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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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The catalog-to-cosmology framework for weak lensing and galaxy clustering for LSST

We present TXPipe, a modular, automated and reproducible pipeline for ingesting catalog data and performing all the calculations required to obtain quality-assured two-point measurements of lensing and clustering, and their covariances, with the metadata necessary for parameter estimation. The pipeline is developed within the Rubin Observatory Legacy Survey of Space and Time (LSST) Dark Energy Science Collaboration (DESC), and designed for cosmology analyses using LSST data. In this paper, we present the pipeline for the so-called 3x2pt analysis -- a combination of three two-point functions that measure the auto- and cross-correlation between galaxy density and shapes. We perform the analysis both in real and harmonic space using TXPipe and other LSST-DESC tools. We validate the pipeline using Gaussian simulations and show that it accurately measures data vectors and recovers the input cosmology to the accuracy level required for the first year of LSST data under this simplified scenario. We also apply the pipeline to a realistic mock galaxy sample extracted from the CosmoDC2 simulation suite (Korytov et al. 2019). TXPipe establishes a baseline framework that can be built upon as the LSST survey proceeds. Furthermore, the pipeline is designed to be easily extended to science probes beyond the 3x2pt analysis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Fast and Accurate Core Analysis by the Full-Immersion Pressure-Pulse Decay: Part 2—Practice and Demonstration

Summary This study continues the work of presenting a novel approach for making petrophysical assessments of tight core samples. This method, the full-immersion pressure-pulse decay (Hannon 2019), involves applying a rapid increase in pressure in a chamber surrounding the entire outer surface area of a cylindrical sample, shutting the system in, and monitoring the pressure decay in the chamber as it reaches a new equilibrium. A precursor article covered the numerical simulator designed to model flow through the sample, demonstrating its performance and accuracy in addition to providing a first-order comparison between the speed and shape of the pressure-decay responses of the full-immersion method with those of other similar transient methods. This study covers the parameter-estimation procedure and experimental verification through a proof-of-concept laboratory investigation. The investigations provided here demonstrate that under appropriate, achievable experimental conditions, the pressure data can be analyzed in such a way that returns an estimate of the porosity and apparent permeabilities both parallel and perpendicular to bedding from a single test performed on a single cylindrical sample. After determining these experimental conditions (the uniqueness window), this report outlines a data-inversion strategy to estimate the petrophysical properties (porosity, horizontal permeability, and vertical permeability) from each test. This strategy is put to the test through comparisons with measurements performed by a commercial core laboratory. A common set of samples recovered from an outcrop of a tight-gas sandstone formation were investigated using the full-immersion method, and their results are compared with those from conventional steady-state measurement procedures performed by the commercial laboratory. Comparisons between petrophysical characterizations of these samples, which had permeabilities between 25 nd and 2.3 μd, demonstrated close agreement in most cases. However, whereas steady-state measurements performed at the professional laboratory required 4 to 5 hours of testing time per measurement of a single permeability, similar assessments using the full-immersion technique, requiring approximately 5 to 10 minutes to complete, returned estimates of the horizontal and vertical permeability simultaneously. Additional analyses are provided to determine principal reasons of discrepancies in instances where agreement was not as strong. Based on lessons learned from these experiences, the report closes with suggestions on areas of improvement in the experimental approach. Once complete, these developments should propel this technology to fill a critical need to determine petrophysical properties (porosity and permeability) of tight rocks in a time-efficient manner and in a way that does not compromise their accuracy.

Energy & Fuels↗
DOE OSTI2022

Isotherm Modeling and Techno-Economic Analysis of Contactor Technologies for New Tetraamine-Appended MOF for NGCC Applications

Recently, a family of tetraamine-functionalized metal-organic frameworks (MOF) has been reported as promising sorbent materials for capturing CO2 from flue gas conditions relevant to natural gas combined cycle (NGCC) applications. The main advantages of these materials are their two-step cooperative CO2 adsorption, which gives rise to unusual two step-shaped CO2 adsorption profiles and their high thermal stability. This work presents the modelling of the two-transition isotherm of the tetraamine-appended MOF, N,N'-bis(3-aminopropyl)-1,4-diaminobutane (3-4-3)-appended Mg2(dobpdc), and the techno-economic analysis (TEA) of carbon capture processes utilizing this sorbent. Due to the unusual isotherm shapes of the experimental CO2 adsorption data for tetraamine-appended Mg2(dobpdc) and the strong nonlinearity of CO2 loading with respect to temperature and pressure, we tested two different models which use logistic functions for representing the different isotherm behaviors in the different pressure ranges. The first model uses the quadratic isotherm model in the low-pressure region, the Langmuir isotherm model in the middle pressure range, and the dual site Langmuir isotherm model in the high-pressure range. To model the transition between regions we used the arctangent functions independent of temperature and the thermal effect was accounted by using the Clausius-Clapeyron relation]. The second model is an extension of the weighted dual-site Langmuir isotherm model presented by Hughes et al.. In this extended model, the dual-site Langmuir isotherm is employed in the three transition regions, using temperature-dependent logistic functions to activate or deactivate the isotherm model in the low, middle, and high-pressure ranges. Both models fit the experimental data quite well with root mean squared errors (RMSE’s) of 0.41 and 0.17 for model 1 and model 2, respectively. Since model 2 resulted in a lower RMSE, it was leveraged for the development of the gas/solid contactor models used by the TEA. Specifically, two different contactor models, an axial-flow fixed bed and moving bed contactor, were developed as part of this work. These models are dynamic, pressure-driven, and consist of mass, energy, and momentum conservation equations. A kinetic model was also developed by performing parameter estimation using experimental fixed bed breakthrough data. These models are then used to simulate CO2 capture processes from the flue gas generated from a ~600 gross MW NGCC power plant. A cost model was developed which considers the capital cost of the reactors and the significant operating costs such as steam and electricity. Using NETL’s Framework for the Optimization and Quantification of Uncertainty of Uncertainty and Surrogates tool (FOQUS), which has the capability of linking models built using numerous modelling platforms with derivative-free optimization solvers, a techno-economic optimization of the carbon capture processes was performed which minimizes the cost of capture.

Caballero, Daison↗
DOE OSTI2020

Benchmarking and Improving Microbial-explicit Soil Biogeochemistry Models

Soils represent the largest terrestrial carbon pool on Earth. Yet emerging theories regarding stabilization of soil organic matter remain poorly represented in global-scale models; thus, underestimating the true uncertainty associated with potential terrestrial carbon cycle – climate feedbacks. With this project we created a testbed to compare and evaluate soil biogeochemical models (W. Wieder at the Univ. of CO, Boulder), data synthesis (R. Phillips, Indiana Univ.) and parameter estimation (S Allison, Univ. CA Irvine) to quantify uncertainty associated with potential soil C changes. This project resulted in 14 Presentations, 14 Publications and helped support the training of three graduate students. A significant accomplishment with this work was the creation of a soil biogeochemical testbed, which forces three soil carbon models (CASA, MIMICS, and CORPSE) with common environmental drivers.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A viscoelastic viscoplastic damage model (VPVD)

This report documents the development, implementation, and parameter estimation procedures for aviscoelastic-viscoplastic-viscodamage model. This model is being developed to improve the predictive accuracy of simulations involving plastic bonded explosives (PBX). A representative PBX is PBX9501, which is 95% by weight HMX, 2.5% estane binder and 2.5% nitroplasticizer. Mechanical deformation of this material is primarily accommodated by straining of the polymer binder and rearranging the relatively rigid HMX crystals.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2021

Vibrational Energy Harvesting Using a Cantilever Model

Vibrational energy harvesting (VEH) is a method of capturing incidental mechanical vibrational energy and converting it to electrical energy. This is enabled by two technologies: Electromagnetic induction via a cantilever or piezoelectric devices. When designing a VEH system, a fast forward model is desired for response determination and optimal parameter estimation. An ordinary different equation (ODE) system model is developed for the cantilever system based upon the derivations of [1] and [2], and compared with a full electromechanical COMSOL model.

42 ENGINEERING↗
DOE OSTI2021

Open Source Fault-tolerant Grid Frequency Measurement for Solar Inverters

The Discrete Fourier transform (DFT) based measurement algorithms are one of the most common measurement algorithms for grid parameter estimation such as rms, phase angle, frequency. Over the past few years, many DFT based algorithms have been developed to enhance its measurement accuracy under steady-state and/or dynamic grid conditions. For example, an adaptive band-pass filter utilizing exponential modulation filter has been proposed to reduce measurement errors at the presence of large frequency deviations. Measurement accuracy of different algorithms including FIR filter, extended Kalman filtering (EKF), and enhanced DFT method have been compared in detail under different grid conditions. Two artificial signals that have 90-degree phase difference were constructed by the Clarke transformation to address the frequency spectrum leakage of DFT. A multi-module approach was developed to enhance both steady-state and dynamic measurement accuracies, in which each module was developed to eliminate some specific errors. Besides DFT-based measurement algorithms, some signal model-based algorithms have been developed to further improve the accuracy under dynamic conditions. However, a key drawback of the state-of-the-art algorithms is that they cannot perform measurements accurately during system transient faults. In the Blue Cut Fire event, there was a phase angle jump of about 26 degrees in the voltage waveform during the transient fault. The phase angle jump fault will cause waveform discontinuity, and these algorithms will fail to provide reliable measurements during this period because they typically assume the waveform to be measured is continuous, no matter what method (DFT, PLL, EKF, FIR, or Taylor WLS) is used for estimation. In fact, the measurement errors during the system transient faults like phase-jump is not required in the IEEE Standard. As a result, although a measurement instrument can pass the strict IEEE Standard, it could still be the source of the problem in the future if we have similar system transient faults, which could happen again. Therefore, developing the fault-tolerant measurement technology is the key to solve the problem.

14 SOLAR ENERGY↗
DOE OSTI2021

Developing an Automated Uncertainty Quantification Tool to Improve Watershed-Scale Predictions of Water and Nutrient Cycling

Managing the flow of water, nutrients, and contaminants in watersheds is vital to addressing pressing issues related to water scarcity, access to clean drinking water, energy production, resilience to natural and anthropogenic perturbations, and ecological restoration. Decisions about the management of watersheds critically depend on the accuracy with which the flow of water and chemicals through the watershed can be predicted by computer models. Prediction uncertainty can be reduced by matching the model to data, which are collected in the field at great expense. The contribution of watershed characterization data to reducing uncertainty of relevant model predictions can be evaluated in a so-called data-worth analysis, which provides transparent, quantitative metrics about a data set’s value for the support of relevant watershed management objectives. To achieve this goal, we developed a software package that implements the data-worth analysis approach for use with state-of-the-art watershed models. The purpose of the proposed data-worth analysis is to help decision-makers allocate resources for watershed characterization such that the uncertainty in model predictions can be significantly reduced, which leads to better, more effective management decisions. At the same time, watershed characterization costs can be reduced. The specific technical objectives of this SBIR/STTR Phase II project were to develop a framework and associated software toolsets that implement the uncertainty quantification and data-worth analysis approach for use with state-of-the-art watershed models. This goal was achieved by (A) developing a user-friendly, robust software package that is accessible to a wide audience, including watershed managers, policy-makers, and public stakeholders; (B) by demonstrating application of the prototype on several use cases that are representative of complex watershed management challenges spanning a range of scales and that consider different open-source, DOE-based codes and other modeling platforms; and (C) by gathering information about the needs and requirements from potential users to help guide future developments, ensuring that the final product will be commercially viable. The developed software consists of a graphical user interface that guides the user through a sequence of analysis steps, supported by toolsets that leverage state-of-the-art computational simulation-optimization capabilities. A prototype of the software runs on multiple platforms (PC, Mac, multi-processor Linux environment), is linked to diverse watershed simulators (e.g., ECOSYS, TOUGH2, TOUGHREACT, Amanzi-ATS), performs multiple analysis tasks (predictive simulations, sensitivity analysis, uncertainty analysis, automatic parameter estimation, and data-worth analysis, multicomponent geothermometry), and is readily extensible to include external simulators and analysis tools. The software is being commercialized and will be continually updated to address user needs.

58 GEOSCIENCES↗
DOE OSTI2022

Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions

Many materials of interest to Sandia transition from fluid to solid or have regions of both phases coexisting simultaneously. Currently there are, unfortunately, no material models that can accurately predict this material response. This is relevant to applications that "birth stress" related to geoscience, nuclear safety, manufacturing, energy production and bioscience. Accurately capturing solidification and residual stress enables fully predictive simulations of the evolving front shape or final product. Accurately resolving flow of proppants or blood could reduce environmental impact or lead to better treatments for heart attacks, thrombosis, or aneurism. We will address a science question in this proposal: When does residual stress develop during the critical transition from liquid to solid and how does it affect material deformation? Our hypothesis is that these early phases of stress development are critical to predictive simulation of material performance, net shape, and aging. In this project, we use advanced constitutive models with yield stress to represent both fluid and solid behavior simultaneously. The report provides an abbreviated description of the results from our LDRD "Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions," since we have written four papers that document the work in detail and which we reference. We give highlights of the work and describe the gravitationally driven flow visualization experiment on a model yield stress fluid, Carbopol, at various concentrations and flow rates. We were able to collapse the data on a single master curve by showing it was self-similar. We also describe the Carbopol rheology and the constitutive equations of interest including the Bingham-Carreau-Yasuda model, the Saramito model, and the HB-Saramito model including parameter estimation for the shear and oscillatory rheology. We present several computational models including the 3D moving mesh simulations of both the Saramito models and Bingham-Carreau-Yasuda (BCY) model. We also show results from the BCY model using a 3D level set method and two different ways of handling reduced order Hele-Shaw modeling for generalized Newtonian fluids. We present some first ever two-dimensional results for the modified Jeffries Kamani-Donley-Rogers constitutive equation developed during this project. We include some recent results with a successful Saramito-level set coupling that allows us to tackle problems with complex geometries like mold filling in a thin gap with an obstacle, without the need for remeshing or remapping. We report on some experiments for curing systems where fluorescent particles are used to track material flow. These experiments were carried out in an oven on Sylgard 184 as a model polymerizing system. We conclude the report with a summary of accomplishments and some thoughts on follow-on work.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Developing a Continuous Nuclear Data Evaluation Method for the Resolved and Unresolved Resonance Regions With FITAPI and SAMMY [Poster]

SAMMY is an R-matrix Bayesian fitting program used in the analysis of nuclear cross section data. SAMMY produces separate cross section models in the resolved and unresolved resonance regions. This project develops a new method of continuous evaluation joining both energy regions with FITAPI. Full energy spectrum model introduces cross covariance between physics models allowing more accurate description of uncertainty. Consistency developed between physics models by the use of a unique set of prior parameters. An unresolved region cross section developed with sensitivity to resolved cross section. Incorporation into ORNL FITAPI provides access to greater number of parameter estimation algorithms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Distinguishing Bulk and Surface Recombination By Measuring and Modeling Ultrafast Carrier Dynamics

Distinguishing Bulk and Surface Recombination By Measuring and Modeling Ultrafast Carrier Dynamics The combination of modeling with TRTS and TRPL under multiple excitation conditions improves accuracy and precision of parameter estimation. Ultrafast carrier dynamics can link materials, processing, and device performance to direct the design of more efficient solar cells.

14 SOLAR ENERGY↗
DOE OSTI2024

Extraction of Vibration Data with Imaging

To date, the primary sensing technology used to measure the vibration response has been accelerometers and strain gages mounted directly to the structure and using either wired or, more recently, wireless telemetry. Cost issues with these sensors and the associated data acquisition systems typically limit the numbers that are deployed on in situ structures. Although there are a few structures with larger sensing counts that in some cases exceed over 1000 sensors, more typical numbers range from ten to one hundred sensors resulting in low spatial resolution when they are applied to physically large systems. When one considers that nuclear power plant structures usually have complex geometries, material properties, connectivity and boundary conditions, it is clear these current approaches to vibration measurements can only provide limited information about a system’s dynamics response characteristics. As an alternative, many non-contact measurement technologies have emerged, including point wise measurement methods such as Global Positioning System (GPS), microwave interferometry, and laser Doppler vibrometry (LDV), as well as simultaneous full-field measurement methods such as electronic speckle pattern interferometry, holography interferometry, and muon tomography, some of which can provide high spatial resolution measurements. Among these methods, digital video imaging techniques have emerged as a feasible solution for full-field vibration measurements that provide significantly more detailed dynamic response information because every pixel becomes a measurement point. Furthermore, recent advances in image processing and computer vision algorithms have been successfully used to process video data for experimental and operational modal analysis. Such full-field measurements have the potential to significantly improve many current structural assessment procedures including system identification (modal parameter estimation), structural health monitoring, load reconstruction, model validation, and model updating. Furthermore, more recent full-field imaging techniques can be accomplished with relatively low-cost, commercially-available off-the-shelf cameras. However, these measurement procedures have other limitations that must be considered such as the ability to only measure visibly accessible points on a structure and a more limited dynamic range and bandwidth than can be achieved with accelerometers or strain gages.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Improving the Parameterization of Cloud and Rain Microphysics in E3SM using Novel Observationally-Constrained Bayesian Approach (Final Technical Report)

In this project, we sought to develop new cloud and rain microphysics frameworks within the Energy Exascale Earth System Model (E3SM). This work encompassed two primary avenues of research: 1) Further development of a Bayesian-based scheme called BOSS (Bayesian Observationally-constrained Statistical-physical Scheme) to represent cloud and rain microphysics, testing it in realistic high-resolution cloud models, and implementing it in E3SM; 2) Development of a methodology utilizing machine learning to enable computationally tractable use of tractable use of Markov chain Monte Carlo sampling for Bayesian parameter estimation in Earth system and cloud models. In this project, we adapted the BOSS microphysics scheme, originally formulated for rain-only, to include all liquid-phase microphysical processes for cloud and rain, in particular the processes that mediate between these two categories, for example the conversion from cloud to rain through collision and coalescence of drops. We constrained the scheme via comparison and testing against a detailed model that explicitly represents the evolution of cloud and rain particles, called a bin microphysics scheme.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Five Year Comparison of Mixing Height Determinations at the Savannah River Site

Air quality dispersion modeling is performed for the Savannah River Site (SRS) to demonstrate compliance with applicable regulations. The AMS/EPA Regulatory Model (AERMOD) modeling system is an EPA recommended model for air quality applications with a data preprocessor (AERMET) to incorporate meteorological data collected on site. AERMET parameterizes or calculates meteorological variables that are not directly measured onsite. One of the parameters estimated by AERMET is the atmospheric mixing height. While the mixing height is not currently a measurement input into AERMET, SRS has the capability to measure the local mixing height. The Savannah River National Laboratory (SRNL) operates a Vaisala CL31 Lidar Ceilometer which estimates mixing height from aerosol backscatter. This study compares the parameterized mixing height from AERMET to the ceilometer estimated mixing height for the current regulatory period at SRS incorporating data from 2015-2019. Results from this study showed the average daily minimum values (morning) from AERMET were an order of magnitude lower than the commonly used Holzworth (1972) method and the ceilometer estimated mixing heights. Additionally, on average, the ceilometer exhibited a daily maximum mixing height value that occurred 1-3 hours later than the AERMET estimated maximum. This difference is likely due to the nighttime atmospheric mixing height assumptions and calculations used by AERMET. The AERMET algorithm cuts off mixing height growth at sunset while the ceilometer data show ongoing evening convection typical of the southeastern United States. These results suggest that the AERMET parametrization scheme assumptions may not be representative of a forested landscape and evening convection which could account for more mixing overnight. The results obtained in this study are significant for air dispersion modeling applications for regulatory purposes and worker safety. Mixing height can impact model estimated pollutant concentrations. A greater mixing height will provide more volume for pollutant dispersion. This report documents efforts to quantify the dependence of mixing height inputs toward a conservative estimated pollutant concentration.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Daily Forecasting of Regional Epidemics of Coronavirus Disease with Bayesian Uncertainty Quantification, United States

To increase situational awareness and support evidence-based policymaking, we formulated a mathematical model for coronavirus disease transmission within a regional population. This compartmental model accounts for quarantine, self-isolation, social distancing, a nonexponentially distributed incubation period, asymptomatic persons, and mild and severe forms of symptomatic disease. We used Bayesian inference to calibrate region-specific models for consistency with daily reports of confirmed cases in the 15 most populous metropolitan statistical areas in the United States. We also quantified uncertainty in parameter estimates and forecasts. This online learning approach enables early identification of new trends despite considerable variability in case reporting.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Applying Particle Swarm Optimization and Extended Kalman Filtering to Model Kaplan Generation Dynamics for Hydropower Systems

Variable renewable generation is increasing the need for hydropower plants to provide fast and flexible grid support, which places new demands on plant-level dynamic models used for monitoring, control, and operational decision-making. This need is especially important for hydroelectric systems, where turbine and generator dynamics are strongly coupled, nonlinear, and time-varying, making accurate real-time representation difficult. To address this problem, this paper develops a digital twin (DT) framework for a synchronous generator–Kaplan turbine system using an explicit separation of slow turbine dynamics and fast generator dynamics. The turbine subsystem is represented by a six-coefficient model, whose parameters are identified offline using particle swarm optimization, while the generator subsystem is updated online through an extended Kalman filter for real-time state and parameter estimation. These models are integrated within a closed-loop simulation that includes a proportional–integral–derivative–double-derivative governor and excitation system, allowing the DT to track plant behavior under realistic operating conditions. Unlike prior studies that treat turbine and generator modeling separately or rely mainly on simulated inputs, the proposed framework is validated using real operational data from a hydropower plant. Results show that the DT reproduces terminal voltage, active power, and reactive power with a normalized root mean square error of approximately 5%. This hybrid offline–online formulation constitutes the main contribution of the work, providing an adaptive and practically deployable DT for hydropower systems with direct relevance to control improvement, performance monitoring, and grid-support applications under high renewable penetration.

13 HYDRO ENERGY↗
DOE OSTI2020

A Novel Machine Learning Approach to Disentangle Multitemperature Regions in Galaxy Clusters

The hot intracluster medium (ICM) surrounding the heart of galaxy clusters is a complex medium that comprises various emitting components. Although previous studies of nearby galaxy clusters, such as the Perseus, the Coma, or the Virgo cluster, have demonstrated the need for multiple thermal components when spectroscopically fitting the ICM’s X-ray emission, no systematic methodology for calculating the number of underlying components currently exists. In turn, underestimating or overestimating the number of components can cause systematic errors in the emission parameter estimations. In this paper, we present a novel approach to determining the number of components using an amalgam of machine learning techniques. Synthetic spectra containing a various number of underlying thermal components were created using well-established tools available from the Chandra X-ray Observatory. The dimensions of the training set was initially reduced using principal component analysis and then categorized based on the number of underlying components using a random forest classifier. Our trained and tested algorithm was subsequently applied to Chandra X-ray observations of the Perseus cluster. Our results demonstrate that machine learning techniques can efficiently and reliably estimate the number of underlying thermal components in the spectra of galaxy clusters, regardless of the thermal model (MEKAL versus APEC). We also confirm that the core of the Perseus cluster contains a mix of differing underlying thermal components. We emphasize that although this methodology was trained and applied on Chandra X-ray observations, it is readily portable to other current (e.g., XMM-Newton, eROSITA) and upcoming (e.g., Athena, Lynx, XRISM) X-ray telescopes. The code is publicly available at https://github.com/XtraAstronomy/Pumpkin.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The Weak Form Is Stronger Than You Think

The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern computational and applied mathematics. In this work we provide a survey of both the history and recent developments for several fields in which the weak form can play a critical role. In particular, we highlight several recent advances in weak form versions of equation learning, parameter estimation, and coarse graining, which offer surprising noise robustness, accuracy, and computational efficiency. We note that this manuscript is a companion piece to our October 2024 SIAM News article of the same name. Here we provide more detailed explanations of mathematical developments as well as a more complete list of references. Lastly, we note that the software with which to reproduce the results in this manuscript is also available on our group's GitHub website https://github.com/MathBioCU .

26A33, 35D30, 62FXX, 62JXX, 65L09, 65M32, 68Q32,↗