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At least 1,135 records · Page 63

From Optimization to Sampling Through Gradient Flows

Optimization and sampling algorithms play a central role in science and engineering as they enable finding optimal predictions, policies, and recommendations, as well as expected and equilibrium states of complex systems. The notion of “optimality” is formalized by the choice of an objective function, while the notion of an “expected” state is specified by a probabilistic model for the distribution of states. Optimizing rugged objective functions and sampling multimodal distributions is computationally challenging, especially in high-dimensional problems. Here, for this reason, many optimization and sampling methods have been developed by researchers working in disparate fields such as Bayesian statistics, molecular dynamics, genetics, quantum chemistry, machine learning, weather forecasting, econometrics, and medical imaging.

Trillos, N. García↗

EBIS Beam Intensity Online Optimization with GPTune and Offline Analysis with XGBoost

The application of machine learning techniques to accelerator research has led to significant breakthroughs in optimization strategies. This paper presents a pioneering study using a novel machine learning algorithm, GPTune, to optimize beam intensity by adjusting parameters in the EBIS injection and extraction beam lines. Our research demonstrates substantial improvements, achieving a remarkable 22% and 70% increase in beam intensity at two separate measurement locations.

43 PARTICLE ACCELERATORS↗

Machine Learning Classical Interatomic Potentials for Molecular Dynamics from First-Principles Training Data

The ever-increasing power of modern super-computers, along with the availability of highly scalable atomistic simulation codes, has begun to revolutionize predictive modeling of materials. In particular, molecular dynamics (MD) has led to breakthrough advances in diverse fields, including tribology, catalysis, sensing, and nanoparticle self-assembly. Furthermore, recent integration of MD simulations with X-ray characterization has demonstrated promise in real-time 3-D characterization of materials on the atomic scale. The popularity of MD is driven by its applicability at disparate length/time scales, ranging from ab initio MD (hundreds of atoms and tens of picoseconds) to all-atom classical MD (millions of atoms over microseconds), and coarse-grained (CG) models (micrometers and tens of microseconds). Nevertheless, a substantial gap persists between AIMD, which is highly accurate but restricted to extremely small sizes, and those based on classical force fields (atomistic and CG) with limited accuracy but access to larger length/time scales. The accuracy and predictive power of classical MD simulations is dictated by the empirical force fields, and their capability to capture the relevant physics. Here, we discuss some of our recent work on the use of machine learning (ML) to combine the accuracy and flexibility of electronic structure calculations with the speed of classical potentials. Our ML framework attempts to bridge the significant gulf that exists between the handful of research groups that develop new interatomic potential models (often requiring several years of effort), and the increasingly large user community from academia and industry that applies these models. Our data-driven approach represents significant departure from the status quo and involves several steps including generation and manipulation of extensive training data sets through electronic structure calculations, defining novel potential functional forms, employing state-of-the-art ML algorithms to formulate highly optimized training procedures, and subsequently developing user-friendly workflow tools integrating these algorithms on high-performance computers (HPCs). Our ML approach shows marked success in developing force fields for a wide range of materials from metals, oxides, nitrides, and heterointerfaces to two-dimensional (2D) materials.

Chan, Henry↗

Real-Time Optimal Power Flow

Future power networks are expected to incorporate a large number of distributed energy resources, which introduce randomness and fluctuations as well as fast control capabilities. But traditional optimal power flow methods are only appropriate for applications that operate on a slow timescale. In this paper, we build on recent work to develop a real-time algorithm for AC optimal power flow, based on quasi-Newton methods. The algorithm uses second-order information to provide suboptimal solutions on a fast timescale, and can be shown to track the optimal power flow solution when the estimated second-order information is sufficiently accurate. We also give a specific implementation based on L-BFGS-B method, and show by simulation that the proposed algorithm has good performance and is computationally efficient.

Tang, Yujie↗

A Hybrid Energy System Workflow for Energy Portfolio Optimization

This manuscript develops a workflow, driven by data analytics algorithms, to support the optimization of the economic performance of an Integrated Energy System. The goal is to determine the optimum mix of capacities from a set of different energy producers (e.g., nuclear, gas, wind and solar). A stochastic-based optimizer is employed, based on Gaussian Process Modeling, which requires numerous samples for its training. Each sample represents a time series describing the demand, load, or other operational and economic profiles for various types of energy producers. These samples are synthetically generated using a reduced order modeling algorithm that reads a limited set of historical data, such as demand and load data from past years. Numerous data analysis methods are employed to construct the reduced order models, including, for example, the Auto Regressive Moving Average, Fourier series decomposition, and the peak detection algorithm. All these algorithms are designed to detrend the data and extract features that can be employed to generate synthetic time histories that preserve the statistical properties of the original limited historical data. The optimization cost function is based on an economic model that assesses the effective cost of energy based on two figures of merit: the specific cash flow stream for each energy producer and the total Net Present Value. An initial guess for the optimal capacities is obtained using the screening curve method. The results of the Gaussian Process model-based optimization are assessed using an exhaustive Monte Carlo search, with the results indicating reasonable optimization results. The workflow has been implemented inside the Idaho National Laboratory’s Risk Analysis and Virtual Environment (RAVEN) framework. The main contribution of this study addresses several challenges in the current optimization methods of the energy portfolios in IES: First, the feasibility of generating the synthetic time series of the periodic peak data; Second, the computational burden of the conventional stochastic optimization of the energy portfolio, associated with the need for repeated executions of system models; Third, the inadequacies of previous studies in terms of the comparisons of the impact of the economic parameters. The proposed workflow can provide a scientifically defendable strategy to support decision-making in the electricity market and to help energy distributors develop a better understanding of the performance of integrated energy systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Heat transfer optimization of uo 2 -mo fuel using genetic algorithms

Two genetic algorithm (GA) methods were applied to thermal finite element models to optimize the heat transfer efficacy of a UO 2 -Mo composite fuel pellet with typical pressurized water reactor fuel geometry. Mo additions to UO 2 have been shown to increase the thermal conductivity, thus reducing centerline temperatures and temperature gradients. Previous studies evaluated uniformly dispersed Mo or continuous Mo internal geometries (e.g., fins, plates, discs) that were selected using engineering intuition. The current study uses two different implementations of the same GA to optimize Mo placement and minimize the fuel temperature with the only constraint being a maximum 10% Mo volume fraction. One approach superimposed Mo line elements onto the monolithic UO 2 pellet model, and the other converted entire UO 2 volume elements to Mo. The former method generated 1D heat transfer connections between nodes, whereas the latter method allowed for the formation of 3D structures. Features of the optimal fuel design produced by the GAs included dispersed Mo near the centerline that shifted the peak fuel temperature outward by 0.6 mm, Mo chains in the high-heat-flux region in the mid-to-outer radial zone, and a large continuous structure that spanned the full radius and height of the pellet and accounted for 87.7 % of the total Mo in the pellet. Analysis of this design indicates that the optimal Mo configuration is a balance between creating continuous heat transfer pathways and optimally dispersing Mo to minimize the heat transfer distance through UO 2 . This architecture ultimately produced an effective thermal conductivity of 11.3 W/m·K under the assumed boundary conditions. This result is higher than any previous values from the literature. In conclusion, potential fabrication methods and challenges are discussed in addition to the implications on fuel performance.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Fault-tolerant bandwidth reservation strategies for data transfers in high-performance networks

Many next-generation e-science applications need fast and reliable transfer of large volumes of data with guaranteed performance, which is typically enabled by the bandwidth reservation service in high-performance networks. One prominent issue in such network environments with large footprints is that node and link failures are inevitable, hence potentially degrading the quality of data transfer. We consider two generic types of bandwidth reservation requests (BRRs) concerning data transfer reliability: (i) to achieve the highest data transfer reliability under a given data transfer deadline, and (ii) to achieve the earliest data transfer completion time while satisfying a given data transfer reliability requirement. We propose two periodic bandwidth reservation algorithms with rigorous optimality proofs to optimize the scheduling of individual BRRs within BRR batches. The efficacy of the proposed algorithms is illustrated through extensive simulations in comparison with scheduling algorithms widely adopted in production networks in terms of various performance metrics.

97 MATHEMATICS AND COMPUTING↗

Scalable Deep Learning via I/O Analysis and Optimization

Scalable deep neural network training has been gaining prominence because of the increasing importance of deep learning in a multitude of scientific and commercial domains. Consequently, a number of researchers have investigated techniques to optimize deep learning systems. Much of the prior work has focused on runtime and algorithmic enhancements to optimize the computation and communication. Despite these enhancements, however, deep learning systems still suffer from scalability limitations, particularly with respect to data I/O. This situation is especially true for training models where the computation can be effectively parallelized, leaving I/O as the major bottleneck. In fact, our analysis shows that I/O can take up to 90% of the total training time. Thus, in this article, we first analyze LMDB, the most widely used I/O subsystem of deep learning frameworks, to understand the causes of this I/O inefficiency. Based on our analysis, we propose LMDBIO—an optimized I/O plugin for scalable deep learning. LMDBIO includes six novel optimizations that together address the various shortcomings in existing I/O for deep learning. Lastly, our experimental results show that LMDBIO significantly outperforms LMDB in all cases and improves overall application performance by up to 65-fold on a 9,216-core system.

97 MATHEMATICS AND COMPUTING↗

NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training

This paper presents NSGA-PINN, a multi-objective optimization framework for the effective training of physics-informed neural networks (PINNs). The proposed framework uses the non-dominated sorting genetic algorithm (NSGA-II) to enable traditional stochastic gradient optimization algorithms (e.g., ADAM) to escape local minima effectively. Additionally, the NSGA-II algorithm enables satisfying the initial and boundary conditions encoded into the loss function during physics-informed training precisely. We demonstrate the effectiveness of our framework by applying NSGA-PINN to several ordinary and partial differential equation problems. In particular, we show that the proposed framework can handle challenging inverse problems with noisy data.

Lu, Binghang (ORCID:0009000160016632)↗

Derivative-free robust optimization by outer approximations

We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subproblems encountered. We demonstrate the practical benefits of the algorithm on a new class of test problems.

59 BASIC BIOLOGICAL SCIENCES↗

Application of a convolutional neural network in permeability prediction: A case study in the Jacksonburg-Stringtown oil field, West Virginia, USA

Permeability is a critical parameter for understanding subsurface fluid flow behavior, managing reservoirs, enhancing hydrocarbon recovery, and sequestering carbon dioxide. In general, permeability is measured in the laboratory based on subsurface core samples, calculated from well logs or estimated from well tests. However, laboratory measurements and well tests are expensive, time-consuming, and usually limited to a few core samples or wells in a hydrocarbon field or carbon storage site. Machine-learning techniques are good options for generating a rapid, robust, and cost-effective permeability prediction model because of their strengths to recognize the potential interrelationships between input and output variables. Convolutional neural networks (CNN), as a good pattern recognition algorithm, are widely used in image processing, natural language processing, and speech recognition, but are rarely used with regression problems and even less often in reservoir characterization. We have developed a CNN regression model to estimate the permeability in the Jacksonburg-Stringtown oil field, West Virginia, which is a potential carbon storage site and enhanced oil recovery operations field. We also evaluate the concept of the geologic feature image, which is converted from geophysical well logs. Five variables, including two commonly available conventional well logs (the gamma rays [GRs] and bulk density) and three well-log-derived variables (the slopes of the GR and bulk density curves, and shale content), are used to generate a geologic feature image. The CNN treats the geologic feature image as the input and the permeability as the desired output. In addition, the permeability predicted using traditional backpropagation artificial neural networks, which are optimized by genetic algorithms and particle swarm optimization, is compared with the permeability estimated using our CNN. Our results indicate that the CNN regression model provides more accurate permeability predictions than the traditional neural network.

Geochemistry & Geophysics↗

Controlled precision QUBO-based algorithm to compute eigenvectors of symmetric matrices

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix which is based on solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of symmetric matrices; It can compute the eigenvector/eigenvalue pair to essentially any arbitrary precision, and with minor modifications, can also solve the generalized eigenvalue problem. Performance is analyzed on small random matrices and selected larger matrices from practical applications.

97 MATHEMATICS AND COMPUTING↗

NEXTorch: A Design and Bayesian Optimization Toolkit for Chemical Sciences and Engineering

Automation and optimization of chemical systems require well-informed decisions on what experiments to run to reduce time, materials, and/or computations. Data-driven active learning algorithms have emerged as valuable tools to solve such tasks. Bayesian optimization, a sequential global optimization approach, is a popular active-learning framework. Past studies have demonstrated its efficiency in solving chemistry and engineering problems. Here we introduce NEXTorch, a library in Python/PyTorch, to facilitate laboratory or computational design using Bayesian optimization. NEXTorch offers fast predictive modeling, flexible optimization loops, visualization capabilities, easy interfacing with legacy software, and multiple types of parameters and data type conversions. It provides GPU acceleration, parallelization, and state-of-the-art Bayesian optimization algorithms and supports both automated an d human-in-the-loop optimization. The comprehensive online documentation introduces Bayesian optimization theory and several examples from catalyst synthesis, reaction condition optimization, parameter estimation, and reactor geometry optimization. NEXTorch is open-source and available on GitHub

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nearly optimal state preparation for quantum simulations of lattice gauge theories

Here, we present several improvements to the recently developed ground-state preparation algorithm based on the quantum eigenvalue transformation for unitary matrices (QETU), apply this algorithm to a lattice formulation of U(1) gauge theory in (2+1) dimensions, as well as propose an alternative application of QETU, a highly efficient preparation of Gaussian distributions. The QETU technique was originally proposed as an algorithm for nearly optimal ground-state preparation and ground-state energy estimation on early fault-tolerant devices. It uses the time-evolution input model, which can potentially overcome the large overall prefactor in the asymptotic gate cost arising in similar algorithms based on the Hamiltonian input model. We present modifications to the original QETU algorithm that significantly reduce the cost for the cases of both exact and Trotterized implementation of the time evolution circuit. We use QETU to prepare the ground state of a U(1) lattice gauge theory in two spatial dimensions, explore the dependence of computational resources on the desired precision and system parameters, and discuss the applicability of our results to general lattice gauge theories. We also demonstrate how the QETU technique can be utilized for preparing Gaussian distributions and wave packets in a way which outperforms existing algorithms for as little as n q ≳ 2–5 qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimal damping profile ratios for stabilization of perfectly matched layers in general anisotropic media

Conventional perfectly matched layers (PML) can be unstable for certain kinds of anisotropic media. Multi-axial PML removes such instability using nonzero damping coe cients in the directions tangential with the PML interface. While using non-zero damping pro le ratios can stabilize PML, it is important to obtain the smallest possible damping pro le ratios to minimize arti cial re ections caused by these non-zero ratios, particularly for 3D general anisotropic media. Using the eigenvectors of the PML system matrix, we develop a straightforward and e cient numerical algorithm to determine the optimal damping pro le ratios to stabilize PML in 2D and 3D general anisotropic media. Numerical examples show that our algorithm provides optimal damping pro le ratios to ensure the stability of PML and complex-frequency-shifted PML for elastic-wave modeling in 2D and 3D general anisotropic media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evolutionary Optimization of a Charge Transfer Ionic Potential Model for Ta/Ta-Oxide Heterointerfaces

Heterostructures of tantalum and its oxide are of tremendous technological interest for a myriad of technological applications, including electronics, thermal management, catalysis and biochemistry. In particular, local oxygen stoichiometry variation in TaO x memristors comprising of thermodynamically stable metallic (Ta) and insulating oxide (Ta 2 O 5 ) have been shown to result in fast switching on the subnanosecond timescale over a billion cycles. This rapid switching opens up the potential for advanced functional platforms such as stateful logic operations and neuromorphic computation. Despite its broad importance, an atomistic scale understanding of oxygen stoichiometry variation across Ta/TaO x heterointerfaces, such as during early stages of oxidation and oxide growth, is not well understood. This is mainly due to the lack of a unified interatomic potential model for tantalum oxides that can accurately describe metallic (Ta), ionic (TaO x ) as well as mixed (Ta/TaO x interfaces) bonding environments simultaneously. To address this challenge, we introduce a Charge Transfer Ionic Potential (CTIP) model for Ta/Ta-oxide system by training against lattice parameters, cohesive energies, equations of state (EOS), elastic properties, and surface energies of the various experimentally observed Ta 2 O 5 polymorphs (hexagonal, orthorhombic and monoclinic) obtained from density functional theory (DFT) calculations. The best CTIP parameters are determined by employing a global optimization scheme driven by genetic algorithms followed by local Simplex optimization. Our newly developed CTIP potential accurately predicts structure, thermodynamics, energetic ordering of polymorphs, as well as elastic and surface properties of both Ta and Ta 2 O 5 , in excellent agreement with DFT calculations and experiments. We employ our newly parameterized CTIP potential to investigate the early stages of oxidation and atomic scale mechanisms associated with oxide growth on Ta surface at various temperatures. Furthermore, the CTIP potential developed in this work is an invaluable tool to investigate atomic-scale mechanisms and transport phenomena underlying the response of Ta/TaO x interfaces to external stimuli (e.g, temperature, pressure, strain, electric field etc.), as well as other interesting dynamical phenomena including the physics of switching dynamics in TaO x based memristors and neuromorphic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

RetSynth: determining all optimal and sub-optimal synthetic pathways that facilitate synthesis of target compounds in chassis organisms

The efficient biological production of industrially and economically important compounds is a challenging problem. Brute-force determination of the optimal pathways to efficient production of a target chemical in a chassis organism is computationally intractable. Many current methods provide a single solution to this problem, but fail to provide all optimal pathways, optional sub-optimal solutions or hybrid biological/non-biological solutions. Here we present RetSynth, software with a novel algorithm for determining all optimal biological pathways given a starting biological chassis and target chemical. By dynamically selecting constraints, the number of potential pathways scales by the number of fully independent pathways and not by the number of overall reactions or size of the metabolic network. This feature allows all optimal pathways to be determined for a large number of chemicals and for a large corpus of potential chassis organisms. Additionally, this software contains other features including the ability to collect data from metabolic repositories, perform flux balance analysis, and to view optimal pathways identified by our algorithm using a built-in visualization module. This software also identifies sub-optimal pathways and allows incorporation of non-biological chemical reactions, which may be performed after metabolic production of precursor molecules. The novel algorithm designed for RetSynth streamlines an arduous and complex process in metabolic engineering. Our stand-alone software allows the identification of candidate optimal and additional sub-optimal pathways, and provides the user with necessary ranking criteria such as target yield to decide which route to select for target production. Furthermore, the ability to incorporate non-biological reactions into the final steps allows determination of pathways to production for targets that cannot be solely produced biologically. With this comprehensive suite of features RetSynth exceeds any open-source software or webservice currently available for identifying optimal pathways for target production.

59 BASIC BIOLOGICAL SCIENCES↗

Efficient phase-factor evaluation in quantum signal processing

Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in principle be obtained for a range of tasks, such as Hamiltonian simulation and the quantum linear system problem. A further benefit of QSP is that it uses a minimal number of ancilla qubits, which facilitates its implementation on near-to-intermediate term quantum architectures. However, there is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits. Existing methods require the use of variable precision arithmetic and can only be applied to polynomials of a relatively low degree. We present here an optimization-based method that can accurately compute the phase factors using standard double precision arithmetic operations. We demonstrate the performance of this approach with applications to Hamiltonian simulation, eigenvalue filtering, and quantum linear system problems. Furthermore, our numerical results show that the optimization algorithm can find phase factors to accurately approximate polynomials of a degree larger than 10000 with errors below 10 -12 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗