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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Exploring Benchmarks for Self-Driving Labs using Color Matching

Self Driving Labs (SDLs) that combine automation of experimental procedures with autonomous decision making are gaining popularity as a means of increasing the throughput of scientific workflows. The task of identifying quantities of supplied colored pigments that match a target color, the color matching problem, provides a simple and flexible SDL test case, as it requires experiment proposal, sample creation, and sample analysis, three common components in autonomous discovery applications. We present a robotic solution to the color matching problem that allows for fully autonomous execution of a color matching protocol. Our solution leverages the WEI science factory platform to enable portability across different robotic hardware, the use of alternative optimization methods for continuous refinement, and automated publication of results for experiment tracking and post-hoc analysis.

Artificial intelligence↗

DOE OSTI2023

Fast estimation of the look-elsewhere effect using Gaussian random fields

Abstract We discuss the use of Gaussian random fields to estimate the look-elsewhere effect correction. We show that Gaussian random fields can be used to model the null-hypothesis significance maps from a large set of statistical problems commonly encountered in physics, such as template matching and likelihood ratio tests. Some specific examples are searches for dark matter using pixel arrays, searches for astronomical transients, and searches for fast-radio bursts. Gaussian random fields can be sampled efficiently in the frequency domain, and the excursion probability can be fitted with these samples to extend any estimation of the look-elsewhere effect to lower p values. In addition, in cases where the Gaussian random field is stationary and the parameter space is Euclidean, the look-elsewhere effect correction can be computed analytically. We demonstrate these methods using two example template matching problems. Finally, we apply these methods to estimate the trial factor of a $$4^3$$ 4 3 accelerometer array for the detection of dark matter tracks in the Windchime project. When a global significance of $$3\sigma $$ 3 σ is required, the estimated trial factor for such an accelerometer array is $$10^{14}$$ 10 14 for a one-second search, and $$10^{22}$$ 10 22 for a 1-year search.

Qin, Juehang (ORCID:0000000182288949)↗

DOE OSTI2025

Co-design of a wave energy converter through bi-conjugate impedance matching

As with other oscillatory power conversion systems, the design of wave energy converters can be understood as an impedance matching problem. By representing the wave energy converter as a multi-port network, two separate but related impedance matching conditions can be established. Satisfying these conditions maximizes power transfer to the load. In practice, these impedance matching conditions may be used to influence the design of the system (including the hull, power take-off, controller, mooring, etc.). To this end, this paper considers some example applications of wave energy converter design with the help of the impedance matching framework.

WEC↗

DOE OSTI2020

Using Graph Edit Distance for Noisy Subgraph Matching of Semantic Property Graphs

The subgraph matching problem is a fundamental problem in graph theory that is known to be NP-complete. In this study, performers were asked to develop algorithms to search for semantic property graphs that were subgraphs of a large knowledge graph. The templates provided contained structural information about the subgraphs and some attributes for each node and edge. There also exists a similarity measure between a set of attribute values that occurs on every node and edge. Algorithms performed well in the case where an exact match existed, but performers were also provided templates that had noise added such that there existed no match in the knowledge graph. Performers were asked to find the closest matches to those noisy subgraphs. To evaluate performance on this task, we developed a version of the graph edit distance algorithm to measure the cost of editing the template graph so that it is isomorphic in structure and attributes to the performer submission.

Ebsch, Christopher L.↗

DOE OSTI2020

Efficient proactive vehicle relocation for on-demand mobility service with recurrent neural networks

One major challenge for on-demand mobility service (OMS) providers is to seamlessly match empty vehicles with trip requests so that the total vacant mileage is minimized. In this work, we develop an innovative data-driven approach for devising efficient vehicle relocation policy for OMS that (1) proactively relocates vehicles before the demand is observed and (2) reduces the inequality among drivers' income so that the proactive relocation policy is fair and is likely to be followed by drivers. Our approach represents the fusion of optimization and machine learning methods, which comprises three steps: First, we formulate the optimal proactive relocation as an optimal/stable matching problems and solve for global optimal solutions based on historical data. Second, the optimal solutions are then grouped and fed to train the deep learning models which consist of fully connected layers and long short-term memory networks. Low rank approximation is introduced to reduce the model complexity and improve the training performances. Finally, we use the trained model to predict the relocation policy which can be implemented in real time. We conduct comprehensive numerical experiments and sensitivity analyses to demonstrate the performances of the proposed method using New York City taxi data. Here, the results suggest that our method will reduce empty mileage per trip by 54-70% under optimal matching strategy, and a 25-32% reduction can also be achieved by following stable matching strategy. We also validate that the predicted relocation policies are robust in the presence of uncertain passenger demand level and passenger trip-requesting behavior.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2019

An End-to-end Deep Convolutional Neural Network for a Multi-scale Image Matching and Localization Problem

Abstract Diverse imaging techniques are utilized in many scientific domains to acquire a rich description of the subject under study and to further discover a variety of its proper- ties. Especially, in sample systems, by probing with optical, electron or x-ray beams, the captured images describe the sample in an extremely large range of length scales. This makes the correlation from one image to another very difficult in addition to the intrinsic appearance complexity of those scientific images. In this paper, we aim to tackle this multi-scale image matching and localization problem by proposing an end-to-end deep convolutional neural net- work. Our proposed network is designed to first generate different filters according to the two queried images originated from different length scales. Then, to compute the correlation map, we use these filters to predict the correspondence between the two images. For the training and evaluation, we collect a number of electron microscopy experiments to form a multi-scaled image patch dataset comprised of various material structures. We observe about 90% accuracy for multi-scale image matching and localization while a triplet-based network shows about 78% accuracy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

A variational mimetic finite difference method for elliptic interface problems on non-matching polytopal meshes with geometric interface inconsistencies

A new variational mimetic finite difference method for elliptic interface problems with perfect and imperfect thermal contacts on non-matching polytopal meshes with geometric interface inconsistencies is developed and analyzed theoretically and numerically. The method is defined on multiple non-matching submeshes with gaps and overlaps along their interfaces. The discrete equations are derived from a minimization problem for the augmented Dirichlet functional. For a perfect thermal contact, the functional uses a modified mimetic gradient with extended stencil which couples unknowns from both sides of an interface, as well as penalty terms to enforce weak continuity of temperature across the interface. The method leads to a symmetric positive definite matrix for any scaling of the penalty terms. For an imperfect thermal contact, the Dirichlet functional is supplemented with a quadratic jump term along the interface related to the interface thermal resistance. We prove that the method conserves the total heat flux across each interface. In conclusion, the obtained results are verified with numerical experiments showing convergence in the discrete L 2 and L ∞ norms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Constrained or unconstrained? Neural-network-based equation discovery from data

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. Here, we briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.

Data-driven discovery↗

DOE OSTI2022

Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models

We derive an asymptotic expansion for the log-likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for parameter estimation: the method of moments and likelihood optimizing algorithms such as Expectation-Maximization (EM). We show that likelihood optimization in the low SNR regime reduces to a sequence of least squares optimization problems that match the moments of the estimate to the ground truth moments one by one. This connection is a stepping stone towards the analysis of EM and maximum likelihood estimation in a wide range of models. A motivating application for the study of low SNR mixture models is cryo-electron microscopy data, which can be modeled as a GMM with algebraic constraints imposed on the mixture centers. We discuss the application of our expansion to algebraically constrained GMMs, among other example models of interest. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Wavefunction matching for solving quantum many-body problems

Ab initio calculations have an essential role in our fundamental understanding of quantum many-body systems across many subfields, from strongly correlated fermions to quantum chemistry and from atomic and molecular systems to nuclear physics. One of the primary challenges is to perform accurate calculations for systems where the interactions may be complicated and difficult for the chosen computational method to handle. Here we address the problem by introducing an approach called wavefunction matching. Wavefunction matching transforms the interaction between particles so that the wavefunctions up to some finite range match that of an easily computable interaction. This allows for calculations of systems that would otherwise be impossible owing to problems such as Monte Carlo sign cancellations. We apply the method to lattice Monte Carlo simulations of light nuclei, medium-mass nuclei, neutron matter and nuclear matter. We use high-fidelity chiral effective field theory interactions and find good agreement with empirical data. These results are accompanied by insights on the nuclear interactions that may help to resolve long-standing challenges in accurately reproducing nuclear binding energies, charge radii and nuclear-matter saturation in ab initio calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Optimization-Driven Scenario Grouping

Scenario decomposition algorithms for stochastic programs compute bounds by dualizing all nonanticipativity constraints and solving individual scenario problems independently. Here, we develop an approach that improves on these bounds by reinforcing a carefully chosen subset of nonanticipativity constraints, effectively placing scenarios into groups. Specifically, we formulate an optimization problem for grouping scenarios that aims to improve the bound by optimizing a proxy metric based on information obtained from evaluating a subset of candidate feasible solutions. We show that the proposed grouping problem is NP-hard in general, identify a polynomially solvable case, and present two formulations for solving the problem: a matching formulation for a special case and a mixed-integer programming formulation for the general case. We use the proposed grouping scheme as a preprocessing step for a particular scenario decomposition algorithm and demonstrate its effectiveness in solving standard test instances of two-stage 0–1 stochastic programs. Using this approach, we are able to prove optimality for all previously unsolved instances of a standard test set. Additionally, we implement this scheme as a preprocessing step for PySP, a publicly available and widely used implementation of progressive hedging, and compare this grouping approach with standard grouping approaches on large-scale stochastic unit commitment instances. Finally, the idea is extended to propose a finitely convergent algorithm for two-stage stochastic programs with a finite feasible region.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

On the scaling of wind turbine rotors

This paper formulates laws for scaling wind turbine rotors. Although the analysis is general, the article primarily focuses on the subscaling problem, i.e., on the design of a smaller-sized model that mimics a full-scale machine. The present study considers both the steady-state and transient response cases, including the effects of aerodynamic, elastic, inertial, and gravitational forces. The analysis reveals the changes to physical characteristics induced by a generic change of scale, indicates which characteristics can be matched faithfully by a subscaled model, and states the conditions that must be fulfilled for desired matchings to hold. Based on the scaling laws formulated here, the article continues by considering the problem of designing scaled rotors that match desired indicators of a full-scale reference. To better illustrate the challenges implicit in scaling and the necessary tradeoffs and approximations, two different approaches are contrasted. The first consists in a straightforward geometric zooming. An analysis of the consequences of zooming reveals that, although apparently simple, this method is often not applicable in practice, because of physical and manufacturing limitations. This motivates the formulation of scaling as a constrained optimal aerodynamic and structural matching problem of wide applicability. Practical illustrations are given considering the scaling of a large reference 10 MW wind turbine of about 180 m in diameter down to three different sizes of 54, 27, and 2.8 m. Results indicate that, with the proper choices, even models characterized by very significant scaling factors can accurately match several key performance indicators. Additionally, when an exact match is not possible, relevant trends can at least be captured.

17 WIND ENERGY↗

DOE OSTI2023

Short-Depth QAOA circuits and Quantum Annealing on Higher-Order Ising Models (Rev.2)

The Quantum Alternating Operator Ansatz (QAOA) and Quantum Annealing (QA) are quantum algorithms that are both based on the adiabatic theorem and both have the goal of sampling the optimal solution(s) of combinatorial optimization problems. Quantum annealing has been physically instantiated on D-Wave devices using superconducting flux qubits, and QAOA can be programmed on digital gate-model quantum computers such as the programmable superconducting transmon qubits devices of the IBMQ series, for instance ibm washington. QAOA and QA address the same types of problems, but it is unclear how they will scale to large problem sizes and to larger and higher-fidelity quantum computers. In this article, we present a direct comparison between QAOA, one and two rounds, run on all 127 qubits of ibm washington and QA run on D-Wave Advantage system4.1 and Advantage system6.1. The problems which allow for this comparison are random Ising model problems whose connectivity matches the heavy hexagonal lattice topology of ibm washington and the Pegasus graph connectivity of the two D-Wave devices. We create two classes of problem instances for this comparison: one with higher order terms (ZZZ variable interactions), linear terms, and quadratic terms, and a separate problem type with only linear and quadratic terms. Our QAOA circuits are novel and extremely short depth, with a CNOT depth of 6 per round, which allows whole chip usage of ibm washington’s heavy hexagonal lattice and can be applied to future heavy-hex chips. We also test the effectiveness of the error suppression technique digital dynamical decoupling on the QAOA circuits. The QAOA circuits compiled to ibm washington are composed of several thousand circuit instructions, approximately 3, 000 depending on the details of the circuit, making these some the largest quantum circuits ever executed on a digital quantum processor. QAOA and QA are compared against the classical heuristic algorithm of simulated annealing and all problem instances are exactly solved using CPLEX in order to evaluate which samplers, if any, correctly found the ground state solution(s) of the problem instances. We find that (i) QA outperforms QAOA on all problem instances, (ii) QAOA samples the problems better than random sampling, and (iii) QAOA angle computation exhibits clear parameter concentration across the ensemble of Ising models.

127 Qubits↗

DOE OSTI2022

Pre-trained network-based transfer learning: A small-sample machine learning approach to nuclear power plant classification problem

Some research topics belonging to classification problems in the nuclear industry, such as fault diagnosis and accident identification, can be solved by feature extraction and subsequent application of statistical machine learning classifiers. Recently, deep neural network-based methods with automatic feature extraction and high accuracy have gained wide attention. They usually require large-scale training data, however, plant fault or accident data are scarce or difficult to obtain. Here this paper proposes a convolutional network (CNN)-based transfer learning method to solve this problem. The network's shallow layer is derived from a pre-trained CNN based on the ImageNet database to automatically extract features, and the deep layer is customized to match the classification problem. Data in non-image formats are converted to image formats and subsequently used to train the network. Case studies of rotating machines fault diagnosis show that the proposed method requires only limited training data to achieve high accuracy.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Streaming Matching and Edge Cover in Practice

Graph algorithms with polynomial space and time requirements often become infeasible for massive graphs with billions of edges or more. State-of-the-art approaches therefore employ approximate serial, parallel, and distributed algorithms to tackle these challenges. However, such approaches require storing the entire graph in memory and thus need access to costly computing resources such as clusters and supercomputers. In this paper, we present practical streaming approaches for solving massive graph problems using limited memory for two prototypical graph problems: maximum weighted matching and minimum weighted edge cover. For matching, we conduct a thorough computational study on two of the semi-streaming algorithms including a recent breakthrough result that achieves a $1/(2+\varepsilon)$-approximation of the weight while using $O( n \log W /\epsilon)$ memory (here $n$ is the number of vertices and $W$ is the maximum edge weight), designed by Paz and Schwartzman [SODA, 2017]. Empirically, we show that the semi-streaming algorithms produce matchings whose weight is close to the best $1/2$-approximate offline algorithm while requiring less time and an order-of-magnitude less memory. For minimum weighted edge cover, we develop three novel semi-streaming algorithms. Two of these algorithms require a single pass through the input graph, require $O(n \log n)$ memory, and provide a 2-approximation guarantee on the objective. We also leverage a relationship between approximate maximum weighted matching and approximate minimum weighted edge cover to develop a two-pass $3/2+\epsilon$-approximate algorithm with the memory requirement of Paz and Schwartzman's semi-streaming matching algorithm. These streaming approaches are compared against the state-of-the-art 3/2-approximate offline algorithm. The semi-streaming matching and the novel edge cover algorithms proposed in this paper can process graphs with several billions of edges in under 30 minutes using 6 GB of memory, which is at least an order of magnitude improvement from the offline (non-streaming) algorithms. For the largest graph, the best alternative offline parallel approximation algorithm (GPA+ROMA) could not finish in three hours even while employing hundreds of processors and 1 TB of memory. We also demonstrate an application of the semi-streaming algorithm by computing a matching using linearly bounded memory on item intersection graphs derived from three machine learning datasets, whereas the existing offline algorithms could not complete on one of these datasets since their memory requirements exceeded 1TB.

Ferdous, S M.↗

DOE OSTI2023

AMG Preconditioners based on parallel hybrid coarsening and multi-objective graph matching

We describe preliminary results from a multi-objective graph matching algorithm, in the coarsening step of an aggregation-based Algebraic MultiGrid (AMG) preconditioner, for solving large and sparse linear systems of equations on high-end parallel computers. We have two objectives. First, we wish to improve the convergence behavior of the AMG method when applied to highly anisotropic problems. Second, we wish to extend the parallel package \texttt{PSCToolkit} to exploit multi-threaded parallelism at the node level on multi-core processors. Our matching proposal balances the need to simultaneously compute high weights and large cardinalities by a new formulation of the weighted matching problem combining both these objectives using a parameter $\lambda$. We compute the matching by a parallel $2/3-\varepsilon$-approximation algorithm for maximum weight matchings. Results with the new matching algorithm show that for a suitable choice of the parameter $\lambda$ we compute effective preconditioners in the presence of anisotropy, i.e., smaller solve times, setup times, iterations counts, and operator complexity.

D'Ambra, Pasqua↗

DOE OSTI2023

Status of CEBAF Upgrades

Extending CEBAF energy reach by increasing the number of recirculations, while using the existing SRF system is being explored. Proposed energy upgrade is based on a new approach to multi-pass acceleration of electrons in a single Fixed Field Alternating Gradient (FFA) beam line, configured with Halbach-style permanent magnets. Encouraged by recent success of CBETA, a proposal was formulated to nearly ?double? CEBAF energy by replacing the highest energy arcs with a pair of FFA arcs. The new non-scaling FFA arcs would support simultaneous transport of additional 6 passes with energies spanning a factor of two. One of the challenges of the multi-pass (11) linac optics is to assure uniform focusing in a vast range of energies, in a fixed field lattice. Here, we propose a triplet lattice that would provide a stable periodic solution covering energy ratio of 1:33. The current CEBAF injection at 123 MeV, makes optical matching in the first linac virtually impossible due to extremely high energy span ratio (1:175). Replacement of the current injector with a 650 MeV recirculating injector will alleviate that problem. Orbital and optical matching from the FFA arcs to the linacs is implemented as a compact non-adiabatic insert. Presented scheme would promise to deliver a 22 GeV beam with normalized emittance of 76 mm·mrad and with a relative energy spread of 1×10-3. Further recirculation beyond 22 GeV is limited by large, 974 MeV per electron, energy loss due to synchrotron radiation

Bogacz, Alex↗

DOE OSTI2026

Efficient many-jet event generation with flow matching

We apply for the first time, to the best of our knowledge, the flow matching method to the problem of phase-space sampling for event generation in high-energy collider physics. By training the model to remap the random numbers used to generate the momenta and helicities of the scattering matrix elements as implemented in the portable partonic event generator pepper, we find substantial efficiency improvements in the studied processes. We focus our study on the highest final-state multiplicities in Drell-Yan and top-antitop pair production used in simulated samples for the Large Hadron Collider, which computationally are the most relevant ones. We find that the unweighting efficiencies improve by factors of 184 and 25, respectively, when compared to the standard approach of using a vegas-based optimization. We also compare continuous normalizing flows trained with flow matching against the previously studied normalizing flows based on coupling layers and find that the former leads to better results, faster training and a better scaling behavior across the studied multiplicity range, while the latter evaluate faster. When combining the advantages of both methods using the regflow approach, we find parton-level unweighted event generation walltime gains of about a factor of 10 at the highest final-state multiplicities.

Bothmann, E. [CERN; Gottingen U.] (ORCID:000000016↗