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At least 289 records · Page 16

Biasing from galaxy trough and peak profiles with the DES Y3 redMaGiC galaxies and the weak lensing mass map

We measure the correspondence between the distribution of galaxies and matter around troughs and peaks in the projected galaxy density, by comparing redMaGiC galaxies (0.15 < z < 0.65) to weak lensing mass maps from the Dark Energy Survey (DES) Y3 data release. We obtain stacked profiles, as a function of angle θ, of the galaxy density contrast δ g and the weak lensing convergence κ, in the vicinity of these identified troughs and peaks, referred to as ‘void’ and ‘cluster’ superstructures. The ratio of the profiles depend mildly on θ, indicating good consistency between the profile shapes. We model the amplitude of this ratio using a function $F(\boldsymbol{\eta }, \theta )$ that depends on cosmological parameters $\boldsymbol{\eta }$, scaled by the galaxy bias. We construct templates of $F(\boldsymbol{\eta }, \theta )$ using a suite of N-body (‘Gower Street’) simulations forward-modelled with DES Y3-like noise and systematics. We discuss and quantify the caveats of using a linear bias model to create galaxy maps from the simulation dark matter shells. We measure the galaxy bias in three lens tomographic bins (near to far): $2.32^{+0.86}_{-0.27}, 2.18^{+0.86}_{-0.23}, 1.86^{+0.82}_{-0.23}$ for voids, and $2.46^{+0.73}_{-0.27}, 3.55^{+0.96}_{-0.55}, 4.27^{+0.36}_{-1.14}$ for clusters, assuming the best-fit Planck cosmology. Similar values with ∼0.1σ shifts are obtained assuming the mean DES Y3 cosmology. The biases from troughs and peaks are broadly consistent, although a larger bias is derived for peaks, which is also larger than those measured from the DES Y3 3 × 2-point analysis. This method shows an interesting avenue for measuring field-level bias that can be applied to future lensing surveys.

cosmology: observations↗

Extremum-seeking control for an Ultrasonic/Sonic Driller/Corer (USDC) driven at high-power

Future NASA exploration missions will increasingly require sampling, in-situ analysis and possibly the return of material to Earth for further tests. One of the challenges to addressing this need is the ability to drill using for low axial loading while operating from light weight platforms (e.g., lander, rover, etc.) as well as operate at planets with low gravity. For this purpose, the authors developed the Ultrasonic/Sonic Driller/Corer (USDC) jointly with Cybersonics Inc. Studies of the operation of the USDC at high power have shown there is a critical need to self-tune to maintain the operation of the piezoelectric actuator at resonance. Performing such tuning is encountered with difficulties and to address them an extremum-seeking control algorithm is being investigated. This algorithm is designed to tune the driving frequency of a time-varying resonating actuator subjected to both random and high-power impulsive noise disturbances. Using this algorithm the performance of the actuator is monitored on a time-scale that is compatible with its slowly time-varying physical characteristics. The algorithm includes a parameter estimator, which estimates the coefficients of a function that characterizes the quality factor of the USDC. Since the parameter estimator converges sufficiently faster than the time-varying drift of the USDC's physical parameters, the proposed extremum-seeking estimation and control algorithm is potentially applicable for use as a closed-loop health monitoring system. Specifically, this system may be programmed to automatically adjust the duty-cycle of the sinusoidal driver signal to guarantee that the quality factor of the USDC does not fall below a user-defined set-point. Such fault-tolerant functionality is especially important in automated drilling applications where it is essential not to inadvertently drive the piezoelectric ceramic crystals of the USDC beyond their capacities. The details of the algorithm and experimental results will be described and discussed in this paper.

Peek-seeking estimation and control↗

Optimized Auxiliary Functions for Robust Mitigation of Finite-Size Errors in Periodic Hybrid Density Functional Theory

When calculating properties of periodic systems at the thermodynamic limit (TDL), the dominant source of finite size error (FSE) arises from the long-range Coulomb interaction, and can manifest as a slowly converging quadrature error when approximating an integral in the reciprocal space by a finite sum. The singularity subtraction (SS) method offers a systematic approach for reducing this quadrature error and thus the FSE. Here, in this work, we first investigate the performance of the SS method in the simplest setting, aiming at reducing the FSE in exact exchange calculations by subtracting the Coulomb contribution with a single, adjustable Gaussian auxiliary function. We demonstrate that a simple fitting method can robustly estimate the optimal Gaussian width and leads to rapid convergence toward the TDL. Furthermore, we suggest new forms of the auxiliary function, whose optimal parameters could also be determined through least-squares fitting. For a range of semiconductors and insulators, the proposed auxiliary functions achieve robust, millihartree-level accuracy in hybrid density functional theory calculations, including cases with sparse k-meshes and large basis sets.

Quiton, Stephen Jon [University of California, Ber↗

A Patch Density Recommendation based on Convergence Studies for Vehicle Panel Vibration Response resulting from Excitation by a Diffuse Acoustic Field

Fluid structural interaction problems that estimate panel vibration from an applied pressure field excitation are quite dependent on the spatial correlation of the pressure field. There is a danger of either over estimating a low frequency response or under predicting broad band panel response in the more modally dense bands if the pressure field spatial correlation is not accounted for adequately. Even when the analyst elects to use a fitted function for the spatial correlation an error may be introduced if the choice of patch density is not fine enough to represent the more continuous spatial correlation function throughout the intended frequency range of interest. Both qualitative and quantitative illustrations evaluating the adequacy of different patch density assumptions to approximate the fitted spatial correlation function are provided. The actual response of a typical vehicle panel system is then evaluated in a convergence study where the patch density assumptions are varied over the same finite element model. The convergence study results are presented illustrating the impact resulting from a poor choice of patch density. The fitted correlation function used in this study represents a Diffuse Acoustic Field (DAF) excitation of the panel to produce vibration response.

Smith, Andrew↗

Some results on contractive mappings as related to pattern recognition

Several of the techniques used in pattern recognition are reformulated as the problem of determining fixed points of a function. If x sub 0 is a fixed point of f and if f is contractive at x sub 0, then, for any y belonging to a sufficiently small neighborhood of x sub 0 the orbit of y will converge to x sub 0. Several general results regarding contractive mappings are developed with emphasis on functions.

Brown, D. R.↗

Synergistic learning with multi-task DeepONet for efficient PDE problem solving

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional machine learning to address issues such as data sparsity and overfitting in neural networks. In this work, we apply MTL to problems in science and engineering governed by partial differential equations (PDEs). However, implementing MTL in this context is complex, as it requires task-specific modifications to accommodate various scenarios representing different physical processes. To this end, we present a multi-task deep operator network (MT-DeepONet) to learn solutions across various functional forms of source terms in a PDE and multiple geometries in a single concurrent training session. We introduce modifications in the branch network of the vanilla DeepONet to account for various functional forms of a parameterized coefficient in a PDE. Additionally, we handle parameterized geometries by introducing a binary mask in the branch network and incorporating it into the loss term to improve convergence and generalization to new geometry tasks. Our approach is demonstrated on three benchmark problems: (1) learning different functional forms of the source term in the Fisher equation; (2) learning multiple geometries in a 2D Darcy Flow problem and showcasing better transfer learning capabilities to new geometries; and (3) learning 3D parameterized geometries for a heat transfer problem and demonstrate the ability to predict on new but similar geometries. Finally, our MT-DeepONet framework offers a novel approach to solving PDE problems in engineering and science under a unified umbrella based on synergistic learning that reduces the overall training cost for neural operators.

42 ENGINEERING↗

Depressurization and two-phase flow of water containing high levels of dissolved nitrogen gas

Depressurization of water containing various concentrations of dissolved nitrogen gas was studied. In a nonflow depressurization experiment, water with very high nitrogen content was depressurized at rates from 0.09 to 0.50 MPa per second and a metastable behavior which was a strong function of the depressurization rate was observed. Flow experiments were performed in an axisymmetric, converging diverging nozzle, a two dimensional, converging nozzle with glass sidewalls, and a sharp edge orifice. The converging diverging nozzle exhibited choked flow behavior even at nitrogen concentration levels as low as 4 percent of the saturation level. The flow rates were independent of concentration level. Flow in the two dimensional, converging, visual nozzle appeared to have a sufficient pressure drop at the throat to cause nitrogen to come out of solution, but choking occurred further downstream. The orifice flow motion pictures showed considerable oscillation downstream of the orifice and parallel to the flow. Nitrogen bubbles appeared in the flow at back pressures as high as 3.28 MPa, and the level at which bubbles were no longer visible was a function of nitrogen concentration.

Simoneau, R. J.↗

Higher Order Bases in a 2D Hybrid BEM/FEM Formulation

The advantages of using higher order, interpolatory basis functions are examined in the analysis of transverse electric (TE) plane wave scattering by homogeneous, dielectric cylinders. A boundary-element/finite-element (BEM/FEM) hybrid formulation is employed in which the interior dielectric region is modeled with the vector Helmholtz equation, and a radiation boundary condition is supplied by an Electric Field Integral Equation (EFIE). An efficient method of handling the singular self-term arising in the EFIE is presented. The iterative solution of the partially dense system of equations is obtained using the Quasi-Minimal Residual (QMR) algorithm with an Incomplete LU Threshold (ILUT) preconditioner. Numerical results are shown for the case of an incident wave impinging upon a square dielectric cylinder. The convergence of the solution is shown versus the number of unknowns as a function of the completeness order of the basis functions.

Fink, Patrick W.↗

Estimation of delays and other parameters in nonlinear functional differential equations

A spline-based approximation scheme for nonlinear nonautonomous delay differential equations is discussed. Convergence results (using dissipative type estimates on the underlying nonlinear operators) are given in the context of parameter estimation problems which include estimation of multiple delays and initial data as well as the usual coefficient-type parameters. A brief summary of some of the related numerical findings is also given.

Banks, H. T.↗

Blocking reduction of Landsat Thematic Mapper JPEG browse images using optimal PSNR estimated spectra adaptive postfiltering

Two representative sample images of Band 4 of the Landsat Thematic Mapper are compressed with the JPEG algorithm at 8:1, 16:1 and 24:1 Compression Ratios for experimental browsing purposes. We then apply the Optimal PSNR Estimated Spectra Adaptive Postfiltering (ESAP) algorithm to reduce the DCT blocking distortion. ESAP reduces the blocking distortion while preserving most of the image's edge information by adaptively postfiltering the decoded image using the block's spectral information already obtainable from each block's DCT coefficients. The algorithm iteratively applied a one dimensional log-sigmoid weighting function to the separable interpolated local block estimated spectra of the decoded image until it converges to the optimal PSNR with respect to the original using a 2-D steepest ascent search. Convergence is obtained in a few iterations for integer parameters. The optimal logsig parameters are transmitted to the decoder as a negligible byte of overhead data. A unique maxima is guaranteed due to the 2-D asymptotic exponential overshoot shape of the surface generated by the algorithm. ESAP is based on a DFT analysis of the DCT basis functions. It is implemented with pixel-by-pixel spatially adaptive separable FIR postfilters. PSNR objective improvements between 0.4 to 0.8 dB are shown together with their corresponding optimal PSNR adaptive postfiltered images.

Linares, Irving↗

Climate change drives convergent evolution of root traits on Sky Island climate relicts

Roots are essential to the strategies plants use to survive in variable environments, yet we know little of how they vary within species. Experimental conditions demonstrate that intraspecific plant root traits respond strongly to variation in the environment; however, it is unclear when these responses can be characterized as evolution in response to selective pressures of climate change over many generations. Sky Islands are model, natural climate relict ecosystems to examine climate-change driven evolution. Utilizing a common garden with replicate genotypes of Populus angustifolia (Narrowleaf cottonwood) from six Sky Island (SI) populations and nine adjacent Mountain Chain (MC) populations across three genetic provenances, we hypothesized that SI root traits have diverged due to historical isolation in warmer, drier climates. When grown in common conditions, populations originating on SI’s showed convergent evolution across three distinct genetic provenances, which was characterized by 44.16% decreased total root length, 42.64% decreased average root volume, 43.31% decreased root surface area, and significantly less root trait variation, relative to adjacent mountain chains. Convergent evolution of root traits from trees originating on SI’s is correlated with changes in mean annual precipitation and potential evapotranspiration in the field over the past ~ 125 years. These results demonstrate a consistent pattern in root trait evolution at the landscape scale and the role of climate on the evolution of root traits in a genetic and geographic context relevant to climate change.

Convergent evolution↗

Galerkin formulation of path integrals in lattice field theory

We present a mathematical framework for Galerkin formulations of path integrals in lattice field theory. The framework is based on using the degrees of freedom (DOFs) associated to a Galerkin discretization as the fundamental lattice variables. We formulate standard concepts in lattice field theory, such as the partition function and correlation functions, in terms of the DOFs. For example, using continuous finite element spaces, we show that the two-point spatial correlation function can be defined between any two points on the domain (as opposed to at just lattice sites) and furthermore, this two-point function satisfies a weak propagator (or Green’s function) identity, in analogy to the continuum case, as well as a convergence estimate obtained from the standard finite element techniques. Furthermore, this framework leads naturally to higher-order formulations of lattice field theories by considering higher-order finite element spaces for the Galerkin discretization. We consider analytical and numerical examples of scalar field theory to investigate how increasing the order of piecewise polynomial finite element spaces affect the approximation of lattice observables. Finally, we sketch an outline of this Galerkin framework in the context of gauge field theories.

97 MATHEMATICS AND COMPUTING↗

Tensor network simulations of quasi-GPDs in the massive Schwinger model

Generalized parton distribution functions (GPDs) are off-diagonal light-cone matrix elements that encode the internal structure of hadrons in terms of quark and gluon degrees of freedom. In this work, we present the first nonperturbative study of quasi-GPDs in the massive Schwinger model, quantum electrodynamics in 1+1 dimensions (QED 2 ), within the Hamiltonian formulation of lattice field theory. Quasidistributions are spatial correlation functions of boosted states, which approach the relevant light-cone distributions in the luminal limit. Using tensor networks, we prepare the first excited state in the strongly coupled regime and boost it to close to the light-cone on lattices of up to 400 lattice sites. We compute both quasiparton distribution functions and, for the first time, quasi-GPDs, and study their convergence for increasingly boosted states. In addition, we perform analytic calculations of GPDs in the two-particle Fock-space approximation and in the Reggeized limit, providing qualitative benchmarks for the tensor network results. Our analysis establishes computational benchmarks for accessing partonic observables in low-dimensional gauge theories, offering a starting point for future extensions to higher dimensions, non-Abelian theories, and quantum simulations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Explainable and Differentiable Reinforcement Learning for Multi-objective Optimization in Particle Accelerators

Operating particle accelerators involves optimizing multiple goals simultaneously, which can be challenging due to trade-offs among objectives. While evolutionary algorithms like the genetic algorithm (GA) have been used for various Multi-Objective Optimization (MOO) tasks, they are not inherently suited for complex control problems. This talk highlights two variations of Reinforcement Learning (RL) for concurrently optimizing heat load and trip rates at the Continuous Electron Beam Accelerator Facility (CEBAF). The problem involves strict constraints on individual states, actions, and overall energy requirements of the beam. First, this talk highlights how differentiability can be harnessed through a Deep Differentiable Reinforcement Learning (DDRL) approach to address MOO issues within particle accelerators. We examine the DDRL method alongside Model Free Reinforcement Learning (MFRL), GA, and Bayesian Optimization (BO). The performance of these methods is assessed by generating a Pareto-front for two objectives. Our findings indicate that DDRL excels in handling high-dimensional problems more effectively than MFRL, BO, and GA. Next, we will show integration of explainable physics-based constraints into RL algorithms to enhance trans- parency and trust in decision-making processes by enabling users to verify that agents adhere to established physical principles. This surrogate function can be modeled using neural networks or sparse dictionary mod- els. By examining the mathematical form of the learned constraint function, we are able to confirm the agent has learned to use the established physics of each environment provided but the surrogate model. In addi- tion, we find that the introduction of a mathematical functional dictionary based surrogate model enables our reinforcement learning algorithms to reliably converge for difficult high-dimensional accelerator controls environments.

Rajput, Kishansingh [Thomas Jefferson National Acc↗

A stochastic constrained optimization technique and its application to detector array processing.

A stochastic projected gradient algorithm is proposed which can be used for finding a constrained optimum point for a concave or convex objective function subject to nonlinear constraints which form a connected region even when only a noisy estimate of the objective function is available. For a constraint described by a single linear equation, convergence to the constrained optimum value is proved, and the rate of convergence of the algorithm to the constrained optimum value is determined. The algorithm is applied to the nonlinear problem of obtaining automatically an array of detectors which forms a beam in a desired direction in space in the presence of interfering noise so as to maximize the SNR subject to a constraint on the super-gain ratio.

Winkler, L. P.↗

Nonlinear initial-boundary value solutions by the finite element method

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

Baker, A. J.↗

Improved method for transonic airfoil design-by-optimization

An improved method for use of optimization techniques in transonic airfoil design is demonstrated. FLO6QNM incorporates a modified quasi-Newton optimization package, and is shown to be more reliable and efficient than the method developed previously at NASA-Ames, which used the COPES/CONMIN optimization program. The design codes are compared on a series of test cases with known solutions, and the effects of problem scaling, proximity of initial point to solution, and objective function precision are studied. In contrast to the older method, well-converged solutions are shown to be attainable in the context of engineering design using computational fluid dynamics tools, a new result. The improvements are due to better performance by the optimization routine and to the use of problem-adaptive finite difference step sizes for gradient evaluation.

Kennelly, R. A., Jr.↗

Improved method for transonic airfoil design-by-optimization

An improved method for use of optimization techniques in transonic airfoil design is demonstrated. FLO6QNM incorporates a modified quasi-Newton optimization package, and is shown to be more reliable and efficient than the method developed previously at NASA-Ames, which used the COPES/CONMIN optimization problem. The design codes are compared on a series of test cases with known solutions, and the effects of problem scaling, proximity of initial point to solution, and objective function precision are studied. In contrast to the older method, well-converged solutions are shown to be attainable in the context of engineering design using computational fluid dynamics tools, a new result. The improvements are due to better performance by the optimization routine and to the use of problem-adaptive finite difference step sizes for gradient evaluation.

Kennelly, R. A., Jr.↗