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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2020

Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Ensemble-based stochastic gradient methods, such as the ensemble optimization (EnOpt) method, the simplex gradient (SG) method, and the stochastic simplex approximate gradient (StoSAG) method, approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increasingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control variables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save on the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control variables using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the proposed gradients saved about 30–50% of the computational cost of the same optimization by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost significantly.

58 GEOSCIENCES↗

DOE OSTI2024

Localized Evaluation for Constructing Discrete Vector Fields

Topological abstractions offer a method to summarize the behavior of vector fields, but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach, which constructs a collection of pairs of simplices in the input mesh that satisfies criteria introduced by Forman's discrete Morse theory. While numerous approaches exist to compute pairs in the restricted case of the gradient of a scalar field, state-of-the-art algorithms for the general case of vector fields require expensive optimization procedures. This paper introduces a fast, novel approach for pairing simplices of two-dimensional, triangulated vector fields that do not vary in time. The key insight of our approach is that we can employ a local evaluation, inspired by the approach used to construct a discrete gradient field, where every simplex in a mesh is considered by no more than one of its vertices. Specifically, we observe that for any edge in the input mesh, we can uniquely assign an outward direction of flow. We can further expand this consistent notion of outward flow at each vertex, which corresponds to the concept of a downhill flow in the case of scalar fields. Working with outward flow enables a linear-time algorithm that processes the (outward) neighborhoods of each vertex one-by-one, similar to the approach used for scalar fields. Here, we couple our approach to constructing discrete vector fields with a method to extract, simplify, and visualize topological features. Empirical results on analytic and simulation data demonstrate drastic improvements in running time, produce features similar to the current state-of-the-art, and show the application of simplification to large, complex flows.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

An Online Dynamic Amplitude-Correcting Gradient Estimation Technique to Align X-ray Focusing Optics

High-brightness X-ray pulses, as generated at synchrotrons and X-ray free electron lasers (XFELs), are used in a variety of scientific experiments. At these facilities, measurements often require optical equipment, e.g Compound Refractive Lenses (CRLs) to be precisely aligned and focused. The lateral alignment of CRLs to a beamline requires precise positioning along four axes: two translational, and the two rotational. At a synchrotron, alignment is often accomplished manually. However, XFEL beamlines present a beam brightness that fluctuates stochastically, making manual alignment a time-consuming endeavor. Automation using simplex or classic stochastic descent often fails, given the errant gradient estimates. Herein we present a dynamic-amplitude correction to the usual gradient based on the combination of a generalized finite difference stencil and a time-dependent sampling pattern. Intensity is recorded periodically, then used to normalize numerical derivatives against fluctuations. Error expectation is analyzed, and efficacy is demonstrated on classic benchmarks. We provide a proof of concept by laterally aligning optics on a simulated XFEL beamline using data recorded at both synchrotron and XFEL facilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Efficient generation of grids and traversal graphs in compositional spaces towards exploration and path planning

Abstract Diverse disciplines across science and engineering deal with problems related to compositions, which exist in non-Euclidean simplex spaces, rendering many standard tools inaccurate or inefficient. This work explores such spaces conceptually in the context of materials discovery, quantifies their computational feasibility, and implements several essential methods specific to simplex spaces through a new high-performance open-source library . Most significantly, we derive and implement an algorithm for constructing a novel n-dimensional simplex graph data structure, containing all discretized compositions and possible neighbor-to-neighbor transitions. Critically, no distance or neighborhood calculations are performed, instead leveraging pure combinatorics and order in procedurally generated simplex grids, keeping the algorithm $${\mathcal{O}}(N)$$ O ( N ) , with minimal memory, enabling rapid construction of graphs with billions of transitions in seconds. Additionally, we demonstrate how such graph representations can be combined to homogeneously express complex path-planning problems, while facilitating efficient deployment of existing high-performance gradient descent, graph traversal, and other optimization algorithms.

Krajewski, Adam M. (ORCID:0000000222660099)↗