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At least 937 records · Page 52

A trust region algorithm for PDE-constrained optimization with bound constraints using reduced order modeling

This paper presents a novel trust region algorithm that relies on proper orthogonal de-composition techniques to construct accurate reduced order models during optimization.The algorithm samples high fidelity snapshots to compute the POD functions that are used to generate reduced order models. The reduced order models are used to replace the computationally intensive high fidelity finite element evaluations during optimization.The proposed algorithm employs a trust region framework to detect loss in predictive ac-curacy in the reduced order model and automatically update the POD functions during optimization. The trust region framework allows the algorithm to use sound mathematical metrics to effectively improve the accuracy and robustness of the reduced order models during optimization. The algorithm also employs a projected gradient algorithm to model bound constraints and compute optimal and feasible controls.This paper also presents an accurate Hessian formulation for topology optimization problems. The proposed trust region framework relies on a quadratic model to update the control. This quadratic model needs reliable second order derivative information to predict the behavior of the objective function within a suitable trust region. If a nonlinear Hessian formulation is used, the computational effort increases due to additional finite element evaluations. The proposed linear Hessian formulation reduces the computational effort and enables the calculation of the second order derivative information without additional finite element model evaluations. Examples in topology optimization are presented to demonstrate the applicability of the proposed algorithm and linear Hessian formulation for large-scale PDE-constrained optimization.

bound constraints↗

Optimizing colormaps with consideration for color vision deficiency to enable accurate interpretation of scientific data

Color vision deficiency (CVD) affects more than 4% of the population and leads to a different visual perception of colors. Though this has been known for decades, colormaps with many colors across the visual spectra are often used to represent data, leading to the potential for misinterpretation or difficulty with interpretation by someone with this deficiency. Until the creation of the module presented here, there were no colormaps mathematically optimized for CVD using modern color appearance models. While there have been some attempts to make aesthetically pleasing or subjectively tolerable colormaps for those with CVD, our goal was to make optimized colormaps for the most accurate perception of scientific data by as many viewers as possible. We developed a Python module, cmaputil , to create CVD-optimized colormaps, which imports colormaps and modifies them to be perceptually uniform in CVD-safe colorspace while linearizing and maximizing the brightness range. The module is made available to the science community to enable others to easily create their own CVD-optimized colormaps. In this paper, we present an example CVD-optimized colormap created with this module that is optimized for viewing by those without a CVD as well as those with red-green colorblindness. This colormap, cividis, enables nearly-identical visual-data interpretation to both groups, is perceptually uniform in hue and brightness, and increases in brightness linearly.

59 BASIC BIOLOGICAL SCIENCES↗

Learning Optimal Multigrid Smoothers via Neural Networks

Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.

97 MATHEMATICS AND COMPUTING↗

Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning

Abstract We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC–AE) has been shown to capture nonlinear solution manifolds but fails to perform adequately when linear subspace approaches such as proper orthogonal decomposition (POD) would be optimal. Besides, most DL-ROM models rely on convolutional layers, which might limit its application to only a structured mesh. The proposed framework in this study relies on the combination of an autoencoder (AE) and Barlow Twins (BT) self-supervised learning, where BT maximizes the information content of the embedding with the latent space through a joint embedding architecture. Through a series of benchmark problems of natural convection in porous media, BT–AE performs better than the previous DL-ROM framework by providing comparable results to POD-based approaches for problems where the solution lies within a linear subspace as well as DL-ROM autoencoder-based techniques where the solution lies on a nonlinear manifold; consequently, bridges the gap between linear and nonlinear reduced manifolds. We illustrate that a proficient construction of the latent space is key to achieving these results, enabling us to map these latent spaces using regression models. The proposed framework achieves a relative error of 2% on average and 12% in the worst-case scenario (i.e., the training data is small, but the parameter space is large.). We also show that our framework provides a speed-up of $$7 \times 10^{6}$$ 7 × 10 6 times, in the best case, and $$7 \times 10^{3}$$ 7 × 10 3 times on average compared to a finite element solver. Furthermore, this BT–AE framework can operate on unstructured meshes, which provides flexibility in its application to standard numerical solvers, on-site measurements, experimental data, or a combination of these sources.

97 MATHEMATICS AND COMPUTING↗

ELSI — An open infrastructure for electronic structure solvers

Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with different structures. The ELectronic Structure Infrastructure (ELSI) project provides an open-source software interface to facilitate the implementation and optimal use of high-performance solver libraries covering cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between. In this paper, we present recent improvements and developments inside ELSI, mainly covering (1) new solvers connected to the interface, (2) matrix layout and communication adapted for parallel calculations of periodic and/or spin-polarized systems, (3) routines for density matrix extrapolation in geometry optimization and molecular dynamics calculations, and (4) general utilities such as parallel matrix I/O and JSON output. The ELSI interface has been integrated into four electronic structure code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on results of a systematic set of large-scale benchmarks performed with Kohn–Sham density-functional theory and density-functional tight-binding theory, we identify factors that strongly affect the efficiency of the solvers, and propose a decision layer that assists with the solver selection process. As a result, we describe a reverse communication interface encoding matrix-free iterative solver strategies that are amenable, e.g., for use with planewave basis sets.

97 MATHEMATICS AND COMPUTING↗

Use of a segmented cell for the combinatorial development of platinum group metal-free electrodes for polymer electrolyte fuel cells

The development of novel platinum group metal (PGM)-free catalysts is a difficult task, particularly when coupled with the integration into a cathode catalyst layer (CCL). The optimization of such PGM-free electrode structures is often non-linear and iterative, making it a demanding task due to the high number of parameters that affect performance. To accelerate both materials discovery and electrode development, this work demonstrates the application of a high-resolution segmented cell (SC) with 121 segments of 0.413 cm 2 size for combinatorial high-throughput PGM-free catalyst screening and CCL optimization. The approach utilizes three flow-field strips with active areas of 4.45 cm 2 each, distributed over 11 segments. Electrodes with identical catalyst material and fabrication method result in reproducible data with typically less than 10% variation between each segment and match in performance with differential single cell data. High throughput testing of combinatorial sample sets, with varied PGM-free electrocatalyst materials or electrode composition, demonstrated the ability to rapidly discern high performing outliers, and establish or confirm trends in electrode optimization. The results indicated significant performance benefits of electrodes with ionomer content of 45 wt% over lower values, and of water rich inks with 82% water content over those with 50%.

30 DIRECT ENERGY CONVERSION↗

Sensitivity of joint contagiousness and susceptibility-based dynamic optimal control strategies for HIV prevention

Predicting the population-level effects of an infectious disease intervention that incorporate multiple modes of intervention is complicated by the joint non-linear dynamics of both infection transmission and the intervention itself. In this paper, we consider the sensitivity of Dynamic Optimal Control Profiles (DOCPs) for the optimal joint investment in both a contagiousness and susceptibility-based control of HIV to bio-behavioral, economic, and programmatic assumptions. The DOCP is calculated using recently developed numerical algorithms that allow controls to be represented by a set of piecewise constant functions that maintain a constant yearly budget. Our transmission model assumes multiple stages of HIV infection corresponding to acute and chronic infection and both within- and between-individual behavioral heterogeneity. We parameterize a baseline scenario from a longitudinal study of sexual behavior in MSM and consider sensitivity of the DOCPs to deviations from that baseline scenario. In the baseline scenario, the primary determinant of the dominant control were programmatic factors, regardless of budget. In sensitivity analyses, the qualitative aspects of the optimal control policy were often robust to significant deviation in assumptions regarding transmission dynamics. In addition, we found several conditions in which long-term joint investment in both interventions was optimal. Our results suggest that modeling in the service of decision support for intervention design can improve population-level effects of a limited set of economic resources. We found that economic and programmatic factors were as important as the inherent transmission dynamics in determining population-level intervention effects. Given our finding that the DOCPs were robust to alternative biological and behavioral assumptions it may be possible to identify DOCPs even when the data are not sufficient to identify a transmission model.

59 BASIC BIOLOGICAL SCIENCES↗

TU-D-207B-02: Delta-Radiomics: The Prognostic Value of Therapy-Induced Changes in Radiomics Features for Stage III Non-Small Cell Lung Cancer Patients

Purpose: To determine how radiomics features change during radiation therapy and whether those changes (delta-radiomics features) can improve prognostic models built with clinical factors. Methods: 62 radiomics features, including histogram, co-occurrence, run-length, gray-tone difference, and shape features, were calculated from pretreatment and weekly intra-treatment CTs for 107 stage III NSCLC patients (5–9 images per patient). Image preprocessing for each feature was determined using the set of pretreatment images: bit-depth resample and/or a smoothing filter were tested for their impact on volume-correlation and significance of each feature in univariate cox regression models to maximize their information content. Next, the optimized features were calculated from the intratreatment images and tested in linear mixed-effects models to determine which features changed significantly with dose-fraction. The slopes in these significant features were defined as delta-radiomics features. To test their prognostic potential multivariate cox regression models were fitted, first using only clinical features and then clinical+delta-radiomics features for overall-survival, local-recurrence, and distant-metastases. Leave-one-out cross validation was used for model-fitting and patient predictions. Concordance indices(c-index) and p-values for the log-rank test with patients stratified at the median were calculated. Results: Approximately one-half of the 62 optimized features required no preprocessing, one-fourth required smoothing, and one-fourth required smoothing and resampling. From these, 54 changed significantly during treatment. For overall-survival, the c-index improved from 0.52 for clinical factors alone to 0.62 for clinical+delta-radiomics features. For distant-metastases, the c-index improved from 0.53 to 0.58, while for local-recurrence it did not improve. Patient stratification significantly improved (p-value<0.05) for overallsurvival and distant-metastases when delta-radiomics features were included. The delta-radiomics versions of autocorrelation, kurtosis, and compactness were selected most frequently in leave-one-out iterations. Conclusion: Weekly changes in radiomics features can potentially be used to evaluate treatment response and predict patient outcomes. High-risk patients could be recommended for dose escalation or consolidation chemotherapy. This project was funded in part by grants from the National Cancer Institute (NCI) and the Cancer Prevention Research Institute of Texas (CPRIT).

60 APPLIED LIFE SCIENCES↗

Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence

In this work, we propose a new Gaussian process regression (GPR)-based multifidelity method: physics-informed CoKriging (CoPhIK). In CoKriging-based multifidelity methods, the quantities of interest are modeled as linear combinations of multiple parameterized stationary Gaussian processes (GPs), and the hyperparameters of these GPs are estimated from data via optimization. In CoPhIK, we construct a GP representing low-fidelity data using physics-informed Kriging (PhIK), and model the discrepancy between low- and highfidelity data using a parameterized GP with hyperparameters identified via optimization. Our approach reduces the cost of optimization for inferring hyperparameters by incorporating partial physical knowledge. We prove that the physical constraints in the form of deterministic linear operators are satisfied up to an error bound. Furthermore, we combine CoPhIK with a greedy active learning algorithm for guiding the selection of additional observation locations. The eciency and accuracy of CoPhIK are demonstrated for reconstructing the partially observed modified Branin function, reconstructing the sparsely observed state of a steady state heat transport problem, and learning a conservative tracer distribution from sparse tracer concentration measurements.

Yang, Xiu↗

A greedy Galerkin method to efficiently select sensors for linear dynamical systems

A key challenge in inverse problems is the selection of sensors to gather the most effective data. In this paper, we consider the problem of inferring the initial condition to a linear dynamical system and develop an efficient control-theoretical approach for greedily selecting sensors. Our method employs a Galerkin projection to reduce the size of the inverse problem, resulting in a computationally efficient algorithm for sensor selection. As a byproduct of our algorithm, we obtain a preconditioner for the inverse problem that enables the rapid recovery of the initial condition. Here, we analyze the theoretical performance of our greedy sensor selection algorithm as well as the performance of the associated preconditioner. Finally, we verify our theoretical results on various inverse problems involving partial differential equations.

97 MATHEMATICS AND COMPUTING↗

A prototype hybrid mode cavity for heterodyne axion detection

In the heterodyne approach to axion detection, axion dark matter induces transitions between two modes of a microwave cavity, resulting in a parametrically enhanced signal power. We describe the fabrication and characterization of a prototype normal conducting cavity specifically optimized for heterodyne detection. Corrugations on the cavity walls support linearly polarized hybrid modes which maximize the signal power while strongly suppressing noise. We demonstrate tuning mechanisms which allow one mode frequency to be scanned across a 4 MHz range, while suppressing cross-coupling noise by at least 80 dB. A future superconducting cavity with identical geometry to our prototype would have the potential to probe orders of magnitude beyond astrophysical bounds.

Li, Zenghai [SLAC]↗

Aperture‐Synthesis Radar Imaging With Compressive Sensing for Ionospheric Research

Abstract Inverse methods involving compressive sensing are tested in the application of two‐dimensional aperture‐synthesis imaging of radar backscatter from field‐aligned plasma density irregularities in the ionosphere. We consider basis pursuit denoising, implemented with the fast iterative shrinkage thresholding algorithm, and orthogonal matching pursuit (OMP) with a wavelet basis in the evaluation. These methods are compared with two more conventional optimization methods rooted in entropy maximization (MaxENT) and adaptive beamforming (linearly constrained minimum variance or often “Capon's Method.”) Synthetic data corresponding to an extended ionospheric radar target are considered. We find that MaxENT outperforms the other methods in terms of its ability to recover imagery of an extended target with broad dynamic range. Fast iterative shrinkage thresholding algorithm performs reasonably well but does not reproduce the full dynamic range of the target. It is also the most computationally expensive of the methods tested. OMP is very fast computationally but prone to a high degree of clutter in this application. We also point out that the formulation of MaxENT used here is very similar to OMP in some respects, the difference being that the former reconstructs the logarithm of the image rather than the image itself from basis vectors extracted from the observation matrix. MaxENT could in that regard be considered a form of compressive sensing.

Hysell, D. L.↗

Flexible organic integrated electronics for self-powered multiplexed ocular monitoring

Smart contact lens has drawn extensive research interests due to the noninvasive real-time detection of the human body to provide biomedical information for health management. However, it has been difficult to accurately measure the physiological signals in tears, and the use of external power source has also hindered the future applications. Here, we demonstrated an organic electrochemical transistor based multiplexed sensors self-powered by the organic solar cells (OSCs). The integrated device was fabricated via simple process including solution blade-coating and thermal evaporation. OSCs were optimized to provide optimal operation voltage for the sensors that exhibit semilog-linear response to the glucose and calcium ions in tear fluids without any peripheral circuits. The sensing signals can be transmitted to the laptop wirelessly through a near filed communication unit. This integrated self-powered multiplexed sensing device will provide real-time monitoring of the biomarkers in tears, prospected to be installed on the smart contact lens for the early detection and diagnosis of diabetes.

36 MATERIALS SCIENCE↗

Flux-pumped impedance-engineered broadband Josephson parametric amplifier

Broadband quantum-limited amplifiers play a critical role in the single-shot readout of superconducting qubits, but a popular implementation, the traveling wave parametric amplifier, involves a complex design and fabrication process. Here, we present a simple design for a Josephson parametric amplifier, using a lumped element resonator comprising a superconducting quantum interference device whose useful bandwidth is enhanced with an on-chip impedance-matching circuit. Additionally, we demonstrate a flux-coupling geometry that maximizes the coupling to the Josepson loop and minimizes spurious excitation of the amplifier resonant circuit. The amplifier, which operates in a flux-pumped mode, is demonstrated with a power gain of more than 20dB over a bandwidth of about 300MHz, where approximate noise measurements indicate quantum-limited pehrformance. A procedure is given for optimizing the bandwidth for this kind of amplifier, using a linearized circuit simulation while minimizing non-linearities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A windowed mean trajectory approximation for condensed phase dynamics

We propose a trajectory-based quasi-classical method for approximating dynamics in condensed phase systems. Building upon the previously developed optimized mean trajectory approximation that has been used to compute linear and nonlinear spectra, we borrow some ideas from filtering trajectory methods to obtain a novel semiclassical method for the dynamical propagation of density matrices. This new approximation is tested rigorously against standard multistate electronic models, spin-boson models, and models of the Fenna–Matthews–Olson complex. For dissipative systems, the current method is significantly better or as good as many other semiclassical methods available, especially at low temperatures and for off-diagonal density matrix elements, whereas for scattering models, the current method bears similar limitations as mean-field propagation schemes. All results are tested against the numerically exact hierarchical equations of motion method. In conclusion, the new method shows excellent agreement across various parameter regimes with numerically exact results, highlighting the robustness and accuracy of our approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Carbon dioxide stimulation of photosynthesis in Liquidambar styraciflua is not sustained during a 12-year field experiment

Elevated atmospheric CO 2 (eCO 2 ) often increases photosynthetic CO 2 assimilation (A) in field studies of temperate tree species, although there is evidence that the increases may decline through time due to biochemical and morphological acclimation, and environmental constraints. Indeed, at the free air CO 2 enrichment (FACE) study in Oak Ridge, Tennessee, A was increased in 12-year-old sweetgum trees following two years of ~40% enhancement of CO 2 . A was re-assessed a decade later to determine if initial enhancement of eCO 2 was sustained through time. Measurements were conducted at prevailing CO 2 and temperature on detached, re-hydrated branches using a portable gas exchange system. Photosynthetic CO 2 response curves (A versus the CO 2 concentration in the intercellular air space (C i ); or A-C i curves) were contrasted with earlier measurements using consistent leaf photosynthesis model equations. We accessed relationships between light-saturated photosynthesis (A sat ), maximum electron transport rate (J max ), maximum Rubisco activity (V cmax ) chlorophyll content and foliar nitrogen (N) and chlorophyll content. In 1999, light-saturated photosynthesis (A sat ) for eCO 2 treatments was 15.4 ± 0.8 μmol m -2 s -1 , 22% higher than aCO 2 treatments (P<0.01). By 2009, A sat declined to <50% of 1999 values, and there was no longer a significant effect of eCO 2 (A sat = 6.9 or 5.7 ± 0.7 μmol m -2 s -1 for eCO 2 or aCO 2 , respectively). In 1999, there was no treatment effect on area-based foliar N; however, by 2008, N content in eCO 2 foliage was 17% less than in aCO 2 foliage. Photosynthetic N use efficiency (A sat :N) was greater in eCO 2 in 1999 resulting in greater A sat despite similar N content, but the enhanced efficiency in eCO 2 trees was lost as foliar N declined to sub-optimal levels. There was no treatment difference in the declining linear relationships between J max or V cmax with declining N, or in the ratio of J max :V cmax through time. Results suggest that initial enhancement of photosynthesis to elevated CO 2 will not be sustained through time if nitrogen becomes limited.

54 ENVIRONMENTAL SCIENCES↗

Data Driven Optimization Framework for Volt-age Regulation in Distribution Systems

This letter proposes a data-driven optimization framework for voltage regulation problems to address the challenge of model inaccuracy and parameter varying. To achieve online voltage optimization, the recursive kernel regression and interior point methods are integrated. The IEEE 123-Bus system and EPRI Ckt5 feeder are selected to validate the effectiveness of the proposed data-driven optimization framework. The proposed method is also compared with a linear function based method.

Hong, Tianqi↗