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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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DOE OSTI2023

Bridging the Gap between Cosmological Simulations with Graph Neural Networks and Domain Adaptation

Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics implementation and numerical approximations across different simulation suites, models trained on data from one cosmological simulation show a drop in performance when tested on another. Similarly, models trained on any of the simulations would also likely experience a drop in performance when applied to observational data. Training on data from two different suites of the CAMELS hydrodynamic cosmological simulations, we examine the generalization capabilities of Domain Adaptive Graph Neural Networks (DA-GNNs). By utilizing GNNs, we capitalize on their capacity to capture structured scale-free cosmological information from galaxy distributions. Moreover, by including unsupervised domain adaptation via Maximum Mean Discrepancy (MMD), we enable our models to extract domain-invariant features. We demonstrate that DA-GNN achieves higher accuracy and robustness on cross dataset tasks (up to 28% better relative error and up to almost an order of magnitude better χ 2 ). Using data visualizations, we show the effects of domain adaptation on proper latent space data alignment. This shows that DA-GNNs are a promising method for extracting domain-independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A guide to the design of the virtual element methods for second- and fourth-order partial differential equations

Here we discuss the design and implementation details of two conforming virtual element methods for the numerical approximation of two partial differential equations that emerge in phase-field modeling of fracture propagation in elastic material. The two partial differential equations are: (i) a linear hyperbolic equation describing the momentum balance and (ii) a fourth-order elliptic equation modeling the damage of the material. Inspired by, we develop a new conforming VEM for the discretization of the two equations, which is implementation-friendly, i.e., different terms can be implemented by exploiting a single projection operator. We use C 0 and C 1 virtual elements for the second-and fourth-order partial differential equation, respectively. For both equations, we review the formulation of the virtual element approximation and discuss the details pertaining the implementation.

42 ENGINEERING↗
DOE OSTI2021

Spherical Parameter Estimation and MPDV Applications

A new algebraic least square approach is presented for estimating effective zero center for verification of MPDV(Multichannel Photon Doppler Velocimetry) probe designs. Unlike previous algebraic least square methods for spherical parameter estimation, the new method can be shown to be concise in mathematic formulations, easy of computations, invariant under rigid -body transformations, no need for numerical approximations, and precise in dealing with precise data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Domain Adaptive Graph Neural Networks for Constraining Cosmological Parameters Across Multiple Data Sets

Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics implementation and numerical approximations across different simulation suites, models trained on data from one cosmological simulation show a drop in performance when tested on another. Similarly, models trained on any of the simulations would also likely experience a drop in performance when applied to observational data. Training on data from two different suites of the CAMELS hydrodynamic cosmological simulations, we examine the generalization capabilities of Domain Adaptive Graph Neural Networks (DA-GNNs). By utilizing GNNs, we capitalize on their capacity to capture structured scale-free cosmological information from galaxy distributions. Moreover, by including unsupervised domain adaptation via Maximum Mean Discrepancy (MMD), we enable our models to extract domain-invariant features. We demonstrate that DA-GNN achieves higher accuracy and robustness on cross-dataset tasks (up to $28\%$ better relative error and up to almost an order of magnitude better $\chi^2$). Using data visualizations, we show the effects of domain adaptation on proper latent space data alignment. This shows that DA-GNNs are a promising method for extracting domain-independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Domain Adaptive Graph Neural Networks for Constraining Cosmological Parameters Across Multiple Data Sets

State of the art astronomical simulations have provided datasets which enabled the training of novel deep learning techniques for constraining cosmological parameters. However, differences in subgrid physics implementation and numerical approximations among simulation suites lead to differences in simulated datasets, which pose a hard challenge when trying to generalize across diverse data domains and ultimately when applying models to observational data. Recent work reveals deep learning algorithms are able to extract more information from complex cosmological simulations than summary statistics like power spectra. We introduce Domain Adaptive Graph Neural Networks (DA-GNNs), trained on CAMELS data, inspired by CosmoGraphNet (Villanueva-Domingo et al 2023). By utilizing GNNs, we can capitalize on their capacity to capture both astrophysical and topological features of galaxy distributions. Mixing these capabilities with domain adaptation techniques such as Maximum Mean Discrepancy (MMD), which enable extraction of domain-invariant features, our framework demonstrates enhanced accuracy and robustness. We present experimental results, including the alignment of distributions across domains through data visualization. These findings suggest that DA-GNNs are an efficient way of extracting domain independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Numerical methods and hypoexponential approximations for gamma distributed delay differential equations

Abstract Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge–Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Post-detonation fireball modeling: Validation of freeze out approximations

A numerical simulation study was performed to examine the post-detonation reaction processes produced by the detonation of a 12 mm diameter hemispherical pentaerythritol tetranitrate (PETN) explosive charge. The simulations used a finite rate detailed chemical reaction model consisting of 59 species and 368 reactions to capture post-detonation reaction processes including air dissociation from Mach 19+ shock waves that initially break out of the PETN charge, reactions within the detonation products during expansion, and afterburning when the detonation products mix with the shock heated air. The multi-species and thermodynamically complete Becker-Kistiakowsky-Wilson real-gas equation of state is used for the gaseous phase to allow for the mixing of reactive species. A recent simplified reactive burn model is used to propagate the detonation through the charge and allow for detailed post-detonation reaction processes. The computed blast, shock structures, and mole fractions of species within the detonation products agree well with experimental measurements. A comparison of the simulation results to equilibrium calculations indicates that the assumption of a local equilibrium is fairly accurate until the detonation products rapidly cool to temperatures in the range of 1500-1900 K by expansion waves. Below this range, the computed results show mole fractions that are nearly chemically frozen within the detonation products for a significant portion of expansion. In conclusion, these results are consistent with the freeze out approximation used in the blast modeling community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Physically interpretable approximations of many-body spectral functions

The rational function approximation provides a natural and interpretable representation of response functions such as the many-body spectral functions. We apply the vector fitting (VFIT) algorithm to fit a variety of spectral functions calculated from the Holstein model of electron-phonon interactions. We show that the resulting rational functions are highly efficient in their fitting of sharp features in the spectral functions, and could provide a means to infer physically relevant information from a spectral data set. The position of the peaks in the approximated spectral function are determined by the location of poles in the complex plane. Additionally, we developed a variant of VFIT that incorporates regularization to improve the quality of fits. With this procedure, we demonstrate it is possible to achieve accurate spectral function fits that vary smoothly as a function of physical conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Analytical solutions of the Arrhenius-Semenov problem for constant volume burn

Analytical solutions to the Semenov thermal ignition problem for constant volume burn governed by Arrhenius reaction kinetics are derived. Specifically, an approximate analytical solution technique for the Arrhenius-Semenov differential equation is derived for reaction orders n ϵ R> 0 and exact solutions are also constructed for reaction orders n ϵ N : n ≤ 3. The approximation technique relies on expansion of the respective nondominant terms in the differential equation at the lower and upper bounds of the reaction progress variable in order to create a pair of integrable series. The two integrated series are then connected to create a single continuous analytical solution. Excellent agreement is observed between the analytical approximation and solutions obtained numerically. The presented approximation constitutes a simple and robust strategy for solving the Arrhenius-Semenov problem analytically.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Numerical simulations of membrane distillation systems with actively heated membranes

Membrane distillation (MD) is a thermal desalination process that is gaining attention for treating hypersaline brines. One recent approach uses composite membranes with a thermally conductive layer that delivers heat to the membrane–feed interface, where it drives evaporation. Though this increases single-pass recovery, it comes with the challenge of promoting lateral heat conduction through the thin membrane. Herein, we develop a 3D, computational fluid dynamics (CFD) model that simulates conjugate heat, mass, and momentum transport in the feed channel and composite membrane. We then use the CFD to verify a simpler numerical model that approximates the feed velocity field analytically. We validate the numerical model experimentally, and use it to investigate the impacts of the conductive layer thickness, feed channel geometry, and operating conditions on temperature and concentration polarization, permeate production, and specific energy consumption. Overall, we find that lateral heating increases permeate production at the expense of increased concentration polarization. In extreme cases, the concentration increases more than four-fold along the membrane surface. Furthermore, we show however, that the feed flow rate and conductive layer thickness can be tailored to mitigate concentration polarization, for only a small reduction in permeate production.

42 ENGINEERING↗
DOE OSTI2021

A multi-center quadrature scheme for the molecular continuum

We report a common way to evaluate electronic integrals for polyatomic molecules is to use Becke’s partitioning scheme (Becke and Chem, 1988) in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed for integrands that fall off rapidly at large distances, such as those approximating bound electronic states. When applied to states in the electronic continuum, however, Becke scheme exhibits slow convergence and it is highly redundant. Here, we present a modified version of Becke scheme that is applicable to functions of the electronic continuum, such as those involved in molecular photoionization and electron–molecule scattering, and which ensures convergence and efficiency comparable to those realized in the calculation of bound states. In this modified scheme, the atomic weights already present in Becke’s partition are smoothly switched off within a range of few bond lengths from their respective nuclei, and complemented by an asymptotically unitary weight. The atomic integrals are evaluated on small spherical grids, centered on each atom, with size commensurate to the support of the corresponding atomic weight. The residual integral of the interstitial and long-range region is evaluated with a central master grid. The accuracy of the method is demonstrated by evaluating integrals involving integrands containing Gaussian Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical Bessel functions centered on the master grid. These functions are representative of those encountered in realistic electron-scattering and photoionization calculations in polyatomic molecules.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Design of double- and multi-bend achromat lattices with large dynamic aperture and approximate invariants

A numerical method to design nonlinear double- and multi-bend achromat (DBA and MBA) lattices with approximate invariants of motion is investigated. The search for such nonlinear lattices is motivated by Fermilab’s Integrable Optics Test Accelerator (IOTA), whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing DBA and MBA lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions J x and J y at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune-spread. Compared to the nominal NSLS-II lattice, the single- and multi-bunch instability thresholds are increased and the bunch-by-bunch feedback gain can be reduced.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Using Hydrodynamic Similarity as a Verification Method for Impact Cratering Simulations in the FLAG Hydrocode

Hydrodynamic codes (hydrocodes) are common tools for modeling hypervelocity impacts to provide insight into the physical phenomenon. Hydrocodes can simulate impacts from micrometer to kilometer spatial scales and reach impact velocities difficult to achieve in experimental settings. However, numerical models are approximations, and demonstrating that a numerical method is capable of providing physical results for these models is essential. In this work, we employ a hydrocode verification technique that leverages hydrodynamic similarity, a mathematical property of the conservation equations of fluid mechanics that form the basis for hydrocode models. Using the FLAG hydrocode, we simulate aluminum (Al) and basalt projectiles and targets at spatial scales spanning 7 orders of magnitude (hundreds of micrometers to kilometers). These materials were chosen because Al-6061 is a common material in spacecraft and satellites and basalt is a useful approximation of rocky astronomical bodies. Our results show that hydrodynamic similarity holds for each material model used and across spatial scales. We show that under certain conditions hydrodynamic similarity can apply in the presence of gravity and that similarity does not hold in the presence of strength models. We conclude that the FLAG hydrocode preserves important mathematical properties of fluid dynamics in hypervelocity impacts of Al-6061 and basalt.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Statistical mechanical model for crack growth

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. In this report an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Embedded random phase approximation for magnetic systems: H 2 dissociative adsorption on Fe(110)

The random phase approximation (RPA), a method for treating electron correlation, has been shown to be superior to standard density functional theory (DFT) approximations in numerous cases. However, the RPA’s computational cost is substantially higher than that of DFT, particularly restricting its application to extended surfaces. The recently introduced embedded RPA (emb-RPA) approach [Wei et al., J. Chem. Phys. 159(19), 194108 (2023)] reduces this computational cost by approximately two orders of magnitude. While previous applications of emb-RPA focused on non-spin-polarized systems, here we extend the approach to ferromagnetic ones. Unlike other embedded correlated wavefunction methods, such as embedded complete active space self-consistent field theory, emb-RPA is advantageous for spin-polarized systems because the RPA is compatible with unrestricted DFT solutions, which are eigenfunctions of the spin angular momentum operator S z but not the total spin-squared operator S 2 . By applying emb-RPA with specific magnetization constraints, we achieved a speedup of two to three orders of magnitude (one order when accounting for the one-time embedding potential optimization cost) with only small errors (∼50 meV) compared to full periodic RPA. Moreover, emb-RPA significantly reduces the over-binding errors of DFT approximations. In conclusion, we anticipate that the acceleration enabled by the spin-polarized emb-RPA approach will broaden the applicability of RPA to magnetic materials.

Density functional theory↗
DOE OSTI2022

Stability of exact solutions of the (2 + 1)-dimensional nonlinear Schrödinger equation with arbitrary nonlinearity parameter κ

In this work, we consider the nonlinear Schrödinger equation (NLSE) in 2+1 dimensions with arbitrary nonlinearity exponent κ in the presence of an external confining potential. Exact solutions to the system are constructed, and their stability as we increase the 'mass' (i.e., the L 2 norm) and the nonlinearity parameter κ is explored. Here we observe both theoretically and numerically that the presence of the confining potential leads to wider domains of stability over the parameter space compared to the unconfined case. Our analysis suggests the existence of a stable regime of solutions for all κ as long as their mass is less than a critical value M*(κ). Furthermore, we find that there are two different critical masses, one corresponding to width perturbations and the other one to translational perturbations. The results of Derrick's theorem are also obtained by studying the small amplitude regime of a four-parameter collective coordinate (4CC) approximation. A numerical stability analysis of the NLSE shows that the instability curve M*(κ) versus κ lies below the two curves found by Derrick's theorem and the 4CC approximation. In the absence of the external potential, κ = 1 demarcates the separation between the blowup regime and the stable regime. In this 4CC approximation, for κ < 1, when the mass is above the critical mass for the translational instability, quite complicated motions of the collective coordinates are possible. Energy conservation prevents the blowup of the solution as well as confines the center of the solution to a finite spatial domain. We call this regime the 'frustrated' blowup regime and give some illustrations. In an appendix, we show how to extend these results to arbitrary initial ground state solution data and arbitrary spatial dimension d.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

A projection-based analytical Jacobian framework for chemical kinetics applications

A major challenge in simulating complex combustion systems with detailed chemical kinetic models is the cost of integrating the chemical source terms, often done using stiff ODE solvers that require frequent Jacobian evaluations. Using analytically derived Jacobian matrices instead of divided-difference-based numerical Jacobian approximations can significantly reduce the associated computational cost. However, ambiguities arise in the formulation of analytical Jacobians because the chemical state of the system, or state vector, can be expressed in multiple ways, involving variables that are typically not independent from one another. Here, in this work, the consequences of those ambiguities on practical calculations are characterized in detail, and a generalized, projection-based framework is proposed as a mitigation strategy. Performances are assessed in a series of test cases involving a variety of configurations and numerical solution approaches. Results show that with proper treatment, commonly used analytical Jacobian formulations can be considered as equivalent for practical purposes, thereby alleviating concerns that the state vector chosen to express the governing equations and corresponding analytical Jacobian may significantly impact the accuracy of the simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗