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At least 73 records · Page 4

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗

Investigation for improving Global Positioning System (GPS) orbits using a discrete sequential estimator and stochastic models of selected physical processes

GEODYNII is a conventional batch least-squares differential corrector computer program with deterministic models of the physical environment. Conventional algorithms were used to process differenced phase and pseudorange data to determine eight-day Global Positioning system (GPS) orbits with several meter accuracy. However, random physical processes drive the errors whose magnitudes prevent improving the GPS orbit accuracy. To improve the orbit accuracy, these random processes should be modeled stochastically. The conventional batch least-squares algorithm cannot accommodate stochastic models, only a stochastic estimation algorithm is suitable, such as a sequential filter/smoother. Also, GEODYNII cannot currently model the correlation among data values. Differenced pseudorange, and especially differenced phase, are precise data types that can be used to improve the GPS orbit precision. To overcome these limitations and improve the accuracy of GPS orbits computed using GEODYNII, we proposed to develop a sequential stochastic filter/smoother processor by using GEODYNII as a type of trajectory preprocessor. Our proposed processor is now completed. It contains a correlated double difference range processing capability, first order Gauss Markov models for the solar radiation pressure scale coefficient and y-bias acceleration, and a random walk model for the tropospheric refraction correction. The development approach was to interface the standard GEODYNII output files (measurement partials and variationals) with software modules containing the stochastic estimator, the stochastic models, and a double differenced phase range processing routine. Thus, no modifications to the original GEODYNII software were required. A schematic of the development is shown. The observational data are edited in the preprocessor and the data are passed to GEODYNII as one of its standard data types. A reference orbit is determined using GEODYNII as a batch least-squares processor and the GEODYNII measurement partial (FTN90) and variational (FTN80, V-matrix) files are generated. These two files along with a control statement file and a satellite identification and mass file are passed to the filter/smoother to estimate time-varying parameter states at each epoch, improved satellite initial elements, and improved estimates of constant parameters.

Goad, Clyde C.↗

HFBTHO-AD: Differentiation of a nuclear energy density functional code

The HFBTHO code implements a nuclear energy density functional solver to model the structure of atomic nuclei. HFBTHO has previously been used to calibrate energy functionals and perform sensitivity analysis by using derivative-free methods. To enable derivative-based optimization and uncertainty quantification approaches, we must compute the derivatives of HFBTHO outputs with respect to the parameters of the energy functional, which are a subset of all input parameters of the code. Here, we use the algorithmic/automatic differentiation (AD) tool Tapenade to differentiate HFBTHO. We compare the derivatives obtained using AD against finite-difference approximation and examine the performance of the derivative computation.

Algorithmic differentiation↗

An infrasound source analysis of the OSIRIS-REx sample return capsule hypersonic re-entry

The OSIRIS-REx sample return capsule's hypersonic re-entry into the atmosphere is a rare opportunity to test a variety of sonic boom source models since the projectile dimensions are well characterized. While the as-flown flight path is unknown, the predicted flight path enables a rough approximation of the source Mach number and location. Six infrasound microphones deployed in the boom carpet along the predicted flight path recorded impulsive signals from the OSIRIS-REx re-entry. Using a suite of atmosphere profiles and the geometric acoustics approximation, we estimate locations with uncertainty estimates along the flight path from which the signals were emitted. Acoustic overpressure and signal duration predictions from Whitham's far field theory, Carlson's simplified sonic boom prediction method, and a drag-dominated hypersonic model are analyzed with uncertainty estimates from the location estimate. While the Carlson simplified sonic boom prediction method could be accurate, our preference is for the drag-dominated source model. Using this source model with an inviscid Burgers's equation solver for propagation, we obtained an excellent match to the recorded data. In conclusion, these results will help better inform future sample return capsule re-entry observation campaigns as well as contribute to a better understanding of high altitude infrasonic sources.

58 GEOSCIENCES↗

Determining Stellar Elemental Abundances from DESI Spectra with the Data-driven Payne

Abstract Stellar abundances for a large number of stars provide key information for the study of Galactic formation history. Large spectroscopic surveys such as the Dark Energy Spectroscopic Instrument (DESI) and LAMOST take median-to-low-resolution (R≲ 5000) spectra in the full optical wavelength range for millions of stars. However, the line-blending effect in these spectra causes great challenges for elemental abundance determination. Here we employDD-Payne, a data-driven method regularized by differential spectra from stellar physical models, to the DESI early data release spectra for stellar abundance determination. Our implementation delivers 15 labels, including effective temperatureT eff , surface gravity log g , microturbulence velocityv mic , and the abundances for 12 individual elements, namely C, N, O, Mg, Al, Si, Ca, Ti, Cr, Mn, Fe, and Ni. Given a spectral signal-to-noise ratio of 100 per pixel, the internal precisions of the label estimates are about 20 K forT eff , 0.05 dex for log g , and 0.05 dex for most elemental abundances. These results agree with the theoretical limits from the Crámer–Rao bound calculation within a factor of 2. The majority of the accreted halo stars contributed by the Gaia–Enceladus–Sausage are discernible from the disk and in situ halo populations in the resultant [Mg/Fe]–[Fe/H] and [Al/Fe]–[Fe/H] abundance spaces. We also provide distance and orbital parameters for the sample stars, which spread over a distance out to ∼100 kpc. The DESI sample has a significantly higher fraction of distant (or metal-poor) stars than the other existing spectroscopic surveys, making it a powerful data set for studying the Galactic outskirts. The catalog is publicly available.

Astronomy & Astrophysics↗

On the integrability cases of the equation of motion for a satellite in an axially symmetric gravitational field.

Investigation of two cases of integrability of a second-order differential equation describing the projection of an axisymmetric satellite orbit on to a plane perpendicular to the rotation axis. It is demonstrated that for these two cases the integration can be carried out either by quadratures or reduced to a first-order differential equation. Analytical and physical properties are expressed, and it is shown that the equation can be derived from the classical plane eikonal equation of geometric optics.

Ghaffari, A.↗

Two-demensional analysis of heat and mass transfer in porous media using the strongly implicit procedure

Numerical results of the heat and mass transfer in a porous matrix are presented. The coupled, nonlinear partial differential equations describing this physical phenomenon are solved in finite difference form for two dimensions, using a new iterative technique (the strongly implicit procedure). The influence of the external environment conditions (heating and pressure) is shown to produce two-dimensional flow in the porous matrix. Typical fluid and solid temperature distributions in the porous matrix and internal pressure distributions are presented.

Curry, D. M.↗

Mesh generation using algebraic techniques

The solution of partial differential equations which describe physical phenomena by the use of coordinate transformations is described. The constraints of the problems are stated in geometric terms and include boundary constraints, uniformity constraints, and internal constraints. Algebraic mesh generations are very satisfactory for these constraints.

Eiseman, P. R.↗

Partitioning and packing mathematical simulation models for calculation on parallel computers

The development of multiprocessor simulations from a serial set of ordinary differential equations describing a physical system is described. Degrees of parallelism (i.e., coupling between the equations) and their impact on parallel processing are discussed. The problem of identifying computational parallelism within sets of closely coupled equations that require the exchange of current values of variables is described. A technique is presented for identifying this parallelism and for partitioning the equations for parallel solution on a multiprocessor. An algorithm which packs the equations into a minimum number of processors is also described. The results of the packing algorithm when applied to a turbojet engine model are presented in terms of processor utilization.

Arpasi, D. J.↗

Mathematical model partitioning and packing for parallel computer calculation

This paper deals with the development of multiprocessor simulations from a serial set of ordinary differential equations describing a physical system. The identification of computational parallelism within the model equations is discussed. A technique is presented for identifying this parallelism and for partitioning the equations for parallel solution on a multiprocessor. Next, an algorithm which packs the equations into a minimum number of processors is described. The results of applying the packing algorithm to a turboshaft engine model are presented.

Arpasi, Dale J.↗

Partitioning And Packing Equations For Parallel Processing

Algorithm developed to identify parallelism in set of coupled ordinary differential equations that describe physical system and to divide set into parallel computational paths, along with parts of solution proceeds independently of others during at least part of time. Path-identifying algorithm creates number of paths consisting of equations that must be computed serially and table that gives dependent and independent arguments and "can start," "can end," and "must end" times of each equation. "Must end" time used subsequently by packing algorithm.

Arpasi, Dale J.↗

Real-Time Simulation of the X-33 Aerospace Engine

This paper discusses the development and performance of the X-33 Aerospike Engine RealTime Model. This model was developed for the purposes of control law development, six degree-of-freedom trajectory analysis, vehicle system integration testing, and hardware-in-the loop controller verification. The Real-Time Model uses time-step marching solution of non-linear differential equations representing the physical processes involved in the operation of a liquid propellant rocket engine, albeit in a simplified form. These processes include heat transfer, fluid dynamics, combustion, and turbomachine performance. Two engine models are typically employed in order to accurately model maneuvering and the powerpack-out condition where the power section of one engine is used to supply propellants to both engines if one engine malfunctions. The X-33 Real-Time Model is compared to actual hot fire test data and is been found to be in good agreement.

Aguilar, Robert↗

Three Paradigms of Lunar Regolith Evolution

Integration of diverse datasets on the Moon may render some paradigms of lunar science either better-defended or vulnerable. We will consider three paradigms commonly used for understanding the processes of lunar regolith evolution in light of new and accumulated data. Our premise is that all data-sets should converge to a single interpretation if a concept or model is to be accepted as a paradigm. If a convergence is lacking, the paradigm needs fresh scrutiny. SteadyState: Lunar regolith evolution is currently understood in terms of comminution, agglutination, and replenishment as described by McKay and coworkers). Briefly, the model envisages continued micrometeoritic bombardment to comminute exposed soil particles to finer sizes while continued agglutination consumes finer sizes to produce larger constructional particles. Eventually, a balance between these two opposing processes achieves a steady state; soils at steady state maintain their mean grain size (M(sub z)). Episodic higher-energy impacts excavate fresh coarse material from below the soil cover, disturb the steady state, and restart the process to achieve a new steady state. It follows that the thickness of the regolith at any site would control the frequency of replenishment; indeed, the thickness of the regolith at Apollo landing sites was predicted by McKay et al. from the average M(sub z) of local soils. However, replenishment may come also from disintegrating boulders and cobbles at the lunar surface, and rates of comminution and agglutination may depend on the properties of target material. Regression between M(sub z) and I(sub s)/Fe(sup 0) (a measure of maturity or total surface exposure) of Apollo soils at different sites shows the following relations and estimated M(sub z) at a high maturity of I(sub s)/Fe(sup 0)= 100. It is possible that Apollo 12 and 15 sites have the thickest regolith and the Apollo 16 site has the thinnest. It is also possible that Apollo 12 and 15 basalts are comminuted faster than Apollo 16 highland rocks and Apollo 14 and 17 soils are products of mixed parentage. If a soil becomes continually finer as it matures until agglutination catches up, and if comminution is differential-dependent on the physical properties of the constituents, then the composition of the bulk soil has to match the composition of some "fulcrum" grain size fraction, say X Grain size fractions >X and <X will complement each other; their mass balance is the bulk soil. It appears that the 10-20-micron size fraction may be the fulcrum. In general, trace-element chemistry and IR reflectance spectra of this size fraction are closest to that of the bulk soil, regardless of maturity that is surprising. Disaggregated products of regolith breccias may also show similar relationships. If the 10-20 gm is the fulcrum (i.e., X as above) for many soil properties (e.g., major element composition, FMR, solar-wind-implanted elements), then this may be the ultimate mean grain size of lunar soils at steady state. However, different properties of soils may find steady states at different grain size fractions. The steady state of solar-wind-implanted elements, on the other hand, will climb up the grain-size scale as agglutinates transfer surface-correlated components into volume correlated components until a saturation level is reached or the rates of replenishment and implantation become equal. The same will be the case with vapor-deposited reduced metals as they too are incorporated inside constructional particles. Properties that are directly affected by soil-maturation processes will thus have different pathways of achieving steady states. Maturity, i.e., cumulative surface exposure, of lunar soils is best quantified by the amount of nanophase superparamagnetic Fe(sup 0) (np-Fe(sup 0)) normalized to Fe content (=I(sub s)/Fe(sup 0). The majority consensus (paradigm?) for the production of np-Fe(sup 0) is associated with the production of agglutinates. Because large doses of solar-wind H are implanted in all lunar soils upon exposure, any melting (e.g., during agglutinate production) triggers a chemical reduction of Fe-bearing minerals resulting in np-Fe(sup 0) production. The quantity of np-Fe(sup 0) is thus dependent on melting events, (i.e., exposure), and limited by the Fe content of the soil. All freshly produced np-Fe(sup 0) resides in agglutinitic glass, as new TEM images show. Apparently, the correction procedure developed by Lucey et al. to estimate the Fe content of the lunar surface from IR-reflectance spectra depends on accepting the above. However, the process of producing np-Fe(sup 0) may be physical rather than chemical. All np-Fe(sup 0) could be deposits from a vapor produced by micrometeoritic impact on lunar soils. If metal-O bonds in target phases are broken, O being "most volatile" will escape leaving an O-deficient vapor to facilitate the production of np-Fe(sup 0). If so, the quantity of np-Fe(sup 0) is dependent on the vaporizing events, (i.e., exposure), and limited by the efficiency of breaking metal-O bonds and the escape of 0. To the extent that strengths of metal-O bonds are dependent on the local crystal field, production of np-Fe(sup 0) may be limited by the mineral composition of target soils and not by their total Fe content. According to this model, vapor-deposited np-Fe(sup 0) should be found at any retentive sites on lunar soil grains. Indeed, TEM images show np-Fe(sup 0) on plagioclase and ilmenite. Incorporation of such pre-irradiated np-Fe(sup 0)-bearing grains into agglutinates may account for eventual increased emplacement of np-Fe(sup 0) in agglutinates. Such a paradigm shift in understanding the origin of np-Fe(sup 0) will raise questions ranging from the unquestionable use of Is/FeO as the universal maturity parameter of lunar soils to global elemental maps of the Moon from remote-sensing data. Additional information is contained in the original.

Basu, A.↗

Scientific machine learning for closure models in multiscale problems: A review

Here, closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have been proposed as a way to tackle the closure problem, combining traditional (physics-based) modeling with data-driven (machine-learned) techniques, typically through enriching differential equations with neural networks. This paper reviews the different reduced model forms, distinguished by the degree to which they include known physics, and the different objectives of a priori and a posteriori learning. The importance of adhering to physical laws (such as symmetries and conservation laws) in choosing the reduced model form and choosing the learning method is discussed. The effect of spatial and temporal discretization and recent trends toward discretization-invariant models are reviewed. In addition, we make the connections between closure problems and several other research disciplines: inverse problems, Mori-Zwanzig theory, and multi-fidelity methods. In conclusion, much progress has been made with scientific machine learning approaches for solving closure problems, but many challenges remain. In particular, the generalizability and interpretability of learned models is a major issue that needs to be addressed further.

97 MATHEMATICS AND COMPUTING↗

Time-Dependent Structure of the Upper Atmosphere

The physical properties of the upper atmosphere are determined mainly by heat conduction, the heat sources and the barometric law. An analysis of the integro-differential equation which describes these physical processes has been carried out. It is found that heating of the thermosphere due to absorption of the solar extreme ultraviolet (EUV) radiation alone cannot explain the observed diurnal variation of density and temperature, since it would yield a maximum of these properties at about 17h local time, instead of 14h where it is observed. Secondly, if the EUV flux is adjusted to give the observed average temperature, then the diurnal variation in density would be much too large compared with the observed amplitude. Thirdly, it would require an extremely high efficiency for the conversion of EUV radiation into heat, if we compare the required flux with Hinteregger's measurements of the EUV flux. Thus, it is necessary to have another heat source in addition to the heating due to absorption of EUV radiation. If an additional beat source is used, which has a maximum at about 9h local time and a flux of 1 erg cm−1 sec−1, a time-dependent model of the upper atmosphere is obtained that is in good agreement with the observed densities. There is evidence that this additional heat source derives its energy ultimately from the solar corpuscular radiation. In this paper we present the results of calculations for a model in the equatorial and temperature zones of the earth, for those times when the average solar activity corresponds to a solar radiation flux of 200×110−22 Wm−2 (cps)−1 at 10.7-cm wavelength. The physical properties (temperature, density, pressure, scale height, mean molecular weight and the number densities of N2, O2, O, He and H) are given as a function of local time and for the altitudes between 120 km and 2050 km.

ATMOSPHERE↗

Numerical simulation of rarefied gas flow through a slit

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

Keith, Theo G., Jr.↗

FDDO and DSMC analyses of rarefied gas flow through 2D nozzles

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas expanding through a two-dimensional nozzle and into a surrounding low-density environment. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere model is used as a molecular model and the no time counter method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by factors of 10 to 40 in CPU time, depending on the degree of rarefaction.

Chung, Chan-Hong↗

The Space-Time Conservation Element and Solution Element Method: A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws: The Two Dimensional Time Marching Schemes - 1

A new high resolution and genuinely multidimensional numerical method for solving conservation laws is being, developed. It was designed to avoid the limitations of the traditional methods. and was built from round zero with extensive physics considerations. Nevertheless, its foundation is mathmatically simple enough that one can build from it a coherent, robust. efficient and accurate numerical framework. Two basic beliefs that set the new method apart from the established methods are at the core of its development. The first belief is that, in order to capture physics more efficiently and realistically, the modeling, focus should be placed on the original integral form of the physical conservation laws, rather than the differential form. The latter form follows from the integral form under the additional assumption that the physical solution is smooth, an assumption that is difficult to realize numerically in a region of rapid chance. such as a boundary layer or a shock. The second belief is that, with proper modeling of the integral and differential forms themselves, the resulting, numerical solution should automatically be consistent with the properties derived front the integral and differential forms, e.g., the jump conditions across a shock and the properties of characteristics. Therefore a much simpler and more robust method can be developed by not using the above derived properties explicitly.

Chang, Sin-Chung↗