Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Smooth approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A discontinuous Galerkin method for general relativistic hydrodynamics in thornado

Discontinuous Galerkin (DG) methods provide a means to obtain high-order accurate solutions in regions of smooth fluid flow while still resolving strong shocks. These and other properties make DG methods attractive for solving problems involving hydrodynamics; e.g., the core-collapse supernova problem. With that in mind we are developing a DG solver for the general relativistic, ideal hydrodynamics equations under a 3+1 decomposition of spacetime, assuming a conformally-flat approximation to general relativity. With the aid of limiters we verify the accuracy and robustness of our code with several difficult test-problems: a special relativistic Kelvin-Helmholtz instability problem, a two-dimensional special relativistic Riemann problem, and a one- and two-dimensional general relativistic standing accretion shock (SAS) problem. We find good agreement with published results, where available. We also establish sufficient resolution for the 1D SAS problem and find encouraging results regarding the standing accretion shock instability (SASI) in 2D.

Dunham, Samuel↗
DOE OSTI2026

High-Performance Semiempirical Excited-State Molecular Dynamics Powered by Graphics Processing Units

Here, this Letter introduces excited-state molecular dynamics in PYSEQM, a GPU-accelerated semiempirical quantum chemistry engine implemented in PyTorch. The new module enables Born–Oppenheimer molecular dynamics (BOMD) using configuration-interaction singles and random phase approximation for excited states, allowing long trajectories and large statistical ensembles to be simulated efficiently on a single GPU. We also implement an extended Lagrangian excited-state BOMD (XL-ESMD) scheme that propagates auxiliary electronic variables, enabling relaxed ground and excited-state convergence thresholds without compromising energy conservation. The excited-state BOMD implementation scales smoothly from small chromophores to a nearly 900-atom dendrimer (taking 6.5 s per MD step). PYSEQM also supports batched execution, allowing many geometries or trajectories to be evaluated in a single GPU launch, substantially increasing throughput and making ensemble-based protocols routine. As a demonstration, we compute absorption, emission, and infrared spectra from trajectories propagated on the ground and first excited states. The XL-ESMD scheme yields identical spectra at significantly lower computational cost, establishing the role of extended Lagrangian based dynamics for efficient excited-state BOMD simulations. Beyond raw performance, PYSEQM’s PyTorch foundation provides automatic differentiation for forces, efficient GPU batching, and seamless interfacing with machine learning models. These capabilities position PYSEQM as a practical platform for machine learning-augmented excited-state dynamics and lay the foundation for future data-driven nonadiabatic excited-state dynamics modeling of ultrafast spectroscopic probes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Bayesian sparse learning with preconditioned stochastic gradient MCMC and its applications

Deep neural networks have been successfully employed in an extensive variety of research areas, including solving partial differential equations. Despite its significant success, there are some challenges in effectively training DNN, such as avoiding overfitting in over-parameterized DNNs and accelerating the optimization in DNNs with pathological curvature. Here, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an adaptive empirical method. That is, one will alternatively sample from the posterior using preconditioned stochastic gradient Langevin Dynamics (PSGLD), and optimize the latent variables via stochastic approximation. The sparsity of the network is achieved while optimizing the hyperparameters with adaptive searching and penalizing. A popular SG-MCMC approach is Stochastic gradient Langevin dynamics (SGLD). However, considering the complex geometry in the model parameter space in nonconvex learning, updating parameters using a universal step size in each component as in SGLD may cause slow mixing. To address this issue, we apply a computationally manageable preconditioner in the updating rule, which provides a step-size parameter to adapt to local geometric properties. Moreover, by smoothly optimizing the hyperparameter in the preconditioning matrix, our proposed algorithm ensures a decreasing bias, which is introduced by ignoring the correction term in the preconditioned SGLD. According to the existing theoretical framework, we show that the proposed algorithm can asymptotically converge to the correct distribution with a controllable bias under mild conditions. Numerical tests are performed on both synthetic regression problems and learning solutions of elliptic PDE, which demonstrate the accuracy and efficiency of the present work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2022

Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the NPIPE and FFP10 data releases

We present a topological analysis of the temperature fluctuation maps from the Planck 2020 Data Release 4 NPIPE dataset and the Planck 2018 Data Release 3 FFP10 dataset. We performed a multiscale analysis in terms of the homology characteristics of the maps, invoking relative homology to account for the analysis in the presence of masks. We performed our analysis for a range of smoothing scales spanning sub- and super-horizon scales corresponding to a full width at half maximum (FWHM) of 5',10',20',40',80',160',320', and 640', and employed simulations based on the standard model for comparison, which assumes the initial fluctuation field to be an isotropic and homogeneous Gaussian random field. Examining the behavior of topological components, represented by the 0D homology group, we find the observations to be approximately 2σ or less deviant from the simulations for all resolutions and scales for the NPIPE dataset. For the FFP10 dataset, we detect a 2.96σ deviation between the observations and simulations at N = 128, FWHM = 80'. For the topological loops, represented by the first homology group, the simulations and observations are consistent within 2σ for most resolutions and scales for both the datasets. However, for the NPIPE dataset, we observe a high deviation between the observation and simulations in the number of loops at FWHM = 320', but at a low dimensionless threshold ν = –2.5. Under a Gaussian assumption, this would amount to a deviation of ~4σ. However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0.0016. Specifically in this case, our tests indicate that the numbers arise from a statistically stable regime, despite being based on small numbers. For the FFP10 dataset, the differences are not as strong as for the NPIPE dataset, indicating a 2.77σ deviation at this resolution and threshold. The Euler characteristic, which is the alternating sum of the ranks of relative homology groups, reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the χ 2 test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the χ 2 test in the final interpretation, as it indicates the most conservative differences. For the NPIPE dataset, we find that the components and loops differ at more than 95%, but agree within the 99% confidence level with respect to the base model at N = 32, FWHM = 320'. The Euler characteristic at this resolution displays a per mil deviation. In contrast, the FFP10 dataset shows that the observations are consistent with the base model within the 95% confidence level, at this and smaller scales. This is consistent with the observations of the Planck analysis pipeline via Minkowski functionals. For the largest smoothing scale, N = 16, FWHM = 640', both datasets exhibit an anomalous behavior of the loops, where FFP10 data exhibit a deviation that is larger by an order of magnitude than that of the NPIPE dataset. In contrast, the values for the topological components and the Euler characteristic agree between observations and model to within a confidence level of 99%. However, for the largest scales, the statistics are based on low numbers and may have to be regarded with caution. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within 2σ.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A primal–dual algorithm for risk minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. Here, this lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Advancement of hybrid fluid-kinetic modeling for HEDP and ICF science

We report on the development progress of a hybrid fluid-kinetic code for simulating fluids and plasmas in a wide range of environments, such as laser–matter interactions, inertial confinement fusion, magnetic confinement fusion, and pulsed power. The suite of numerical tools under development utilizes heterogeneous computer architectures and leverages the benefits of particle–based simulation techniques. By working to combine the kinetic particle-in-cell (PIC) model with a particle-based fluid simulation technique, such as smoothed particle hydrodynamics, we are developing a flexible framework capable of accurately modeling complex flows within and between kinetic and fluid regimes. The TriForce code is under development as a C++ framework for parallel, 3D, particle-based, hybrid fluid-kinetic plasma simulations. The fluid half of TriForce will be based upon the meshless smoothed-particle-hydrodynamics (SPH) approach, well-suited for shear, mixing, and turbulence, whereas the kinetic half resembles a traditional particle-in-cell (PIC) code; other particle-based approaches to fluid modeling that do use a mesh are also possible to use and are under investigation. Maxwell’s electromagnetic field equations are solved either via explicit or implicit algorithms or approximated via resistive magnetohydrodynamics (MHD) using an Ohm’s law and resulting induction equation (extended MHD is under development). A primary goal of enabling direct comparisons, from the same code, between results from the variants of MHD and implicit electromagnetic solutions is to improve our fundamental understanding of systems with magnetic fields. The code is under development to recover results from both radiation-MHD and fully kinetic codes in those limits, and is continuing to be developed from other follow-on grants to operate in between where both descriptions may co-exist and interact. For certain applications, it is desired for a simulation to contain fluid ions and electrons as well as kinetic ions and electrons. Typically, it is too computationally intensive to model a full-scale ICF or HEDP experiment fully kinetically since many cycles are expended with very small time steps on modeling the fluid part of a material that is well treated by the fluid approximation. In this case, many traditional PIC particles can be replaced with a single fluid particle representing the thermal part of the distribution function, and there are fewer needed kinetic particles, which describe the non-thermal part and can be sub-cycled relative to the fluid particle advance. Furthermore, a pure fluid code may, depending on the problem, simply lack many physically important details that are beyond the scope of its reduced approximations and assumptions. In this report, we summarize the objectives achieved in the development of the collisional and kinetic half of the code, and the physics problems to which the code has been applied in the areas of advanced and innovative fusion concepts, pulsed power, and magneto-inertial fusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration.

Gaussian processes and other kernel-based methods are used extensively to construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient algorithm to greedily select training samples that minimize the weighted L p error of kernel-based approximations for a given number of data. The method successively generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and can be implemented using existing pivoted Cholesky factorization methods. Training samples are generated in batches which allows training data to be evaluated (labeled) in parallel. For smooth kernels, the algorithm performs comparably with the greedy integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal and non-tensor product densities. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data using Bayesian inference.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced. This approach is illustrated in the case of the carbon diamond using Slater–Jastrow trial wavefunctions including up to one million Slater determinants. Fixed-node DMC energies obtained with such large expansions are much improved, and the fixed-node error is found to decrease monotonically and smoothly as a function of the number of determinants in the trial wavefunction, a property opening the way to a better control of this error. The cohesive energy extrapolated to the thermodynamic limit is in close agreement with the estimated experimental value. Interestingly, this is also the case at the single-determinant level, thus, indicating a very good error cancellation in carbon diamond between the bulk and atomic total fixed-node energies when using single-determinant nodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Global Microscopic Description of Nucleon-Nucleus Scattering with Quantified Uncertainties

We develop for the first time a microscopic global nucleon-nucleus optical potential with quantified uncertainties suitable for analyzing nuclear reaction experiments at next-generation rare-isotope beam facilities. Within the improved local density approximation and without any adjustable parameters, we begin by computing proton-nucleus and neutron-nucleus optical potentials from a set of five nuclear forces from chiral effective field theory for 1800 target nuclei in the mass range 12 ≤ A ≤ 242 for energies between 0 MeV < E ≲ 150 MeV. We then parameterize a global optical potential for each chiral force that depends smoothly on the projectile energy as well as the target nucleus mass number and isospin asymmetry. Uncertainty bands for elastic scattering observables are generated from a full covariance analysis of the parameters entering in the description of our global optical potential and benchmarked against existing experimental data for stable target nuclei. Since our approach is purely microscopic, we anticipate a similar quality of the model for nucleon scattering on unstable isotopes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Demonstration of acoustic monitoring for structural health of microreactors: Through use of neural networks and resonant ultrasound spectroscopy

Nuclear microreactors prioritize modularity and portability and are intended to be a cost-effective technology for non-conventional nuclear markets. As such, the development of microreactors into a safe and feasible solution for energy security applications will necessitate the development of non-destructive technologies to monitor the integrity of inaccessible reactors components during operation. This demonstration applies linear and nonlinear acoustic techniques, in combination with machine learning, to detect and classify mechanical changes (stress and damage) in a test article which are broadly representative of potential operating challenges within a functioning microreactor. All necessary data has been collected for this demonstration, with minor experimental issues identified that can be addressed in follow-on work. Motivated by the expected conditions within a functioning microreactor, we have demonstrated our monitoring techniques on a core-block-like test article using an unstructured excitation source that approximates the noisy acoustic environment expected during reactor operation. At all stress states mechanically applied to the test article, a machine learning model using an artificial neural network was able to classify with 100% accuracy whether a 3D laser vibrometry point measurement was made on an intact or artificially defective test article. Further, model predictions about whether the defect interface was rough or smooth were 95% accurate, indicating the ability of acoustic techniques to recover defect characteristics. Resonant ultrasound spectroscopy (RUS) was also applied to the dataset to provide further quantitative insights about material properties. RUS analysis was ultimately hampered by several minor experimental and data issues, limiting results to certain cases for this demonstration. Last, analysis using nonlinear RUS exhibited sensitivity to changing levels of applied stresses for each intact and defective state. As presented in this demonstration, acoustic monitoring exhibits sensitivity to stress changes, which are of concern due to high thermal gradients expected during startup and operation. Further, our techniques distinguish between measurements made on intact and damaged test articles.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Insights into the failure mode of the Chelyabinsk meteor from high-fidelity simulation

In 2013, an asteroid with a diameter of approximate 20 m broke up in the atmosphere above the Russian city of Chelyabinsk producing what is known as an airburst event. The event was recorded on video from multiple angles and a 500-kg fragment was recovered from Lake Chebarkul shortly thereafter. These aspects, coupled with the asteroid’s large size, distinguish the Chelyabinsk event as unique. In this study, we use the smoothed particle hydrodynamics method to examine the breakup mode of a Chelyabinsk-sized monolithic asteroid and probe whether a monolithic structure is consistent with observations from the Chelyabinsk event. We model the object as a homogeneous sphere with properties consistent with Chelyabinsk meteorites. We use planar-2D simulations to test the sensitivity of results to variations in the material model and to qualitatively inspect the cause of crack nucleation and fragmentation. We then compare results from a 3D simulation to observations from the event. Our 3D simulation predicts a burst height within 3 km of the observed peak luminosity suggesting the responsible asteroid may have been monolithic.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Efficient generalized boundary detection

Fast, efficient, and robust compression-based methods for detecting boundaries in arbitrary datasets, including sequences (1D datasets), are desired. The methods, each employing three simple algorithms, approximate the information distance between two adjacent sliding windows within a dataset. One of the algorithms calculates an initial ordered list of subsequences; while a second algorithm updates the ordered list of subsequences by dropping a first entry and appending a last entry rather than calculating completely new ordered lists with each iteration. Large values in the distance metric are indicative of boundary locations. A smoothed z-score or a wavelet-based algorithm may then be used to locate peaks in the distance metric, thereby identifying boundary locations. An adaptive version of the method employs a collection of window sizes and corresponding weighting functions, making it more amenable to real datasets with unknown, complex, and changing structures.

Ting, Christina↗
DOE OSTI2025

Optimal Polynomial Smoothers and One‐Sided V‐Cycles for Poisson Problems

The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier‐Stokes equations needs robust preconditioning strategies. One such strategy is multigrid. To realize the potential of multigrid methods, effective smoothing strategies are needed. Chebyshev polynomial smoothers, in conjunction with pointwise Jacobi or additive Schwarz methods (ASMs), prove to be an effective smoother. Other polynomial smoothers, however, may provide superior convergence to the multigrid preconditioner. The authors compare the standard Chebyshev polynomial smoothers to both the novel fourth‐kind Chebyshev polynomial smoothers proposed by Lottes as well as smoothers based on the polynomial of best uniform approximation to as proposed by Kraus, Vassilevski, and Zikatanov. At the cost of symmetry, further improvements may be made. For example, a order polynomial smoother on both sides of the V‐cycle may be substituted with an order polynomial smoother on one side at no additional cost. The choice of omitting the postsmoother in favor of higher‐order polynomial presmoothing is advantageous in cases where the multigrid approximation property constant is large. The authors consider a 2D model problem based on finite differences to motivate the choice of polynomial smoother, order, and whether to apply postsmoothing for the target application of high‐order ‐geometric multigrid methods for GPU architectures. Results from both domains demonstrate the substantial improvement of these approaches over the standard Chebyshev polynomial smoother with a symmetric V‐cycle.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An efficient second-order adaptive procedure for inserting CAD geometries into hexahedral meshes using volume fractions

Here, this paper is concerned with inserting three-dimensional computer-aided design (CAD) geometries into meshes composed of hexahedral elements using a volume fraction representation. An adaptive procedure for doing so is presented. The procedure consists of two steps. The first step performs spatial acceleration using a k-d tree. The second step involves subdividing individual hexahedra in an adaptive mesh refinement (AMR)-like fashion and approximating the CAD geometry linearly (as a plane) at the finest subdivision. The procedure requires only two geometric queries from a CAD kernel: determining whether or not a queried spatial coordinate is inside or outside the CAD geometry and determining the closest point on the CAD geometry’s surface from a given spatial coordinate. We prove that the procedure is second-order accurate for sufficiently smooth geometries and sufficiently refined background meshes. We demonstrate the expected order of accuracy is achieved with several verification tests and illustrate the procedure’s effectiveness for several exemplar CAD geometries.

Adaptive↗
DOE OSTI2024

Statistical properties of filaments in the cosmic web

ABSTRACT In the context of the cosmological and constrained Exploring the Local Universe with the reConstructed Initial Density field (ELUCID) simulation, this study explores the statistical characteristics of filaments within the cosmic web, focussing on aspects such as the distribution of filament lengths and their radial density profiles. Using the classification of the cosmic web environment through the Hessian matrix of the density field, our primary focus is on how cosmic structures react to the two variables $R_{\rm s}$ and $\lambda _{\rm th}$. The findings show that the volume fractions of knots, filaments, sheets, and voids are highly influenced by the threshold parameter $\lambda _{\rm th}$, with only a slight influence from the smoothing length $R_{\rm s}$. The central axis of the cylindrical filament is pinpointed using the medial-axis thinning algorithm of the COsmic Web Skeleton (COWS) method. It is observed that median filament lengths tend to increase as the smoothing lengths increase. Analysis of filament length functions at different values of $R_{\rm s}$ indicates a reduction in shorter filaments and an increase in longer filaments as $R_{\rm s}$ increases, peaking around $2.5R_{\rm s}$. The study also shows that the radial density profiles of filaments are markedly affected by the parameters $R_{\rm s}$ and $\lambda _{\rm th}$, showing a valley at approximately $2R_{\rm s}$, with increases in the threshold leading to higher amplitudes of the density profile. Moreover, shorter filaments tend to have denser profiles than their longer counterparts.

Zhang, Youcai (ORCID:0000000319674091)↗
DOE OSTI2021

srMO-BO-3GP: A sequential regularized multi-objective Bayesian optimization for constrained design applications using an uncertain Pareto classifier

Bayesian optimization (BO) is an efficient and flexible global optimization framework that is applicable to a very wide range of engineering applications. To leverage the capability of the classical BO, many extensions, including multi-objective, multi-fidelity, parallelization, and latent-variable modeling, have been proposed to address the limitations of the classical BO framework. In this work, we propose a novel multi-objective BO formalism, called srMO-BO-3GP, to solve multi-objective optimization problems in a sequential setting. Three different Gaussian processes (GPs) are stacked together, where each of the GPs is assigned with a different task. The first GP is used to approximate a single-objective computed from the multi-objective definition, the second GP is used to learn the unknown constraints, and the third one is used to learn the uncertain Pareto frontier. At each iteration, a multi-objective augmented Tchebycheff function is adopted to convert multi-objective to single-objective, where the regularization with a regularized ridge term is also introduced to smooth the single-objective function. Finally, we couple the third GP along with the classical BO framework to explore the convergence and diversity of the Pareto frontier by the acquisition function for exploitation and exploration. The proposed framework is demonstrated using several numerical benchmark functions, as well as a thermomechanical finite element model for flip-chip package design optimization.

42 ENGINEERING↗
DOE OSTI2021

Schrödinger evolution of two-dimensional black holes

This paper systematically treats the evolving quantum state for two-dimensional black holes, with particular focus on the CGHS model, but also elucidating features generalizing to higher dimensions. This is done in Schrödinger picture(s), to exhibit the dynamic evolution of the state at intermediate times. After a review of classical solutions, also connecting to descriptions of higher-dimensional black holes, it overviews the canonical quantum treatment of the full evolution, including gravitational dynamics. Derived in an approximation to this, following conversion to “perturbation picture”, is the evolution of the quantum matter on the background geometry. Features of the evolving matter state are described, based on choice of a time slicing to put the evolution into ADM form. The choices of slicing as well as coordinates on the slices result in different quantum “pictures” for treating the evolution. If such a description is based on smooth trans-horizon slices, that avoids explicit reference to ultra-planckian modes familiar from traditional treatments, and exhibits the Hawking excitations as emerging from a “quantum atmosphere” with thickness comparable to the inverse temperature. Detailed study of the state exhibits the entanglement structure between Hawking quanta and the partner excitations inside the black hole, and the corresponding “missing information”. This explicit description also allows direct study of the evolution and features, e.g. as seen by infalling observers, of these partner excitations, helping to address various puzzles with them. Explicit treatment of the evolving state, and its extension to higher dimensions, provides further connections to information theory and a starting point for study of corrections that can unitarize evolution, arising from new quantum gravity effects — whether wormholes or something entirely different.

2D Gravity↗