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At least 793 records · Page 44

Smoothing by cubic spline modified applied to solve inverse thermal problem

This paper presents an alternative to cubic spline regularization and its weighted form applied in solving inverse thermal problems. The inverse heat transfer problems are classified as ill-posed, that is, the solution may become unstable, mainly because they are sensitive to random errors deriving from the input data, necessitating a regularization method to soften these effects. The smoothing technique proposed by cubic spline regularization ensures that the global data tend to be more stable, with fewer data oscillations and dependent on a single arbitrary parameter input. It also shows that the weighted cubic spline is able to enhance filter action. The methods have been implemented in order for the search engine to optimize the choice of parameters and weight and, thus, the smoothing gains more flexibility and accuracy. The simulated and experimental tests confirm that the techniques are effective in reducing the amplified noise by inverse thermal problem presented.

97 MATHEMATICS AND COMPUTING↗

Properties of the optimal trajectories for coplanar, aeroassisted orbital transfer

The optimization of trajectories for coplaner, aeroassisted orbital transfer (AOT) from a high Earth orbit (HEO) to a low Earth orbit (LEO) is examined. In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that two impulses are employed, one at HEO exit and one at LEO entry. During the atmospheric pass, the trajectory is controlled via the lift coefficient in such a way that the total characteristic velocity is minimized. First, an ideal optimal trajectory is determined analytically for lift coefficient unbounded. This trajectory is called grazing trajectory, because the atmospheric pass is made by flying at constant altitude along the edge of the atmosphere until the excess velocity is depleted. For the grazing trajectory, the lift coefficient varies in such a way that the lift, the centrifugal force due to the Earth's curvature, the weight, and the Coriolis force due to the Earth's rotation are in static balance. Also, the grazing trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, dynamic pressure, and heating rate. Next, starting from the grazing trajectory results, a real optimal trajectory is determined numerically for the lift coefficient bounded from both below and above. This trajectory is characterized by atmospheric penetration with the smallest possible entry angle, followed by flight at the lift coefficient lower bound. Consistently with the grazing trajectory behavior, the real optimal trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, the dynamic pressure, and the heating rate.

Miele, A.↗

Efficient Gradient-Based Shape Optimization Methodology Using Inviscid/Viscous CFD

The formerly developed preconditioned-biconjugate-gradient (PBCG) solvers for the analysis and the sensitivity equations had resulted in very large error reductions per iteration; quadratic convergence was achieved whenever the solution entered the domain of attraction to the root. Its memory requirement was also lower as compared to a direct inversion solver. However, this memory requirement was high enough to preclude the realistic, high grid-density design of a practical 3D geometry. This limitation served as the impetus to the first-year activity (March 9, 1995 to March 8, 1996). Therefore, the major activity for this period was the development of the low-memory methodology for the discrete-sensitivity-based shape optimization. This was accomplished by solving all the resulting sets of equations using an alternating-direction-implicit (ADI) approach. The results indicated that shape optimization problems which required large numbers of grid points could be resolved with a gradient-based approach. Therefore, to better utilize the computational resources, it was recommended that a number of coarse grid cases, using the PBCG method, should initially be conducted to better define the optimization problem and the design space, and obtain an improved initial shape. Subsequently, a fine grid shape optimization, which necessitates using the ADI method, should be conducted to accurately obtain the final optimized shape. The other activity during this period was the interaction with the members of the Aerodynamic and Aeroacoustic Methods Branch of Langley Research Center during one stage of their investigation to develop an adjoint-variable sensitivity method using the viscous flow equations. This method had algorithmic similarities to the variational sensitivity methods and the control-theory approach. However, unlike the prior studies, it was considered for the three-dimensional, viscous flow equations. The major accomplishment in the second period of this project (March 9, 1996 to March 8, 1997) was the extension of the shape optimization methodology for the Thin-Layer Navier-Stokes equations. Both the Euler-based and the TLNS-based analyses compared with the analyses obtained using the CFL3D code. The sensitivities, again from both levels of the flow equations, also compared very well with the finite-differenced sensitivities. A fairly large set of shape optimization cases were conducted to study a number of issues previously not well understood. The testbed for these cases was the shaping of an arrow wing in Mach 2.4 flow. All the final shapes, obtained either from a coarse-grid-based or a fine-grid-based optimization, using either a Euler-based or a TLNS-based analysis, were all re-analyzed using a fine-grid, TLNS solution for their function evaluations. This allowed for a more fair comparison of their relative merits. From the aerodynamic performance standpoint, the fine-grid TLNS-based optimization produced the best shape, and the fine-grid Euler-based optimization produced the lowest cruise efficiency.

Baysal, Oktay↗

Evolutionary strategy for inverse charge measurements of dielectric particles

Here, we report a computational strategy to obtain the charges of individual dielectric particles from experimental observation of their interactions as a function of time. This strategy uses evolutionary optimization to minimize the difference between trajectories extracted from the experiment and simulated trajectories based on many-particle force fields. The force fields include both Coulombic interactions and dielectric polarization effects that arise due to particle-particle charge mismatch and particle-environment dielectric contrast. The strategy was applied to systems of free falling charged granular particles in a vacuum, where electrostatic interactions are the only driving forces that influence the particles' motion. We show that when the particles' initial positions and velocities are known, the optimizer requires only an initial and final particle configuration of a short trajectory in order to accurately infer the particles' charges; when the initial velocities are unknown and only the initial positions are given, the optimizer can learn from multiple frames along the trajectory to determine the particles' initial velocities and charges. While the results presented here offer a proof-of-concept demonstration of the proposed ideas, the proposed strategy could be extended to more complex systems of electrostatically charged granular matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Efficient shallow Ritz method for 1D diffusion problems

This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or nearly optimal order of the shallow Ritz approximation, we develop a damped block Newton (dBN) method that alternates between updates of the linear and non-linear parameters. Per each iteration, the linear and the non-linear parameters are updated by exact inversion and one step of a modified, damped Newton method applied to a reduced non-linear system, respectively. The computational cost of each dBN iteration is $\mathcal{O}$(n). Starting with the non-linear parameters as a uniform partition of the interval, numerical experiments show that the dBN is capable of efficiently moving mesh points to nearly optimal locations. In conclusion, to improve the efficiency of the dBN further, we propose an adaptive damped block Newton (AdBN) method by combining the dBN with the adaptive neuron enhancement (ANE) method [28].

Diffusion problems↗

iTOUGH2 v7.1

iTOUGH2 (inverse TOUGH2) provides inverse modeling capabilities for TOUGH2, a simulator for multi-dimensional, multi-phase, multi-component, non-isothermal flow and transport in fractured porous media. iTOUGH2 performs sensitivity analyses, data-worth analyses, parameter estimation, and uncertainty propagation analyses in geosciences and reservoir engineering and other application areas. iTOUGH2 supports a number of different combinations of fluids and components (equation-of-state (EOS) modules). In addition, the optimization routines implemented in iTOUGH2 can also be used for sensitivity analysis, automatic model calibration, and uncertainty quantification of any external code that uses text-based input and output files using the PEST protocol. iTOUGH2 solves the inverse problem by minimizing a non-linear objective function of the weighted differences between model output and the corresponding observations. Multiple minimization algorithms (derivative-free, gradient-based, and second-order; local and global) are available. iTOUGH2 also performs Latin Hypercube Monte Carlo simulations for uncertainty propagation analyses. A detailed residual and error analysis is provided. This upgrade includes (a) global sensitivity analysis methods, (b) dynamic memory allocation (c) additional input features and output analyses, (d) increased forward simulation capabilities, (e) parallel execution on multicore PCs and Linux clusters, and (f) bug fixes.

Finsterle, Stefan↗

Guided search for desired functional responses via Bayesian optimization of generative model: Hysteresis loop shape engineering in ferroelectrics

Advances in theoretical modeling across multiple disciplines have yielded generative models capable of high veracity in predicting macroscopic functional responses of materials emerging as a result of complex non-local interactions. Correspondingly, of interest is the inverse problem of finding the model parameter that will yield desired macroscopic responses, such as stress–strain curves, ferroelectric hysteresis loops, etc. Here, we suggest and implement Gaussian process based methods that allow to effectively sample the degenerate parameter space of a complex non-local model to output regions of parameter space which yield desired functionalities. In this work, we discuss the specific adaptation of the acquisition function and sampling function to make the process efficient and balance the efficient exploration of parameter space for multiple possible minima and exploitation to densely sample the regions of interest where target behaviors are optimized. Additionally, this approach is illustrated via the hysteresis loop engineering in ferroelectric materials but can be adapted to other functionalities and generative models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Preparing Li-garnet electrodes with engineered structures by phase inversion and high shear compaction processes

We report solid-state lithium batteries are promising for safety and energy density com-pared with traditional lithium-ion batteries. However, the large interfacial resistance between the electrode and electrolyte is a bottleneck to achieving high-performance solid-state batteries. Engineered electrode structures with a porous scaffold of the solid electrolyte material are promising to lower the interfacial resistance and provide a mechanical support for a thin solid electrolyte layer. In this work, two ceramic processing techniques are used to fabricate porous/dense bilayer architectures based on a Li 6.25 Al 0.25 La 3 Zr 2 O 12 (LLZO) Li-garnet material. Finger-like vertically aligned pores are created by the phase inversion (PI) process. A water bath presaturated with Li salt prevents Li loss during the PI solvent exchange step. Pore size and porosity can be optimized by adjusting the bath temperature. The high shear compaction process was used to prepare LLZO tapes with 40, 60, and 80 vol% poreformer. The porosity of the tapes after sintering is 39.5%, 58.4%, and 75.4%, respectively. Microtomography exhibits the porosity, pore shape, and pore distribution of the tapes. A typical cathode material LiNi 0.33 Mn 0.33 Co 0.33 O 2 (NMC) is filled into the pores via vacuum infiltration, and a dense cathode layer is formed within the garnet scaffold.

25 ENERGY STORAGE↗

SU-F-T-618: Evaluation of a Mono-Isocentric Treatment Planning Software for Stereotactic Radiosurgery of Multiple Brain Metastases

Purpose: To evaluate planning performance of an automated treatment planning software (BrainLAB; Elements) for stereotactic radiosurgery (SRS) of multiple brain metastases. Methods: Brainlab’s Multiple Metastases Elements (MME) uses single isocentric technique to treat up to 10 cranial planning target volumes (PTVs). The planning algorithm of the MME accounts for multiple PTVs overlapping with one another on the beam eyes view (BEV) and automatically selects a subset of all overlapping PTVs on each arc for sparing normal tissues in the brain. The algorithm also optimizes collimator angles, margins between multi-leaf collimators (MLCs) and PTVs, as well as monitor units (MUs) using minimization of conformity index (CI) for all targets. Planning performance was evaluated by comparing the MME-calculated treatment plan parameters with the same parameters calculated with the Volumetric Modulated Arc Therapy (VMAT) optimization on Varian’s Eclipse platform. Results: Figures 1 to 3 compare several treatment plan outcomes calculated between the MME and VMAT for 5 clinical multi-targets SRS patient plans. Prescribed target dose was volume-dependent and defined based on the RTOG recommendation. For a total number of 18 PTV’s, mean values for the CI, PITV, and GI were comparable between the MME and VMAT within one standard deviation (σ). However, MME-calculated MDPD was larger than the same VMAT-calculated parameter. While both techniques delivered similar maximum point doses to the critical cranial structures and total MU’s for the 5 patient plans, the MME required less treatment planning time by an order of magnitude compared to VMAT. Conclusion: The MME and VMAT produce similar plan qualities in terms of MUs, target dose conformation, and OAR dose sparing. While the selective use of PTVs for arc-optimization with the MME reduces significantly the total planning time in comparison to VMAT, the target dose homogeneity was also compromised due to its simplified inverse planning algorithm used.

60 APPLIED LIFE SCIENCES↗

Numerical optimization in Hilbert space using inexact function and gradient evaluations

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

Carter, Richard G.↗

Numerical model for the Programmable Multirole Furnace (PMZF)

The present account of the Programmable Multizone Furnace numerical model uses various examples to illustrate the ways in which the model serves as an optimization, test, prediction, and visualization tool; a numerical PID-control algorithm obtains the desired sample temperature distributions and allows the model to solve an inverse heat transfer problem where the desired sample temperature profile is the input and the required heater power distribution is the output of numerical simulations. Parametric studies show how the total power consumption of the furnace is affected by such design variables as the conductivity.

Kassemi, M.↗

Cluster Analysis of Spectroscopic Line Profiles and EUV Emission in RMHD Simulations and Observations of the Solar Atmosphere

Spatially-resolved observations from the IRIS, SDO/AIA, and other space mission and ground-based telescopes, coupled with realistic 3D RMHD simulations, are a powerful tool for analysis of processes in the solar atmosphere. To better understand the dynamical and thermodynamic properties in the simulation data and their connection to observations, it is essential to determine similarities in the behaviors of the synthesized and observed emission. However, the complexity of observational data and physical processes makes comparison of observations and modeling results difficult. In this work, we show the initial results of application of K-Means clustering (unsupervised machine learning) algorithm to two different problems: 1) recognition of the typical spectroscopic line profiles observed by IRIS during solar flares and their typical dynamic behavior; 2) recognition of shocks and heating events in synthetic AIA emission data obtained from StellarBox quiet-Sun simulations. The average silhouette width technique for the KMeans algorithm is utilized in different ways to obtain optimal numbers of clusters. We discuss application of the emission clustering to visualizations of the computational volume, understanding its evolutionary trends and behavior patterns, and inversion (reconstruction) of physical properties of the solar atmosphere from synthesizes emission data.

Sadykov, Viacheslav↗

Assessing Relay Communications for Mars Sample Return Surface Mission Concepts

The Mars Sample Return (MSR) Campaign would be a 3-mission campaign concept supported by NASA and ESA to return samples from the Mars surface. MSR would, for the first time ever, present a need to communicate with multiple surface assets that are co-located on Mars in a coordinated effort to accomplish the unified objective of fetching, transporting, and returning samples from Mars. Currently, Mars surface assets relay data to and from Earth using a number of orbiters in what’s known as the Mars Relay Network (MRN). This network is characterized by a small number of surface assets distributed across the Martian globe and a larger number of orbiters to provide relay services. As of June 2020, there are two surface assets for which five orbiters are providing relay. During the MSR Campaign, there would be two rovers and a lander that all would require relay communication from a small number of Mars orbiters to meet the aggressive MSR timeline. The inversion of the current MRN paradigm, a system of many surface assets requiring relay and few orbiters to provide relay, necessitates the unique challenge of optimally allocating relay passes to maximize the operational capability of all assets. The allocation must consider a large number of trade variables including Mars asset operational requirements and Earth ground system constraints, including staffing schedules, operations planning across time zones, and more. To address these telecommunication challenges, the Mars Asset Relay Mission Link Allocation Design Environment (MARMLADE) tool was developed. It is a MATLAB-based tool to assign orbiter passes or Direct-From-Earth (DFE) links to each of the three surface assets and quantify the operational efficiency of each surface asset.MARMLADE uses a data set of simulated Mars relay orbiter geometry and telecommunication capabilities provided by JPL’s Telecom Orbit Analysis and Simulation Tool (TOAST) software to compute which asset should get each pass based on a series of heuristics and predictions of all assets’ states. Within MARMLADE, the user can provide inputs including the option for time-based pass splitting, fixed FWD data rate capabilities, DFE communication capabilities, and link parameters allowing for the assessment of complex operations and hardware trades using surface mission operational efficiency as a primary figure of merit. As the MSR mission concepts continue to mature, MARMLADE is being used to assess ability of all MSR elements to meet the surface mission timeline requirements and to provide relay link allocations to each of the MSR surface assets.This paper will describe the motivation and design of the MARMLADE tool and how it is being used to perform campaign and mission level trades, generate requirements, and support development of the MSR surface mission scenarios.

Lee, Charles↗

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗

Optical filters made from random metasurfaces using Bayesian optimization

Abstract We theoretically investigate the ability to design optical filters from a single material and a single layer of randomly dispersed resonant dielectric particles, defining a random metasurface. Using a Bayesian and generalized Mie inverse-design approach, we design particle radii distributions that give rise to longpass, shortpass, bandpass, and bandstop spectral bands in the infrared. The optical response is shown to be directly related to electric and magnetic multipole scattering of the constituent particles and their near field coupling. We discuss the effect of the particle size distribution and particle–particle coupling interactions on filter design in random systems lacking long-range order.

Materials Science↗

Translation and rotation equivariant normalizing flow (TRENF) for optimal cosmological analysis

ABSTRACT Our Universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work, we develop translation and rotation equivariant normalizing flow (TRENF), a generative normalizing flow (NF) model which explicitly incorporates these symmetries, defining the data likelihood via a sequence of Fourier space-based convolutions and pixel-wise non-linear transforms. TRENF gives direct access to the high dimensional data likelihood p(x|y) as a function of the labels y, such as cosmological parameters. In contrast to traditional analyses based on summary statistics, the NF approach has no loss of information since it preserves the full dimensionality of the data. On Gaussian random fields, the TRENF likelihood agrees well with the analytical expression and saturates the Fisher information content in the labels y. On non-linear cosmological overdensity fields from N-body simulations, TRENF leads to significant improvements in constraining power over the standard power spectrum summary statistic. TRENF is also a generative model of the data, and we show that TRENF samples agree well with the N-body simulations it trained on, and that the inverse mapping of the data agrees well with a Gaussian white noise both visually and on various summary statistics: when this is perfectly achieved the resulting p(x|y) likelihood analysis becomes optimal. Finally, we develop a generalization of this model that can handle effects that break the symmetry of the data, such as the survey mask, which enables likelihood analysis on data without periodic boundaries.

79 ASTRONOMY AND ASTROPHYSICS↗

End-to-end optimization for battery materials and molecules by combining graph neural networks and reinforcement learning

The National Renewable Energy Laboratory (NREL), together with the Colorado School of Mines (CSM) and Colorado State University (CSU), has developed a machine learning-enhanced approach to design new battery materials. Currently, such materials are designed in part via numerous expensive high-fidelity computational simulations that predict the performance of a given composition. Even with computational screening tools, the vast landscape of possible molecular or crystal structures exceeds current and future computational capacity. Improving the efficiency by which new materials can be optimized will therefore disrupt the cost, risk, and time required to bring new energy solutions to the marketplace. Predicting the properties of an organic molecule or periodic crystalline material given its structure has grown increasingly common. These approaches leverage large-scale computational and experimental databases and ML approaches such as graph neural networks. The inverse design problem of finding a material that possesses desired properties is substantially more challenging, since enumerating all valid material structures is not feasible. In this project, we leveraged recent success in reinforcement learning to efficiently navigate this high-dimensional search space. Just as algorithms can find the optimal chess moves from nearly limitless options, we train an approach to evolve a simple starting structure into a complex structure that possess the desired properties. Our solution has been demonstrated by applying it to two related design application tasks for short- and long-term energy storage, respectively: (1) the design of solid-state ion conductors and (2) the design of organic redox-active materials. The project has resulted an open-source software library for material design, documented examples of applying the library to both organic and inorganic material optimization, and peer-reviewed publications detailing the data, computational models, and resulting candidate materials.

25 ENERGY STORAGE↗