify the processes that are most responsible for systematic biases and the magnitude and uncertainty of future projections so that more relevant performance tests can be developed. At the same time, there are many aspects of ESM evaluation that are well established and considered an essential part of systematic evaluation but have been implemented ad hoc with little community coordination. Given the diversity and complexity of ESM analysis, we argue that the CMIP community has reached a critical juncture at which many baseline aspects of model evaluation need to be performed much more efficiently and consistently. We provide a perspective and viewpoint on how a more systematic, open, and rapid performance assessment of the large and diverse number of models that will participate in current and future phases of CMIP can be achieved, and announce our intention to implement such a system for CMIP6. Accomplishing this could also free up valuable resources as many scientists are frequently "re-inventing the wheel" by re-writing analysis routines for well-established analysis methods. A more systematic approach for the community would be to develop and apply evaluation tools that are based on the latest scientific knowledge and observational reference, are well suited for routine use, and provide a wide range of diagnostics and performance metrics that comprehensively characterize model behaviour as soon as the output is published to the Earth System Grid Federation (ESGF). The CMIP infrastructure enforces data standards and conventions for model output and documentation accessible via the ESGF, additionally publishing observations (obs4MIPs) and reanalyses (ana4MIPs) for model intercomparison projects using the same data structure and organization as the ESM output. This largely facilitates routine evaluation of the ESMs, but to be able to process the data automatically alongside the ESGF, the infrastructure needs to be extended with processing capabilities at the ESGF data nodes where the evaluation tools can be executed on a routine basis. Efforts are already underway to develop community-based evaluation tools, and we encourage experts to provide additional diagnostic codes that would enhance this capability for CMIP. And, at the same time, we encourage the community to contribute observations and reanalyses for model evaluation to the obs4MIPs and ana4MIPs archives. The intention is to produce through the ESGF a widely accepted quasi-operational evaluation framework for CMIP6 that would routinely execute a series of standardized evaluation tasks. Over time, as this capability matures, we expect to produce an increasingly systematic characterization of models which, compared with early phases of CMIP, will more quickly and openly identify the strengths and weaknesses of the simulations. This will also reveal whether long-standing model errors remain evident in newer models and will assist modelling groups in improving their models. Finally, this framework will be designed to readily incorporate updates, including new observations and additional diagnostics and metrics as they become available from the research community.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Estimating active layer thickness and volumetric water content from ground penetrating radar measurements in Barrow, Alaska

Ground penetrating radar (GPR) has emerged as an effective tool for estimating active layer thickness (ALT) and volumetric water content (VWC) within the active layer. In August 2013, we conducted a series of GPR and probing surveys using a 500 MHz antenna and metallic probe around Barrow, Alaska. Here, we collected about 15 km of GPR data and 1.5 km of probing data. We describe the GPR data processing workflow from raw GPR data to the estimated ALT and VWC. We then include the corresponding uncertainties for each measured and estimated parameter. The estimated average GPR-derived ALT was 41 cm, with a standard deviation of 9 cm. The average probed ALT was 40 cm, with a standard deviation of 12 cm. The average GPR-derived VWC was 0.65, with a standard deviation of 0.14.

58 GEOSCIENCES↗
DOE OSTI2018

Advancing our predictive understanding of river corridor exchange

Despite decades of research, we lack an accurate framework to predict and manage hydrologic exchange in the river corridor and the associated ecosystem services and functions at the scales of stream reaches and entire networks. While many individual studies have been conducted to investigate specific mechanisms, they have not been synthesized to account for heterogeneity in space, nonstationarity, and multiscale feedbacks that typify the river corridor. As a result, contradictory predictions of exchange flux, geometry, and timescale are prevalent in the literature. We attribute these contradictions to (a) failure to account for multiscale feedbacks and (b) uncertainty in the information content of common measurement methods. Here, we apply the concept of interacting multiscale spatial and time‐variable domains to the river corridor to demonstrate why more complete multiscale characterization is necessary to achieve predictive understanding. Next, we highlight uncertainties and inconsistencies in measurement methods which may obfuscate our understanding of river corridor exchange. Finally, we briefly outline four necessary advances to achieve predictive understanding of river corridor exchange: standardization of metadata, critical evaluation of the information content and support volumes for measurement techniques, multiscale model‐data integration, and advancing theoretical models of river corridor exchange. This article is categorized under: Science of Water > Hydrological Processes Water and Life > Nature of Freshwater Ecosystems Science of Water > Methods

Ward, Adam S.↗
DOE OSTI2018

Search for the pair production of third-generation squarks with two-body decays to a bottom or charm quark and a neutralino in proton–proton collisions at $\sqrt{s}$ = 13 TeV

Results are presented from a search for the pair production of third-generation squarks in proton–proton collision events with two-body decays to bottom or charm quarks and a neutralino, which produces a significant imbalance in the transverse momentum. The search is performed using a sample of proton–proton collision data at s=13TeV recorded by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9 fb−1 . No statistically significant excess of events is observed beyond the expected contribution from standard model processes. Exclusion limits are set in the context of simplified models of bottom or top squark pair production. Models with bottom squark masses up to 1220 GeV are excluded at 95% confidence level for light neutralinos, and models with top squark masses of 510 GeV are excluded assuming that the mass splitting between the top squark and the neutralino is small.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

L-TERRA [SWR-15-34]

Lidar (light detection and ranging) instruments are often used in wind energy studies in place of meteorological towers, as they can collect measurements at higher heights than met towers and are more easily moved to different parts of a site. While lidars can accurately measure mean wind speeds, they frequently measure different values of turbulence intensity (TI) than would be measured by a cup anemometer on a tower. Discrepancies in TI values are caused by several factors, including instrument noise and volume averaging. The inability of lidars to accurately measure turbulence is a significant barrier to replacing met towers with lidars in the future. There is currently no accepted standard process for quantifying and removing these errors in lidar TI measurements. The Software is an error reduction algorithm for lidar-measured turbulence. The algorithm is trained using co-located lidar and meteorological tower data. Lidar-measured parameters, such as wind speed, shear, and TI, will be used to predict the difference between the lidar- and tower-measured TI. The algorithm will be disseminated as a set of computer code that can be used by lidar users and manufacturers to correct lidar TI data in real time or in post-processing.

Newman, Jennifer↗
DOE OSTI2022

Data for: Patel et al. Carbon flux estimates are sensitive to data source: A comparison of field and lab temperature sensitivity data

This dataset contains data and code used for the paper "Carbon flux estimates are sensitive to data source: A comparison of field and lab temperature sensitivity data" [DOI COMING SOON]A large literature exists on mechanisms driving soil production of the greenhouse gases CO2 and CH4. Measurements of these gases’ fluxes are often performed using closed-chamber incubations in the laboratory or in situ, i.e., in the field. Although it is common knowledge that measurements obtained through field studies vs. laboratory incubations can diverge because of the vastly different conditions of these environments, few studies have systematically examined these patterns. It is crucial to understand the magnitude and reasons for any differences, as these data are used to parametrize and benchmark ecosystem- to global-scale models, which are then susceptible to the biases of the source data. Here, we specifically examine how greenhouse gas measurements may be influenced by whether the measurement/incubation was conducted in the field vs. laboratory, focusing on CO2 and CH4 measurements. We use Q10 of greenhouse gas flux (temperature sensitivity) for our analyses, because of the ubiquity of this metric in biological and Earth system sciences and its importance to many modeling frameworks. We predicted that laboratory measurements would be less variable, but also less representative of true field conditions. However, there was greater variability in the Q10 values calculated from lab-based measurements of CO2 fluxes, because lab experiments explore extremes rarely seen in situ, and reflect the physical and chemical disturbances occurring during sampling, transport, and incubation. Overall, respiration Q10 values were significantly greater in laboratory incubations (mean = 4.19) than field measurements (mean = 3.05), with strong influences of incubation temperature and climate region/biome. However, this was in part because field measurements typically represent total respiration (Rs), whereas lab incubations typically represent heterotrophic respiration (Rh), making direct comparisons difficult to interpret. Focusing only on Rh-derived Q10, these values showed almost identical distributions across laboratory (n = 1110) and field (n = 581) experiments, providing strong support for using the former as an experimental proxy for the latter, although we caution that geographic biases in the extant data make this conclusion tentative. Due to a smaller sample size of CH4 Q10 data, we were unable to perform a comparable robust analysis, but we expect similar interactions with soil temperature, moisture, and environmental/climatic variables. Our results here suggest the need for more concerted efforts to document and standardize these data, including sample and site metadata. This dataset contains a compressed (.zip) archive of the data and R scripts used for this manuscript. The dataset includes files in .csv format, which can be accessed and processed using MS Excel or R. This archive can also be accessed on GitHub at https://github.com/kaizadp/field_lab_q10 (DOI: 10.5281/zenodo.7106554).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Baseline Evaluation of Eddy Current Testing for PWSCC Susceptible Materials

This technical letter report (TLR) summarizes technical efforts focused on assessments of eddy current testing (ET) examinations using various mockups for obtaining baseline surface and subsurface conditions on materials susceptible to primary water stress corrosion cracking (PWSCC). The scope of this work included nondestructive evaluation characterization of weld surfaces on mockups that were identified for application of various surface peening approaches. All of the work reported here was conducted prior to planned peening of these surfaces to evaluate pre-peening conditions, and subsequently compare the baseline ET results with post-peening conditions. The overall objective of this work was to demonstrate the effectiveness of employing ET for detecting near/sub-surface defects on mockups in support of peening assessments for surface stress improvement and mitigation of PWSCC in these materials. The U.S. Nuclear Regulatory Commission has communicated their expectations to industry for eddy current inspections of peened, inlayed, and onlayed dissimilar metal welds and is interested in better understanding detection performance and sensitivity of ET techniques to support the development of a technical foundation for detection and sizing limits, effective ET qualification requirements, alternate inspections or programs for evaluating PWSCC mitigation processes, and development of ET acceptance standards that can be referenced in the appropriate American Society of Mechanical Engineers Section XI Code Case (N-770-X). This TLR provides a technical discussion focused on the ET data obtained, the analysis, and conclusions drawn from surface examinations of various plate standards and actual components extracted from cancelled nuclear power plants.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Applying Waveform Correlation to Mining Blasts Using a Global Sparse Network

Agencies that monitor for underground nuclear tests are interested in techniques that automatically characterize mining blasts to reduce the human analyst effort required to produce high-quality event bulletins. Waveform correlation is effective in finding similar waveforms from repeating seismic events, including mining blasts. We report the results of an experiment that uses waveform templates recorded by multiple International Monitoring System stations of the Comprehensive Nuclear-Test-Ban Treaty for up to 10 years prior to detect and identify mining blasts that occur during single weeks of study. We discuss approaches for template selection, threshold setting, and event detection that are specialized for mining blasts and a sparse, global network. We apply the approaches to two different weeks of study for each of two geographic regions, Wyoming and Scandinavia, to evaluate the potential for establishing a set of standards for waveform correlation processing of mining blasts that can be effective for operational monitoring systems with a sparse network. We compare candidate events detected with our processing methods to the Reviewed Event Bulletin of the International Data Centre to develop an intuition about potential reduction in analyst workload.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2020

Applying Waveform Correlation to Mining Blasts Using a Global Sparse Network

Agencies that monitor for underground nuclear tests are interested in techniques that automatically characterize mining blasts to reduce the human analyst effort required to produce high-quality event bulletins. Waveform correlation is effective in finding similar waveforms from repeating seismic events, including mining blasts. We report the results of an experiment that uses waveform templates recorded by multiple International Monitoring System stations of the Preparatory Commission for the Comprehensive Nuclear-Test-Ban Treaty Organization for up to 10 years prior to the time period of interest to detect and identify mining blasts that occur during single weeks of study. We discuss approaches for template selection, threshold setting, and event detection that are specialized for mining blasts and a sparse, global network. We apply the approaches to two different weeks of study for each of two geographic regions, Wyoming and Scandinavia, to evaluate the potential for establishing a set of standards for waveform correlation processing of mining blasts that can be effective for operational monitoring systems with a sparse network. We compare candidate events detected with our processing methods to the Reviewed Event Bulletin of the International Data Centre to develop an intuition about potential reduction in analyst workload.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2024

Offline Power Systems Applications Enabled by Phasor Measurement Units: Technical Assistance to the Power Sectors of Southeast Asia

This report provides a brief overview of several offline (non-real-time) applications facilitated by high-resolution time-synchronized measurements recorded by phasor measurement units (PMUs). The high reporting rate and time-synchronization of PMU records provide a detailed view of power system dynamics, enabling electric utilities to obtain a better understanding of their systems. In this report, the following applications have been reviewed: Power plant model validation, System model validation, Ringdown oscillation analysis, Frequency response analysis, Postmortem analysis of disturbance events Along with a brief technical background of the applications above, applicable North American Electric Reliability Corporation (NERC) standards have been discussed, and examples of implementation in North American organizations have been provided. Implementing several of the discussed applications may need a preliminary stage of data gathering from multiple entities, and several frameworks and process flows have been formulated by organizations around the world for this purpose. However, the data-gathering stage has not been considered in the scope of the present report.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

High-frequency Data Integration for Landscape Model Calibration of Carbon Fluxes Across Diverse Tidal Marshes

Terrestrial Aquatic Interfaces (TAIs), and tidal wetlands in particular, store large amounts of carbon yet are not well represented in Earth System Models (ESMs). Predictions of carbon cycling and greenhouse gas (GHG) emissions in tidal wetlands are highly uncertain. Eddy covariance (EC) towers provide ecosystem-scale GHG flux data at a temporal resolution (every 30min) that is helpful for parameterizing and improving mechanistic realism in ESMs. We propose to use a network of eddy covariance towers and standardized ancillary data streams, along with mesocosm experiments and statistical analyses, across diverse tidal wetlands of North America to develop and improve biogeochemical modeling at the TAI. Our overarching objective is to improve understanding and process-based modeling of gross primary productivity (GPP) and CH4 emission responses, both non-linear and asynchronous, to stressors including plant inundation, disturbance, salinity and nitrogen loading.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Global Simulation of Bioenergy Crop Productivity: Analytical Framework and Case Study for Switchgrass

A global energy crop productivity model that provides geospatially explicit quantitative details on biomass potential and factors affecting sustainability would be useful, but does not exist now. This study describes a modeling platform capable of meeting many challenges associated with global-scale agro-ecosystem modeling. We designed an analytical framework for bioenergy crops consisting of six major components: (i) standardized natural resources datasets, (ii) global field-trial data and crop management practices, (iii) simulation units and management scenarios, (iv) model calibration and validation, (v) high-performance computing (HPC) simulation, and (vi) simulation output processing and analysis. The HPC-Environmental Policy Integrated Climate (HPC-EPIC) model simulated a perennial bioenergy crop, switchgrass (Panicum virgatum L.), estimating feedstock production potentials and effects across the globe. This modeling platform can assess soil C sequestration, net greenhouse gas (GHG) emissions, nonpoint source pollution (e.g., nutrient and pesticide loss), and energy exchange with the atmosphere. It can be expanded to include additional bioenergy crops (e.g., miscanthus, energy cane, and agave) and food crops under different management scenarios. The platform and switchgrass field-trial dataset are available to support global analysis of biomass feedstock production potential and corresponding metrics of sustainability.

Kang, Shujiang↗
DOE OSTI2018

Ambient monitoring to inform the protection of beneficial uses and achieve water quality goals in Sinclair and Dyes Inlets, Puget Sound, WA

Currently discharge limits enforced under the Clean Water Act are focused on meeting water quality standards at the end of the pipe and environmental performance is measured based on meeting the discharge limits; but meeting discharge limits has very little to do with achieving water quality goals for coastal and estuarine ecosystems. Therefore, an effective monitoring and assessment program is needed to assess continuous process improvement, evaluate the ecological conditions, and provide metrics that can inform effective management of coastal and estuarine water quality. As part of an integrated Environmental Investment (ENVVEST) project for Sinclair and Dyes Inlets (ENVVEST 2006; Johnston et al. 2009) a network of monitoring stations was established to characterize environmental conditions, assess potential impacts, and establish environmental quality trends within the Inlets. Water, sediment, and biota monitoring locations were selected that were co-located near suspected sources (industrial, waste water, and stormwater outfalls; marinas, stream mouths, and other sources) or were representative of ambient marine and nearshore conditions. Water column stations and effluents from industrial outfalls were sampled seasonally for trace metals (Cd, Cr, Cu, Hg, Pb, and Zn) using analytical procedures appropriate for seawater (Strivens, Brandenberger and Johnston, 2018), conventional parameters (salinity, dissolved and total organic carbon, total and suspended solids, dissolved O2, pH, turbidity, NO2+NO3, NH4, N, and P), and toxicity. Effluent and water column toxicity tests included mysid shrimp (Americamysis bahia) 96 hr survival, sand dollar (Dendraster excentricus) or purple sea urchin (Strongylocentrotus purpuratus) 96 hr embryo development, QwikLite – dinoflagellate (Pyrocystis lunula) 24 hr bioluminescence response, mussel larvae (Mytilus sp.) 48 hr larvae survival and development, and kelp (Macrocystis pyrifera) 48 hr growth and germination. Additionally, indigenous mussels (Mytilis spp.) were sampled biennially for contaminant residues of metals, polycyclic aromatic hydrocarbons (PAHs), polychlorinated biphenyls (PCBs), lipid content, and stable isotopes of C and N. The mussel data were compared to benchmarks of ecological effects (Johnston et al. 2007, Applied Biomonitoring 2009), samples obtained from a local seafood market harvested from Penn Cove on Whidbey Island (PKPLPC), and data from the national mussel watch status and trends monitoring program (Kimbrough et al. 2008). Results from 2009-2016 showed that dissolved metals nearly always met water quality standards and that water quality in Navy nearshore areas appeared to improve after best management practices (BMPs) for industrial process improvements (US Navy 2012) were completed in Sept. 2013 (Figure 1). In general, toxicity from exposure to whole effluent samples was not observed and ambient water samples were not toxic to test organisms, except that ambient toxicity was only observed during the presence of algal blooms which showed that toxicity was highly correlated with the abundance of the toxic algae Gymnodinium splendens (Rosen et al. 2009). Overall, mussel tissue residues were below benchmarks at most locations (Figure 2), however there were locations that had elevated levels of PAHs, PCBs, Hg, and Cu. Results from the monitoring provide metrics that are being used to assess progress toward meeting environmental quality goals for the watershed.

ENVVEST, PSEMP↗
DOE OSTI2017

Development of an update to ISA S67.04 and RP 67.04: 'Setpoints for Nuclear Safety-Related Instrumentation for Nuclear Power Plants' - 146

The purpose of this paper is to provide an overview of the update to International Society of Automation (ISA) Standard ISA S67.04 - 2006, 'Setpoints for Nuclear Safety-Related Instrumentation for Nuclear Power Plants', and ISA RP 67.04-2000, 'Methodologies for Determination of Setpoints for Nuclear Safety-Related Instrumentation'. Significant advances have occurred on the utility, Nuclear Steam Supply System (NSSS) vendor, and regulatory side, related to improved techniques for analysis and monitoring. These and other changes, including those related to Technical Specifications and surveillance interval extensions, are being included in the latest update to this primary standard for setpoint control in nuclear plants in the U.S. and around the world. In 2016, the ISA S67.04 Committee agreed to proceed with a revision to this Standard and Recommended Practice, with major updates in the following areas: 1. Definitions - Updates for improved definitions based on TSTF-493, Rev 4, RIS-2006-17 and NRC updated Regulatory Guide (RG) 1.105 2. 95/95 - Updates based on improved guidance on the development of component input data and analysis techniques for 95% probability/95% confidence calculations 3. TSTF-493, RIS 2006-17 updates for Technical Specification input and to support changes 4. NRC input from updates in the Regulatory Guide 1.105 and Branch Technical Position BTP-7-12 revision process. 5. Improved guidance from the Electric Power Research Institute (EPRI) in References 7, 8 and 9. These standards are being updated with a new version anticipated to be issued as a draft in 2017 and submitted for ISA approval in 2019. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve forward, inverse, and mixed stochastic problems in a unified manner based on a limited number of scattered measurements. Unlike standard GANs relying solely on data for training, here we encoded into the architecture of GANs the governing physical laws in the form of stochastic differential equations (SDEs) using automatic differentiation. In particular, we applied Wasserstein GANs with gradient penalty (WGAN-GP) for its enhanced stability compared to vanilla GANs. We first tested WGAN-GP in approximating Gaussian processes of different correlation lengths based on data realizations collected from simultaneous reads at sparsely placed sensors. We obtained good approximation of the generated stochastic processes to the target ones even if there is a mismatch between the input noise dimensionality and the effective dimensionality of the target stochastic processes. We also studied the overfitting issue for both the discriminator and the generator, and we found that overfitting occurs also in the generator in addition to the discriminator as previously reported. Subsequently, we considered the solution of elliptic SDEs requiring approximations of three stochastic processes, namely the solution, the forcing, and the diffusion coefficient. Here again, we assumed data collected from simultaneous reads at a limited number of sensors for the multiple stochastic processes. Furthermore, three generators were used for the PI-GANs: two of them were feed forward deep neural networks (DNNs), while the other one was the neural network induced by the SDE. For the case where we have one group of data, we employed one feed forward DNN as the discriminator, while for the case of multiple groups of data we employed multiple discriminators in PI-GANs. We solved forward, inverse, and mixed problems without changing the framework of PI-GANs, obtaining both the means and the standard deviations of the stochastic solution and the diffusion coefficient in good agreement with benchmarks. In this work, we have demonstrated the effectiveness of PI-GANs in solving SDEs for about 120 dimensions. In principle, PI-GANs could tackle very high dimensional problems given more sensor data with low-polynomial growth in computational cost.

97 MATHEMATICS AND COMPUTING↗