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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

A linearized Euler analysis of unsteady flows in turbomachinery

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗
NASA NTRS1987

Potential surfaces for O atom-polymer reactions

Ab initio quantum chemistry methods are used to study the energetics of interactions of O atoms with organic compounds. Polyethylene (CH2)n has been chosen as the model system to study the interactions of O(3P) and O(1D) atoms with polymers. In particular, H abstraction is investigated and polyethylene is represented by a C3 (propane) oligomeric model. The gradient method, as implemented in the GRADSCF package of programs, is used to determine the geometries and energies of products and reactants. The saddle point, barrier geometry is determined by minimizing the squares of the gradients of the potential with respect to the internal coordinates. To correctly describe the change in bonding during the reaction at least a two configuration MCSCF (multiconfiguration self consistent field) or GVB (generalized valence bond) wave function has to be used. Basis sets include standard Pople and Dunning sets, however, increased with polarization functions and diffuse p functions on both the C and O atoms. The latter is important due to the O(-) character of the wave function at the saddle point and products. Normal modes and vibrational energy levels are given for the reactants, saddle points and products. Finally, quantitative energetics are obtained by implementing a small CAS (complete active space) approach followed by limited configuration interaction (CI) calculations. Comparisons are made with available experimental data.

Laskowski, B. C.↗
NASA NTRS1989

Calculation of unsteady flows in turbomachinery using the linearized Euler equations

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗
NASA NTRS2001

Reliability Assessment for COTS Components in Space Flight Applications

Systems built for space flight applications usually demand very high degree of performance and a very high level of accuracy. Hence, the design engineers are often prone to selecting state-of-art technologies for inclusion in their system design. The shrinking budgets also necessitate use of COTS (Commercial Off-The-Shelf) components, which are construed as being less expensive. The performance and accuracy requirements for space flight applications are much more stringent than those for the commercial applications. The quantity of systems designed and developed for space applications are much lower in number than those produced for the commercial applications. With a given set of requirements, are these COTS components reliable? This paper presents a model for assessing the reliability of COTS components in space applications and the associated affect on the system reliability. We illustrate the method with a real application.

Krishnan, G. S.↗
NASA NTRS2007

Finding Uncertainties that Cause the Age Dependence of Dose Limits to Be Immature

Space radiation permissible exposure limits (PEL) are intended to set acceptable levels of cancer risks, and avoid any clinical significant non-cancer effects. The 1989 recommendation of the National Council of Radiation Protection and Measurements (NCRP) recommended a strong age dependence of dose limits that departed drastically from the then mature 1970 dose limits recommendations from the National Academy of Science, which were independent of age. In 2000, the NCRP recommended revised limits that showed a similar trend of risk with age to the 1989 report. In this model, the cancer risk per Sv varies by more than 2-fold for ages between 30- and 50-yr. Therefore for galactic cosmic rays exposure, astronaut age has a larger influence on risk then radiation shielding mass or material composition, vehicle propulsion method, or position in the solar cycle. For considering the control of mission costs and resources, the possibility of using astronaut age as a trade variable in mission design could be considered. However, the uncertainties in describing the age dependence on risk have not been fully explored. We discuss biological factors that influence the age dependence of radiation risks, including susceptibility, expression and latency, and radiation quality. These factors depend not only on the individual s age, but also their genetic sensitivity and interaction with other environmental factors. Epidemiological data is limited in describing the age dependence on risk. The 2005, BEIR VII report recommends an age dependence for cancer risk attributable solely to the life-table disagreeing strongly with the NCRP model. However, BEIR VII also noted the limited power of human data for concomitantly describing both age and age after exposure dependences of cancer risks. Many experimental studies have shown that high LET radiation (e.g., high charge and energy (HZE) nuclei and neutrons) display reduced latency compared to low LET radiation, suggesting distinct biological factors are important. We discuss potential molecular mechanisms that would influence the age dependence of radiation risks. A probability distribution function for the uncertainties in age-dependence of risk models is described and predictions for Mars missions discussed. Our report suggests that theoretical considerations based on new experimental studies are needed to ensure the correct age dependence in space radiation risk models and the resulting Astronaut PEL.

Cucinotta, Francis A.↗
DOE OSTI1968

Kryptonate Hydrogen Detection System (Final Report)

A prototype model of a multipurpose instrument which demonstrates the applicability of the Kryptonate® technique for detecting hydrogen gas was developed. This report describes the construction of the instrument and presents a laboratory evaluation of its performance. Performance was excellent. The instrument was designed to detect hydrogen in air at concentrations of 0-3% by volume, and to detect hydrogen in nitrogen or other inert gas at concentrations of 0-10% by volume. Other detection levels (both higher and lower) could be set if required. Ultimate response times can be made of the order of 0.5 seconds. The instrument is an all solid state device operating from 120V 60 Hz power source. The instrument has been designed to enable modifications to be made with a minimum amount of difficulty.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Performance-portable Binary Neutron Star Mergers with AthenaK

We introduce an extension to the AthenaK code for general-relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes using a 3+1 conservative Eulerian formulation. Like the fixed-spacetime GRMHD solver, we use standard finite-volume methods to evolve the fluid and a constrained-transport scheme to preserve the divergence-free constraint for the magnetic field. We also utilize a first-order flux correction (FOFC) scheme to reduce the need for an artificial atmosphere and optionally enforce a maximum principle to improve robustness. We demonstrate the accuracy of AthenaK using a set of standard tests in flat and curved spacetimes. Using a SANE accretion disk around a Kerr black hole, we compare the new solver to the existing solver for stationary spacetimes using the so-called "HARM-like" formulation. We find that both formulations converge to similar results. We also include the first published binary neutron star (BNS) mergers performed on graphical processing units (GPUs). Thanks to the FOFC scheme, our BNS mergers maintain a relative error of $\mathcal{O}$(10 –11 ) or better in baryon mass conservation up to collapse. Finally, we perform scaling tests of AthenaK on OLCF Frontier, where we show excellent weak scaling of ≥80% efficiency up to 32,768 GPUs and 74% up to 65,536 GPUs for a GRMHD problem in dynamical spacetimes with six levels of mesh refinement. AthenaK achieves an order-of-magnitude speedup using GPUs compared to CPUs, demonstrating that it is suitable for performing numerical relativity problems on modern exascale resources.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Vibrationally resolved ionization cross sections for the ground state and electronically excited states of the hydrogen molecule and its isotopomeres

An existing set of vibrationally resolved ionization cross section for the ground state and the first excited states of the hydrogen molecule, based on the Gryzinski method, is extended by cross sections for the isotopomeres of H{sub 2} (i.e. D{sub 2}, T{sub 2}, HD, HT, and DT), both for non-dissociative and dissociative ionizations. The comparison of cross sections for non-dissociative ionization of H{sub 2} with results obtained by the Molecular Convergent Close-Coupling method gives a very good agreement. The compiled tables give non-dissociative and dissociative cross sections for the ground state and the five energetically lowest electronically excited states of H{sub 2} and its isotopomeres, in each case for the first 9 vibrational levels. Data for all vibrational levels of the excited states is available online.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Liquid Phase Modeling in Porous Media: Adsorption of Methanol and Ethanol in H-MFI in Condensed Water

Zeolites are used in the chemical and separation industries for their exceptional selectivity, adsorption capacity, regenerability, and stability in gas and liquid phase processing. Here, we developed an explicit solvation method for predicting solvent/condensed phase effects on adsorption free energies in microporous media such as zeolites based on the hybrid quantum mechanical/molecular mechanical free energy perturbation (QM/MM-FEP) technique. Our explicit solvation method for zeolite systems, called eSZS, aims to capture site-specific interactions during the adsorption process at the Brønsted acid sites of H-MFI zeolite while still considering the diverse configuration space of the solvent molecules. This strategy is ideal for chemical reactions or adsorbates that interact with the microporous medium in few distinct adsorbate/transition state configurations, i.e., the harmonic or similar approximations are acceptable for the adsorbate/transition state while such approximations break down for the solvent molecules that require extensive configuration space sampling. In this way, our approach effectively overcomes the limitations of implicit solvation models and classical force field methods for describing solvation effects on chemical reactions within porous materials such as zeolites. Specifically, in this study, we investigated various aspects of our hybrid QM/MM approach, including QM cluster size dependencies in a periodic electrostatically embedded cluster model (PEECM), rules for link atoms at the QM/MM boundary, and functional and basis set considerations for converged and reasonably accurate gas and aqueous phase methanol and ethanol adsorption free energy predictions in H-MFI. For gas phase adsorption of methanol and ethanol in H-MFI at a Brønsted acid site in T12 position, we compute adsorption free energies at 298 K of −0.61 and −0.75 eV, respectively, using a PEECM containing 50 Si and 1 Al atom with ωB97x-D/def2-TZVP level of theory. For solvent effect calculations, we sample the aqueous phase using grand canonical Monte Carlo (GCMC) simulations to (1) obtain a mean field of electrostatic interactions in the reaction system and (2) perform a rigorous free energy perturbation calculation. Similar to the experimentally and computationally observed endergonic solvation effects observed for hydrocarbon adsorption on metal surfaces, we also observe that a condensed aqueous environment destabilizes methanol and ethanol at these acid sites in H-MFI at 298 K. Specifically, the computed solvation free energies of adsorption (ΔΔG solv ) for methanol and ethanol are +0.44 and +0.54 eV, respectively. From this study, it is evident that adsorbates (methanol and ethanol) are competing with water for adsorption space inside the H-MFI zeolite, leading to an endergonic solvation effect. Here, we expect that the endergonic, aqueous solvent effect during adsorption in microporous zeolites is highly tunable by changing the pore size and hydrophobicity of the microporous material as this will affect the water density inside the pore structure.

Adsorption↗
DOE OSTI2020

Planck 2018 results - IV. Diffuse component separation

We present full-sky maps of the cosmic microwave background (CMB) and polarized synchrotron and thermal dust emission, derived from the third set of Planck frequency maps. These products have significantly lower contamination from instrumental systematic effects than previous versions. The methodologies used to derive these maps follow closely those described in earlier papers, adopting four methods (Commander, NILC, SEVEM, and SMICA) to extract the CMB component, as well as three methods (Commander, GNILC, and SMICA) to extract astrophysical components. Our revised CMB temperature maps agree with corresponding products in the Planck 2015 delivery, whereas the polarization maps exhibit significantly lower large-scale power, reflecting the improved data processing described in companion papers; however, the noise properties of the resulting data products are complicated, and the best available end-to-end simulations exhibit relative biases with respect to the data at the few percent level. Using these maps, we are for the first time able to fit the spectral index of thermal dust independently over 3° regions. We derive a conservative estimate of the mean spectral index of polarized thermal dust emission of β d = 1.55 ± 0.05, where the uncertainty marginalizes both over all known systematic uncertainties and different estimation techniques. For polarized synchrotron emission, we find a mean spectral index of β s = -3.1 ± 0.1, consistent with previously reported measurements. We note that the current data processing does not allow for construction of unbiased single-bolometer maps, and this limits our ability to extract CO emission and correlated components. The foreground results for intensity derived in this paper therefore do not supersede corresponding Planck 2015 products. For polarization the new results supersede the corresponding 2015 products in all respects.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1996

SeaWiFS Technical Report Series: SeaWiFS Calibration and Validation Quality Control Procedures - Volume 38

This document provides five brief reports that address several quality control procedures under the auspices of the Calibration and Validation Element (CVE) within the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) Project. Chapter 1 describes analyses of the 32 sensor engineering telemetry streams. Anomalies in any of the values may impact sensor performance in direct or indirect ways. The analyses are primarily examinations of parameter time series combined with statistical methods such as auto- and cross-correlation functions. Chapter 2 describes how the various onboard (solar and lunar) and vicarious (in situ) calibration data will be analyzed to quantify sensor degradation, if present. The analyses also include methods for detecting the influence of charged particles on sensor performance such as might be expected in the South Atlantic Anomaly (SAA). Chapter 3 discusses the quality control of the ancillary environmental data that are routinely received from other agencies or projects which are used in the atmospheric correction algorithm (total ozone, surface wind velocity, and surface pressure; surface relative humidity is also obtained, but is not used in the initial operational algorithm). Chapter 4 explains the procedures for screening level-, level-2, and level-3 products. These quality control operations incorporate both automated and interactive procedures which check for file format errors (all levels), navigation offsets (level-1), mask and flag performance (level-2), and product anomalies (all levels). Finally, Chapter 5 discusses the match-up data set development for comparing SeaWiFS level-2 derived products with in situ observations, as well as the subsequent outlier analyses that will be used for evaluating error sources.

Hooker, Stanford B.↗
NASA NTRS1998

Determination of an Infrared Reference Frame

The mission of the European Space Agency's Hipparcos satellite was to provide high precision astrometric and photometric data for over 100,000 stars and somewhat lower precision data on over a million additional stars. These observations were made in the optical band (340 - 850 nm) and resulted in median precisions of better than 1 milli-arcsec (mas) in position and parallax and I mas/yr in proper motion. The Hipparcos frame is inertial within an estimated uncertainty of +/- 0.25 mas/yr. The other important wavelength band for astrometry has been the radio band. A reference frame has been defined based on absolute Very Long Baseline Interferometry (VLBI) positions of several hundreds of radio sources. There have been a number of projects to refine the link between the optical and radio reference frames. In recent years there has been increasing interest in the astrometry of infrared sources. For example, stars with circumstellar shells can be observed in both the optical and radio (e.g. SiO maser emission). The infrared emission from such sources is dominated by thermal dust emission. The spatial distribution of radiation in the three bands is expected to be quite different. In 1982 we proposed a number of infrared-selected sources (S(sub 10 micron) greater than or approx. equal to 100 J(sub y)) for inclusion in the Hipparcos Input Catalog. Most of those sources were observed, and in Sutton (1997) we report the optical astrometric results (position, proper motion, and parallax) for 87 such sources. These sources were selected to have reasonable agreement between infrared and optical positions, and so may be used as primary standards for future infrared astrometry. They are well distributed across the sky, but exhibit some bias towards the galactic plane and the northern hemisphere. We have also obtained a set of 1480 secondary standards (unpublished) A comparison between optical positions and 86 GHz SiO maser positions for 10 sources indicates coincidence at the 0.15 arcsec level, consistent with current uncertainties in the SiO positions. Improved measurements of the SiO maser positions are needed. VLBI data show that SiO maser spots can be distributed in broken rings of radii 10 - 30 mas, presumably centered on the stellar position. However the SiO flux may be distributed asymmetrically, in which case the flux-weighted center of the SiO emission can be different from the stellar position. We have also published a related paper on phase fluctuations in millimeter interferometry (Sutton and Hueckstaedt 1996). Radiometric monitoring of emission from atmospheric water vapor may be a method for correcting for such fluctuations. This is relevant to positional determinations at centimeter and millimeter wavelengths. The integration of visible, infrared, and radio astrometry is one of our principal goals.

Sutton, Edmund C.↗
NASA NTRS1999

Solar-Cycle Changes in GONG P-Mode Widths and Amplitudes 1995-1998

We search for a solar cycle variation in mode widths and amplitudes derived from 3-month GONG time series. The variation of mode width and amplitude observed in GONG data are the combined effects of fill factor, temporal variation, and measurement uncertainties. The largest variation is caused by the fill factor resulting in modes with increased width and reduced amplitude when fill is lower. We assume that the solar cycle variation is the only other systematic variation beside the temporal window function effect. We correct all currently available data sets for the fill factor and simultaneously derive the solar cycle variation. We find an increase of about 3% on average in mode width from the previous minimum to Oct. 1998 and a decrease of about 7% and 6% in mode amplitude and mode area (width x amplitude). We find no l dependence of the solar-cycle changes. As a function of frequency, these changes show a maximum between 2.7 and 3.3 mHz with about 47% higher than average values for mode width and about 29% and 36% higher ones for mode amplitude and area. We estimate the significance of these rather small changes by a pre-whitening method and find that the results are significant at or above the 99.9% level with mode area showing the highest level of significance and mode width the lowest. The variation in background amplitude is most likely not significant and is consistent with a zero change.

Komm R. W.↗
NASA NTRS2004

Open Platform for Limit Protection with Carefree Maneuver Applications

This Open Platform for Limit Protection guides the open design of maneuver limit protection systems in general, and manned, rotorcraft, aerospace applications in particular. The platform uses three stages of limit protection modules: limit cue creation, limit cue arbitration, and control system interface. A common set of limit cue modules provides commands that can include constraints, alerts, transfer functions, and friction. An arbitration module selects the "best" limit protection cues and distributes them to the most appropriate control path interface. This platform adopts a holistic approach to limit protection whereby it considers all potential interface points, including the pilot's visual, aural, and tactile displays; and automatic command restraint shaping for autonomous limit protection. For each functional module, this thesis guides the control system designer through the design choices and information interfaces among the modules. Limit cue module design choices include type of prediction, prediction mechanism, method of critical control calculation, and type of limit cue. Special consideration is given to the nature of the limit, particularly the level of knowledge about it, and the ramifications for limit protection design, especially with respect to intelligent control methods such as fuzzy inference systems and neural networks.

Jeram, Geoffrey J.↗
DOE OSTI2024

ASMS 2024 Investigation of Uranyl Perchlorate Anion Complexes in the Gas Phase via Infrared Multiphoton Dissociation and Collision Induced Dissociation

Investigation of Uranyl Perchlorate Anion Complexes in the Gas Phase via Infrared Multiphoton Dissociation and Collision Induced Dissociation Brittany D. M. Hodges, Christopher A. Zarzana, JungSoo Kim, Jonathan Martens, and W. C. M. Berden Introduction (120 words max) Effects of electronic structure on chemical bonding and reactivity play critical roles shaping the chemical bonding and reactivity behaviors of heavy elements. Understanding the role of f electrons in bond formation between the actinide-series elements like uranium with other ligands is critical for solving technical challenges associated with these heavy elements, important to nuclear fuel cycles, efficient separations of rare earth metals, and understanding the chemistry of stored nuclear fuels and related environmental management sites. In this study, we further examine the interactions between uranyl and the perchlorate ion in order to understand the structures of these ions through the use of IRMPD. Here we report the IRMPD spectra of [UO2(ClO4)3]-, [UO3(ClO4)2]-, and a proposed transition state. Methods (120 word max) IRMPD spectra and CID spectra were acquired using a Bruker amaZon QIT/MS instrument at the Free-Electron Lasers for Infrared eXperiments (FELIX) laboratory at Radboud University. The FELIX QIT/MS is modified to allow for the high-intensity tunable IR beam from FELIX to be directed into the ion packet, resulting in multiphoton dissociation that is measured only when the IR frequency is in resonance with an adequately high absorption vibrational mode of the mass-selected complex. DFT geometry optimizations and frequency calculations using the Gaussian suite of programs were performed using B3LYP, TPSSh, and PBE0 level of theory with 6-31+G(d) basis for the O, C, H, and N atoms and the SDD basis set for U. The SDD basis set employs the Stuttgart/Dresden effective core potential. Preliminary Data or Plenary Speakers Abstract (300 words max) Metal ion clusters of uranyl perchlorate were formed via direct electrospray ionization. For each metal ligand complex of interest, the parent ion was isolated and collision induced dissociation fragmentation and Infrared Multiphoton Dissociation (IRMPD) fragmentation spectra were acquired. Results presented here are the first look at the IRMPD spectra of [UO3(ClO4)2]-, [UO2(ClO4)3]-. Structures were examined using Gaussian at different levels of theory B3LYP level of theory, TPPSh and PBE0 levels, to reflect the behaviors of uranium metal ligand complexes most accurately. In these structures, we identified an overlap between each of these uranyl stretches resulting in their largely being obscured by a perchlorate mode. The CID product spectra agree with similar structures reported by Groenewold for uranyl nitrate in 2006 (10.1021/ja058106n).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2002

Design of a Dual Waveguide Normal Incidence Tube (DWNIT) Utilizing Energy and Modal Methods

This report investigates the partition design of the proposed Dual Waveguide Normal Incidence Tube (DWNIT). Some advantages provided by the DWNIT are (1) Assessment of coupling relationships between resonators in close proximity, (2) Evaluation of "smart liners", (3) Experimental validation for parallel element models, and (4) Investigation of effects of simulated angles of incidence of acoustic waves. Energy models of the two chambers were developed to determine the Sound Pressure Level (SPL) drop across the two chambers, through the use of an intensity transmission function for the chamber's partition. The models allowed the chamber's lengthwise end samples to vary. The initial partition design (2" high, 16" long, 0.25" thick) was predicted to provide at least 160 dB SPL drop across the partition with a compressive model, and at least 240 dB SPL drop with a bending model using a damping loss factor of 0.01. The end chamber sample transmissions coefficients were set to 0.1. Since these results predicted more SPL drop than required, a plate thickness optimization algorithm was developed. The results of the algorithm routine indicated that a plate with the same height and length, but with a thickness of 0.1" and 0.05 structural damping loss, would provide an adequate SPL isolation between the chambers.

Betts, Juan F.↗
NASA NTRS1994

Apparatus and methods for humidity control

Apparatus is provided which controls humidity in a gas. The apparatus employs a porous interface that is preferably a manifolded array of stainless steel tubes through whose porous surface water vapor can pass. One side of the porous interface is in contact with water and the opposing side is in contact with gas whose humidity is being controlled. Water vapor is emitted from the porous surface of the tubing into the gas when the gas is being humidified, and water vapor is removed from the gas through the porous surfaces when the gas is being dehumidified. The temperature of the porous interface relative to the gas temperature determines whether humidification or dehumidification is being carried out. The humidity in the gas is sensed and compared to the set point humidity. The water temperature, and consequently the porous interface temperature, are automatically controlled in response to changes in the gas humidity level above or below the set point. Any deviation from the set point humidity is thus corrected.

Dinauer, William R.↗
DOE OSTI2023

Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics

Abstract We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of $$C^{\infty }$$ C ∞ bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy .

97 MATHEMATICS AND COMPUTING↗