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At least 559 records · Page 31

Linear convergence of accelerated conditional gradient algorithms in spaces of measures

A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding coefficients. Under general assumptions, a sub-linear [see formula in PDF] rate in the objective functional is obtained, which is sharp in most cases. To improve efficiency, one can fully resolve the finite-dimensional subproblems occurring in each iteration of the method. We provide an analysis for the resulting procedure: under a structural assumption on the optimal solution, a linear [see formula in PDF] convergence rate is obtained locally.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

MOOSE Optimization Module Overview: Application to Residual Stress Inversion in Nuclear Fuel Plates

Manufacturing methods, material selections and unique plate geometries used in low enriched uranium plate fuels for the High Performance Research Reactor (HPRR) have led to concerns about the residual stresses effect on bond strength of the fuel/cladding interfaces and overall fuel performance under irradiation. The current HPRR plate fuel test program performed residual stress calculations using the contour method with experimental displacement data obtained by incrementally cutting the plate fuel. In this work, we use a gradient based inverse optimization module developed within the MOOSE framework to estimate normal and shear residual stresses within the plate fuels using displacement data taken from a cut placed in the HPRR fuel plate. These results are verified against residual stress calculations obtained from the contour method. The inversion protocol used in this work utilizes two meshes to separately discretize the physics and parameter space. This allows a fine mesh to be used to fully resolve the physics and geometry of the forward problem. A coarser mesh is used to resolve the parameter space with spatially varying mesh density determined from a sensitivity analysis. The adaptive resolution of the parameter space essentially has the effect of regularization as it is designed to achieve the bias-variance tradeoff.

42 ENGINEERING↗

Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.

Autoencoders↗

Scalable Implementation of Mean-Field and Correlation Methods Based on Lie-Algebraic Similarity Transformation of Spin Hamiltonians in the Jordan–Wigner Representation

Recent work has highlighted that the strong correlation inherent in spin Hamiltonians can be effectively reduced by mapping spins to Fermions via the Jordan−Wigner transformation (JW). The Hartree−Fock method is straightforward in the Fermionic domain and may provide a reasonable approximation to the ground state. Correlation with respect to the Fermionic mean field can be recovered based on Lie-algebraic similarity transformation (LAST) with two-body correlators. Specifically, a unitary LAST variant eliminates the dependence on site ordering, while a nonunitary LAST yields size-extensive correlation energies. Whereas the first recent demonstration of such methods was restricted to small spin systems, we present efficient implementations using analytical gradients for the optimization with respect to the mean-field reference and the LAST parameters, thereby enabling the treatment of larger clusters, including systems with local spins s > $\frac{1}{2}$.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Do optimization methods in deep learning applications matter?

With advances in deep learning, exponential data growth and increasing model complexity, developing efficient optimization methods are attracting much research attention. Several implementations favor the use of Conjugate Gradient (CG) and Stochastic Gradient Descent (SGD) as being practical and elegant solutions to achieve quick convergence, however, these optimization processes also present many limitations in learning across deep learning applications. Recent research is exploring higher-order optimization functions as better approaches, but these present very complex computational challenges for practical use. Comparing first and higher-order optimization functions, in this paper, our experiments reveal that Levemberg-Marquardt (LM) significantly supersedes optimal convergence but suffers from very large processing time increasing the training complexity of both, classification and reinforcement learning problems. Our experiments compare off-the-shelf optimization functions(CG, SGD, LM and L-BFGS) in standard CIFAR, MNIST, CartPole and FlappyBird experiments.The paper presents arguments on which optimization functions to use and further, which functions would benefit from parallelization efforts to improve pretraining time and learning rate convergence.

Ozyildirim, Buse Melis↗

NMPC for Setpoint Tracking Operation of a Solid Oxide Electrolysis Cell System

Solid oxide electrolysis cells (SOECs) are a promising technology to generate hydrogen through water electrolysis. However, intermittent renewable energy requires SOECs to transition between hydrogen production setpoints as the price of electricity fluctuates. A well-functioning control system is important to avoid cell degradation during setpoint tracking operation. In this work, we apply nonlinear model predictive control (NMPC) to an SOEC module and supporting equipment and compare NMPC performance to classical PI control while ramping between hydrogen production setpoints. We find that these control methods provide similar performance in many metrics, but NMPC significantly reduces cell thermal gradients during the setpoint transition.

Allan, Douglas↗

A Look At Dissolved Organic Carbon In Streams and Its Effect On DGT Hg Collection

Savannah River Site (SRS) and Oak Ridge National Laboratory (ORNL) were both major material production sites for the U.S.'s nuclear program during the 20. century. Both sites discharged mercury (Hg) to streams. Oak Ridge streams have accumulated significant levels of Hg from early 'historical' discharges. Diffusive Gradient in Thin Films (DGT) samplers may be a labor and material saving method to monitor the Hg contamination of streams at both sites. Humic and Fulvic acids are released during the degradation of plant and animal residue. They are part of the Dissolved Organic Matter that colors the black water streams of the southern U.S.. Humic acid and Fulvic acids have a tendency to sequester heavy metals, like Hg, and may interfere with the reactions needed to draw the Hg through the thin films of the DGT samplers. Project Objective: Use a UV-Vis spectrophotometer to estimate the levels of Dissolved Organic Carbon (DOC) in the streams selected to test the effect of DOC on DGT samplers. Conclusion: UV-Vis is a convenient way to estimate the amount of DOC in streams and may be used to provide more context in DGT Hg sampling. efforts. Future Work: Analyze data from SRS and ORNL DGT samples; Compare the results of the DGT samplers with more traditional speciating methods from ORNL; Use a TOC Spectrophotometer to gain a more accurate picture of stream DOC.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

River Dissolved Oxygen Prediction Using Machine Learning Models and Wireless Sensor Measurements

Simultaneous flooding&heat and droughts&heat events can potentially destabilize hydro-meteorological conditions to deteriorate the water quality of Neches River. Machine learning (ML) models utilizing wireless sensor measurements have been applied to predict water quality and optimize various water management strategies. This study aims to develop ML models to predict dissolved oxygen (DO) prediction under various hydro-meteorological conditions and enhance water management decision-making. Wireless sensor measurements of DO, water temperature, sample depth, conductivity, turbidity, and pH, along with discharge from the United States Geological Survey stations, are collected for model inputs at the Pine Island Bayou C749 station (PIB-C749) and Neches River Saltwater Barrier (SWB). Multilayer perceptron neural networks, recurrent neural networks, long short-term memory (LSTM), and bidirectional LSTM (BiLSTM) with and without attention mechanism (AT) are tested to determine the best model, which is applied the rolling forecast method to predict 14-day DO. Traditional and recurrent transfer learning (TL and RTL) methods are adopted to overcome insufficient data at the SWB. The input feature importance analysis using the integrated gradients (IG) algorithm is applied to determine dominant inputs. The results show LSTM-based models are capable handling long sequential data. AT-BiLSTM and RTL-LSTM demonstrate the best performance at the PIB-C749 (RMSE=0.054) and the SWB (RMSE=0.028), respectively. TL and RTL methods significantly improve model performance at the SWB. DO, temperature, and pH show higher importance, consistent with hydrodynamics and water chemistry. Both best models are applied to predict 14-day DO and demonstrate reasonable performance for decision-making. Hydro-meteorological conditions of 2017 flood and 2012 drought events are simulated and reveal that possible hypoxia occurs after flooding due to increasing temperature and turbidity, and DO concentration decreases significantly under heat and drought conditions. In conclusion, LSTM-based models utilizing wireless sensor data can be a timely and effective approach to make appropriate decisions on water resource management.

54 ENVIRONMENTAL SCIENCES↗

A hybrid finite volume method and smoothed particle hydrodynamics approach for efficient and accurate blast simulations

Modeling strong shock waves in fluids remains a persistent challenge in computational physics. Essential to research efforts in industry and defense, numerous methods have been devised to improve the accuracy and efficiency of shock simulations. A novel, hybrid Finite Volume Method (FVM)-Smoothed Particle Hydrodynamics (SPH) approach is capable of further improving efficiency and retaining accuracy by exploiting the favorable characteristics of each respective method. This hybrid approach is presented for shock capturing in compressible fluids. The Python framework Pyro2 is employed to simulate a coarse FVM mesh, while the Python framework PySPH is utilized to model the fluid in regions with high gradients through SPH particles. The performance of the hybrid FVM-SPH scheme, compared to the individual FVM and SPH methods, is assessed in 1 kt and 10 kt blast simulations. Our results indicate that the hybrid approach offers higher computational efficiency than SPH while preserving its accuracy and characteristics. The hybrid approach had a relative speedup of 11.3x and 22.3x over the FVM and SPH approaches for the 1 kt simulation and a relative speedup of 14.7x and 20.9x over the FVM and SPH approaches for the 10 kt simulation. The hybrid SPH algorithm enables future compressible fluid simulations with more extensive capabilities than grid-based methods alone, presenting potential applications in modeling fluid-structure interactions and solid deformation and fracturing in blast simulations.

Myers, Conner↗

Core–Shell Gold Nanoparticle-Star Copolymer Composites with Gradient Transfer and Transport Properties: Toward Electro-Optical Sensors and Catalysis

A series of hybrid core–shell nanomaterials was prepared by solvent phase transfer methods with gold (Au) nanoparticles (NPs) as a core and star copolymers (h-PEI-b-PCL-Cbz) as a shell—consisting of hyperbranched polyethyleneimine (h-PEI) with different poly(ε-caprolactone) (PCL) chain lengths and a carbazole-contained terminating agent (Cbz). By varying the PCL chain length, these core–shell nanomaterials exhibited gradient energy transfer properties, surface hydrophobicity, electropolymerizability, and ionic probe transport and diffusion properties. The systematic copolymer formation was verified with quadruple-detector size exclusion chromatography (SEC) and 1H nuclear magnetic resonance (NMR). High-resolution atomic force microscopy-infrared spectroscopy (AFM-IR) chemical mapping verified nanoparticle-substrate adhesion and film formation. The design of these hybrid NPs and elucidation of gradient properties will be useful for future applications of the core–shell systems in electro-optical sensing and catalysis.

36 MATERIALS SCIENCE↗

DeepONet-grid-UQ: A trustworthy deep operator framework for predicting the power grid’s post-fault trajectories

This paper proposes a novel data-driven method for the reliable prediction of the power grid’s post-fault trajectories, i.e., the power grid’s dynamic response after a disturbance or fault. Here, the proposed method is based on the recently proposed concept of Deep Operator Networks (DeepONets). Unlike traditional neural networks that learn to approximate functions, DeepONets are designed to approximate nonlinear operators, i.e., mappings between infinite-dimensional spaces. Under this operator framework, we design a novel and efficient DeepONet that (i) takes as inputs the trajectories collected before and during the fault and (ii) outputs the predicted post-fault trajectories. In addition, we endow our method with the much-needed ability to balance efficiency with reliable/trustworthy predictions via uncertainty quantification. To this end, we propose and compare two novel methods that enable quantifying the predictive uncertainty. First, we propose a Bayesian DeepONet (B-DeepONet) that uses stochastic gradient Hamiltonian Monte-Carlo to sample from the posterior distribution of the DeepONet trainable parameters. Then, we design a Probabilistic DeepONet (Prob-DeepONet) that uses a probabilistic training strategy to enable quantifying uncertainty at virtually no extra computational cost. Finally, we validate the proposed methods’ predictive power and uncertainty quantification capability using the New York-New England power grid model.

24 POWER TRANSMISSION AND DISTRIBUTION↗

High-Nickel Cathodes with Mechanical and Interfacial Robustness via Tailored Concentration Gradients for Stable Li-Ion Batteries

Here, we have developed a versatile mathematical framework integrated with an automated reactor system to design and reify highly customizable full concentration gradient (FCG) in high-nickel cathodes for advanced Li-ion batteries. This method provides precise and independent control of the average composition, slope, and curvature of FCGs, enabling the optimization of structural and mechanical properties of the cathode materials. We have showcased this method with Ni 0.8 Co 0.1 Mn 0.1 (OH) 2 precursors of controlled FCGs, which unlocked an optimized cathode with excellent cycling stability without crack formation after repeated cycles. This work opens up new possibilities for the design and manufacturing of advanced cathode materials, enabling safer, high-performance batteries.

25 ENERGY STORAGE↗

Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods

We examine the role of self-interaction errors (SIE) removal on the evaluation of magnetic exchange coupling constants. In particular we analyze the effect of scaling down the self-interaction-correction (SIC) for three non-empirical density functional approximations (DFAs) namely, the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and recent SCAN family of meta-GGA functionals. To this end, we employ three one-electron SIC methods: Perdew-Zunger [Perdew, J. P.; Zunger, A. Phys. Rev. B, 1981, 23, 5048] SIC, the orbitalwise scaled SIC method [Vydrov, O. A. et al., J. Chem. Phys. 2006, 124, 094108], and the recent local scaling method [Zope, R. R. et al., J. Chem. Phys. 2019, 151, 214108]. We compute the magnetic exchange coupling constants using the spin projection and non projection approaches for sets of molecules composed of dinuclear and polynuclear H-He models, organic radical molecules, and chlorocuprate, and compare these results against accurate theories and experiment. Our results show that for the systems that mainly consist of single electron regions, PZSIC performs well but for more complex organic systems and the chlorcuprates, an overcorrecting tendency of PZSIC combined with the DFAs utilized in this work is more pronounced, and in such cases LSIC with kinetic energy density ratio performs better than PZSIC. Furthermore, analysis of the results in terms of SIC corrections to the density and to the total energy shows that both density and energy correction are required to obtain an improved prediction of magnetic exchange couplings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evaluating the Ratio of Electron and Hole Mobilities from a Single Bulk Sample Using Photo-Seebeck Effect

When a semiconductor is under photoexcitation, the voltage response to a temperature gradient is the photo-Seebeck effect. In this work, we study this effect, focusing on the contribution from transport of photo-excited carriers. We demonstrate that by combining photo-Seebeck with photoconductivity measurements, one can determine the ratio between electron and hole mobilities, and hence both of them when one is known. This is found for the case of defect-free samples, where no detail on the absorbance, carrier lifetime or recombination is necessary. Our method reported here does not require chemical doping, which could introduce defects and is often not feasible. It applies to both thin film and bulk samples. Experiment wise, photo-Seebeck effect is relatively easy to implement, or added to existing systems. In a broader context, for semiconductors with significant influence from defects, our result suggests that the photo-Seebeck behavior can still be understood. In this case another photo-transport property is necessary, in order to identify the mobilities of carriers and information regarding the defects. This framework integrates the information from photoexcitation and thermal gradients to provide a general method to determine fundamental electronic properties of materials.

36 MATERIALS SCIENCE↗

Sparsity for Gradient-Based Optimization of Wind Farm Layouts

Optimizing wind farm layouts is an important step in designing an efficient wind farm. Optimizing wind farm layouts is also a difficult task due to computation times increasing with the number of turbines present in the farm. The most computationally expensive part of gradient-based optimization is calculating the gradient. In order to reduce the expense of gradient calculation, we performed a study on the use of sparsity in wind farm layout optimization. This paper presents the findings of the sparsity study and provides a method to use sparsity in wind farm layout optimization. We tested this sparsity method by optimizing multiple farms with sparse methods and compared the results to optimizations of the same farms using traditional methods. By using the sparse method to optimize multiple farms, we found that the objective results were comparable between sparse and traditional methods and that sparse methods were 4 times faster than traditional methods on average. We expect more speedups with improved methodology and larger wind farms. By using sparse methods, it is possible to solve the wind farm layout optimization problem more efficiently, thus allowing for a more thorough study of the wind farm layout design space without excessive computational costs. Further work is required to refine the method and prepare for testing on real-world wind farm layout applications.

gradient↗

Microstructure evolution of gadolinium doped cerium oxide under large thermal gradients

In this report the effects of large thermal gradient annealing on the microstructure of 10 mol% gadolinium doped ceria (GDC) were investigated. GDC powder was prepared by solvent deficient method and sintered at 1650 °C for 10 h to achieve dense ceramics with ~8 μm grain size. The densified GDC samples were subsequently annealed using a 60 W infrared laser at over 2100 °C for 1 h under a thermal gradient equivalent to ~0.3–0.5 °C/μm. The post-annealed samples at 2150 °C for 1 h exhibit grains with average length and width of 37 and 28 μm, respectively. Electron backscattered diffraction (EBSD) analysis revealed that the post-annealed sample at 2150 °C consists of grains oriented close to five principal directions (<4 3 10>, <0 0 1> and <13 1 14> on [0 0 1], and <7 6 20> and <7 2 7> on [0 1 0]) within a tolerance angle of ±10°, whereas the grains of the pre-annealed sample are randomly oriented. Gadolinium diffuses 20–30 μm away from the irradiated surface, with the measured composition of regions deeper than 30 μm, Ce 0.86 Gd 0.14 O 1.93 , is close to that of the pre-annealed sample, Ce 0.87 Gd 0.13 O 1.94 . Enhancement of total conductivity of the post-annealed GDC (1.1 × 10 -3 S cm -1 at 500 °C, and 2.1 × 10 -2 S cm -1 at 700 °C) is observed when compared to the pre-annealed GDC (3.1 × 10 -5 S cm -1 at 500 °C, and 1.7 × 10 -3 S cm -1 at 700 °C), and points to the decrease in the grain boundary (GB) resistivity. This could be attributed to both the change in GB area and grain alignment.

36 MATERIALS SCIENCE↗

Computation of forces and stresses in solids: Towards accurate structural optimization with auxiliary-field quantum Monte Carlo

The accurate computation of forces and other energy derivatives has been a long-standing challenge for quantum Monte Carlo methods. A number of technical obstacles contribute to this challenge. We discuss how these obstacles can be removed with the auxiliary-field quantum Monte Carlo (AFQMC) approach. AFQMC is a general, high-accuracy, many-body total-energy method for molecules and solids. The implementation of back-propagation for pure estimators allows direct calculation of gradients of the energy via the Hellmann-Feynman theorem. A planewave basis with norm-conserving pseudopotentials is used for the study of periodic bulk materials. Completeness of the planewave basis minimizes the effect of so-called Pulay terms. The ionic pseudopotentials, which can be incorporated in AFQMC in exactly the same manner as in standard independent-electron methods, regulate the force and stress estimators and eliminate any potential divergence of the Monte Carlo variances. The resulting approach allows applications of full geometry optimizations in bulk materials. As a result, it also paves the way for many-body computations of the phonon spectrum in solids.

36 MATERIALS SCIENCE↗

Variational actor-critic algorithms,

We introduce a class of variational actor-critic algorithms based on a variational formulation over both the value function and the policy. The objective function of the variational formulation consists of two parts: one for maximizing the value function and the other for minimizing the Bellman residual. Besides the vanilla gradient descent with both the value function and the policy updates, we propose two variants, the clipping method and the flipping method, in order to speed up the convergence. We also prove that, when the prefactor of the Bellman residual is sufficiently large, the fixed point of the algorithm is close to the optimal policy.

97 MATHEMATICS AND COMPUTING↗