Computing Sciences

libEnsemble is a Python-based toolkit for running dynamic ensembles, developed as part of the DOE Exascale Computing Project. The toolkit utilizes a unique generator–simulator–allocator paradigm, where generators produce input for simulators, simulators evaluate those inputs, and allocators decide whether and when a simulator or generator should be called. The generator steers the ensemble based on simulation results. Generators may, for example, apply methods for numerical optimization, machine learning, or statistical calibration. libEnsemble communicates between a manager and workers. Flexibility is provided through multiple manager–worker communication substrates each of which has different benefits. These include Python’s multiprocessing, mpi4py, and TCP. Multisite ensembles are supported using Balsam or Globus Compute. We overview the unique characteristics of libEnsemble as well as current and potential interoperability with other packages in the workflow ecosystem. We highlight libEnsemble’s dynamic resource features: libEnsemble can detect system resources, such as available nodes, cores, and GPUs, and assign these in a portable way. These features allow users to specify the number of processors and GPUs required for each simulation; and resources will be automatically assigned on a wide range of systems, including Frontier, Aurora, and Perlmutter. Such ensembles can include multiple simulation types, some using GPUs and others using only CPUs, sharing nodes for maximum efficiency. We also describe the benefits of libEnsemble’s generator–simulator coupling, which easily exposes to the user the ability to cancel, and portably kill, running simulations based on models that are updated with intermediate simulation output. We demonstrate libEnsemble’s capabilities, scalability, and scientific impact via a Gaussian process surrogate training problem for the longitudinal density profile at the exit of a plasma accelerator stage. The study uses gpCAM for the surrogate model and employs either Wake-T or WarpX simulations, highlighting efficient use of resources that can easily extend to exascale.

This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the gradients and dynamically control the accuracy of these approximations by adjusting the sample sizes used in stochastic realizations. We analyze the theoretical properties of the proposed framework on nonconvex functions. Our analysis yields sublinear convergence results to the neighborhood of the solution, and establishes the optimal worst-case iteration complexity (O(ε−1)) and sample complexity (O(ε−2)) for each gradient estimation method to achieve an ε-accurate solution. Finally, we demonstrate the performance of the proposed framework and the quality of the gradient estimation methods through numerical experiments on nonlinear least squares problems.

The Fayans energy density functional (EDF) has been very successful in describing global nuclear properties (binding energies, charge radii, and especially differences of radii) within nuclear density functional theory. In a recent study, supervised machine learning methods were used to calibrate the Fayans EDF. Building on this experience, in this work we explore the effect of adding isovector pairing terms, which are responsible for different proton and neutron pairing fields, by comparing a 13D model without the isovector pairing term against the extended 14D model. At the heart of the calibration is a carefully selected heterogeneous dataset of experimental observables representing ground-state properties of spherical even-even nuclei. To quantify the impact of the calibration dataset on model parameters and the importance of the new terms, we carry out advanced sensitivity and correlation analysis on both models. The extension to 14D improves the overall quality of the model by about 30%. The enhanced degrees of freedom of the 14D model reduce correlations between model parameters and enhance sensitivity.

This work proposes a framework for large-scale stochastic derivative-free optimization (DFO) by introducing STARS, a trust-region method based on iterative minimization in random subspaces. This framework is both an algorithmic and theoretical extension of a random subspace derivative-free optimization (RSDFO) framework, and an algorithm for stochastic optimization with random models (STORM). Moreover, like RSDFO, STARS achieves scalability by minimizing interpolation models that approximate the objective in low-dimensional affine subspaces, thus significantly reducing per-iteration costs in terms of function evaluations and yielding strong performance on largescale stochastic DFO problems. The user-determined dimension of these subspaces, when the latter are defined, for example, by the columns of so-called Johnson-Lindenstrauss transforms, turns out to be independent of the dimension of the problem. For convergence purposes, inspired by the analyses of RSDFO and STORM, both a particular quality of the subspace and the accuracies of random function estimates and models are required to hold with sufficiently high, but fixed, probabilities. Using martingale theory under the latter assumptions, an almost sure global convergence of STARS to a first-order stationary point is shown, and the expected number of iterations required to reach a desired first-order accuracy is proved to be similar to that of STORM and other stochastic DFO algorithms, up to constants.

The ptychographic iterative engine (PIE) is a widely used algorithm that enables phase retrieval at nanometer-scale resolution over a wide range of imaging experiment configurations. By analyzing diffraction intensities from multiple scanning locations where a probing wavefield interacts with a sample, the algorithm solves a difficult optimization problem with constraints derived from the experimental geometry as well as sample properties. The effectiveness at which this optimization problem is solved is highly dependent on the ordering in which we use the measured diffraction intensities in the algorithm, and random ordering is widely used due to the limited ability to escape from stagnation in poor-quality local solutions. In this study, we introduce an extension to the PIE algorithm that uses ideas popularized in recent machine learning training methods, in this case minibatch stochastic gradient descent. Our results demonstrate that these new techniques significantly improve the convergence properties of the PIE numerical optimization problem.

This study proposes an approach of leveraging information gathered from multiple traffic data sources at different resolutions to obtain approximate inference on the traffic distribution of Chicago's O'Hare Airport area. Specifically, it proposes the ingestion of traffic datasets at different resolutions to build spatiotemporal models for predicting the distribution of traffic volume on the road network. Due to its good adaptability and flexibility for spatiotemporal data, the Gaussian process (GP) regression was employed to provide short-term forecasts using data collected by loop detectors (sensors) and supplemented by telematics data. The GP regression is used to make predictions of the distribution of the proportion of sensor data traffic volume represented by the telematics data for each location of the sensors. Consequently, the fitted GP model can be used to determine the approximate traffic distribution for a testing location outside of the training points. Policymakers in the transportation sector can find the results of this work helpful for making informed decisions relating to current and future transportation conditions in the area.

The types of constraints encountered in black-box simulation-based optimization problems differ significantly from those addressed in nonlinear programming. We introduce a characterization of constraints to address this situation. We provide formal definitions for several constraint classes and present illustrative examples in the context of the resulting taxonomy. This taxonomy, denoted KARQ, is useful for modeling and problem formulation, as well as optimization software development and deployment. It can also be used as the basis for a dialog with practitioners in moving problems to increasingly solvable branches of optimization.

We consider the solution of finite-sum minimization problems, such as those appearing in nonlinear least-squares or general empirical risk minimization problems. We are motivated by problems in which the summand functions are computationally expensive and evaluating all summands on every iteration of an optimization method may be undesirable. We present the idea of stochastic average model (SAM) methods, inspired by stochastic average gradient methods. SAM methods sample component functions on each iteration of a trust-region method according to a discrete probability distribution on component functions; the distribution is designed to minimize an upper bound on the variance of the resulting stochastic model. We present promising numerical results concerning an implemented variant extending the derivative-free model-based trust-region solver POUNDERS, which we name SAM-POUNDERS.