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With a lifelong passion for problem-solving and a love of production, Becky Butlin has helped lead the National Ignition Facility Target Fabrication Team through obstacles and challenges for the past six years.
The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to hardware constraints. In this work, we develop an algorithm that decomposes the QAOA input problem graph into a smaller problem and solves MaxCut using QAOA on the reduced graph. The algorithm requires a subroutine that can be classical or quantum—in this work, we implement the algorithm twice on each graph. One implementation uses the classical solver Gurobi in the subroutine and the other uses QAOA. We solve these reduced problems with QAOA. On average, the reduced problems require only approximately 1/10 of the number of vertices than the original MaxCut instances. Furthermore, the average approximation ratio of the original MaxCut problems is 0.75, while the approximation ratios of the decomposed graphs are on average of 0.96 for both Gurobi and QAOA. With this decomposition, we are able to measure optimal solutions for ten 100-vertex graphs by running single-layer QAOA circuits on the Quantinuum trapped-ion quantum computer H1-1, sampling each circuit only 500 times. This approach is best suited for sparse, particularly k-regular graphs, as k-regular graphs on n vertices can be decomposed into a graph with at most $\frac{nk}{k+1}$ vertices in polynomial time. Further reductions can be obtained with a potential trade-off in computational time. In conclusion, while this paper applies the decomposition method to the MaxCut problem, it can be applied to more general classes of combinatorial optimization problems.
Chris Saunders and three technologists are in high demand from Sandia's deep learning teams, and they're kept busy by building new clusters of computer nodes for researchers who need the power of supercomputing on a smaller scale. Sandia researchers working on Laboratory Directed Research & Development (LDRD) projects, or innovative ideas for solutions on short timeframes, formulate new ideas on old themes and frequently rely on smaller cluster machines to help solve problems before introducing their code to larger HPC resources. These research teams need an agile hardware and software environment where nascent ideas can be tested and cultivated on a smaller scale. Saunders and his team at Sandia's Science and Engineering Computing Environments are successfully enabling this research by creating pipelines for emerging code—from Cloud, to containers, to virtual machines—that build the right environment quickly to help teams solve their problems in a matter of days rather than months. While the larger HPC sources are available, it's these smaller clusters that can rapidly build a foundation for teams to build on for later development on larger systems.
STOMP is a numerical simulator, developed by PNNL, for solving problems involving multifluid coupled flow and reactive transport in geologic media. The code has been under development at PNNL for more than twentyfive years. This release of STOMP will allow users to directly access the software, and will be limited to selected operational modes. The initial release will include STOMPW. Additional operational modes will be released depending on market trends and user needs.The STOMP simulator has been available to parties outside of PNNL via license agreements. A new trend in projects supported by the U.S. government is that software be available as open source. This release of the STOMP software will meet that need. The initial target operational mode, STOMPW, is one that solves isothermal problems involving variably saturated geologic systems with nonreactive solutes and reactive species. The capabilities of this simulator are often applied to environmental stewardship and restoration problems, such as those at the Hanford Site.
There are generally three types of scientific software users: users that solve problems using existing science software tools, researchers that explore new approaches by extending existing code, and educators that teach students scientific concepts. Python is a general-purpose programming language that is accessible to beginners, such as students, but also as a language that has a rich scientific programming ecosystem that facilitates writing research software. Additionally, as high-performance computing (HPC) resources become more readily available, software support for parallel processing becomes more relevant to scientific software.There currently are no Python-based evolutionary computation frameworks that support all three types of scientific software users. Moreover, some support synchronous concurrent fitness evaluation that do not efficiently use HPC resources. We pose here a new Python-based EC framework that uses an established generalized unified approach to EA concepts to provide an easy to use toolkit for users wishing to use an EA to solve a problem, for researchers to implement novel approaches, and for providing a low-bar to entry to EA concepts for students. Additionally, this toolkit provides a scalable asynchronous fitness evaluation implementation friendly to HPC that has been vetted on hardware ranging from laptops to the world’s fastest supercomputer, Summit.
Wave energy converter (WEC) technology development has not yet delivered the desired commercial maturity nor, and more importantly, the techno-economic performance. The reasons for this have been recognized and fundamental requirements for successful WEC technology development have been identified. This paper describes a multi-year project pursued in collaboration by the National Renewable Energy Laboratory and Sandia National Laboratories to innovate and develop new WEC technology. It specifies the project strategy, shows how this differs from the state-of-the-art approach and presents some early project results. Based on the specification of fundamental functional requirements of WEC technology, structured innovation and systemic problem solving methodologies are applied to invent and identify new WEC technology concepts. Using Technology Performance Levels (TPL) as an assessment metric of the techno-economic performance potential, high performance technology concepts are identified and selected for further development. System performance is numerically modelled and optimized and key performance aspects are empirically validated. The project deliverables are WEC technology specifications of high techno-economic performance technologies of TPL 7 or higher at TRL 3 with some key technology challenges investigated at higher TRL. These wave energy converter technology specifications will be made available to industry for further, full development and commercialisation (TRL 4 - TRL 9).
Demonstrations of quantum advantage for certain sampling problems have generated considerable excitement for quantum computing and have further spurred the development of circuit-model quantum computers, which represent quantum programs as a sequence of quantum gates acting on a finite number of qubits. Amongst this excitement, analog quantum computation has become less prominent, with the expectation that circuit-model quantum computers will eventually be sufficient for emulating analog quantum computation and thus rendering analog quantum computation obsolete. In this work we explore the basic requirements for emulating a specific analog quantum computation in the circuit model: the preparation of a biased superposition of degenerate ground states of an Ising Hamiltonian using an adiabatic evolution. We show that the overhead of emulation is substantial even for this simple problem. This supports using analog quantum computation for solving time-dependent Hamiltonian dynamics in the short term and midterm, assuming analog errors can be made low enough and coherence times long enough to solve problems of practical interest.
Peridynamics is a nonlocal extension of classical continuum mechanics that is well-suited for solving problems with discontinuities such as cracks. This paper extends the peridynamic formulation to decompose a problem domain into a number of smaller overlapping subdomains and to enable the use of different time steps in different subdomains. This approach allows regions of interest to be isolated and solved at a small time step for increased accuracy while the rest of the problem domain can be solved at a larger time step for greater computational efficiency. Lastly, performance of the proposed method in terms of stability, accuracy, and computational cost is examined and several numerical examples are presented to corroborate the findings.
Hybrid Energy Storage System has been widely applied in aerospace, electric vehicle, and microgrid applications. The advantages are that they include complimentary technologies with both high power and energy capabilities. HESS have the potential to be useful to the bulk power systems, for example to increase the value of energy produced by variable generation resource through enabling participation in ancillary service markets. Actualizing the benefits of HESSs requires optimizing the combined ramping capability of aggregated HESS resources. To provide quality ancillary service, source of HESSs locating at multiple sites of variable generation resource must be optimally sized and cohesively controlled. Optimizing aggregated resources can be formulated as an optimization problem. Successfully solving this problem not only requires using effective solution methods but also depends on accurately and rapidly setting the necessary parameters in the problem formula. This article proposes a novel framework with double-layer structure to solve the optimization problem of aggregating ramping capability. Program developed on the upper layer focuses on solving the optimization of aggregating ramping capability among multiple HESSs and is compatible with most existing optimization algorithms. Program on lower layer of the framework targets at optimizing the local control of a single HESS based on a thorough analytics of HESS operation strategy presented in this article. Result of local optimization is also provided to upper layer program for updating the parameters in formula of optimization problem. Real time hardware-in-the-loop test is conducted to verify the performance of the optimization framework developed. The work presented is expected to provide guidance for implementing this framework in practical operation.
From a young age, Katie Mussack has delighted in problem solving, critical thinking and discovery. “Playing with math was just part of our family culture,” she says. Her parents were both math teachers, and her engineer grandfather introduced her to science. As a physicist with the XTD Integrated Design & Assessment group (XTD-IDA), she is following those passions to new heights.
In recent years, a number of quantum computing devices with small numbers of qubits have become available. A hybrid quantum local search (QLS) approach that combines a classical machine and a small quantum device to solve problems of practical size is presented. Herein, the proposed approach is applied to the network community detection problem. QLS is hardware-agnostic and easily extendable to new quantum computing devices as they become available. It is demonstrated to solve the 2-community detection problem on graphs of sizes of up to 410 vertices using the 16-qubit IBM quantum computer and D-Wave 2000Q, and compare their performance with the optimal solutions. The results herein demonstrate that QLS performs similarly in terms of quality of the solution and the number of iterations to convergence on both types of quantum computers and it is capable of achieving results comparable to state-of-the-art solvers in terms of quality of the solution including reaching the optimal solutions.
We present new methods for solving a broad class of bound-constrained nonsmooth composite minimization problems. These methods are specially designed for objectives that are some known mapping of outputs from a computationally expensive function. We provide accompanying implementations of these methods: in particular, a novel manifold sampling algorithm (MS-P) with subproblems that are in a sense primal versions of the dual problems solved by previous manifold sampling methods and a method (GOOMBAH) that employs more difficult optimization subproblems. For these two methods, we provide rigorous convergence analysis and guarantees. We demonstrate extensive testing of these methods. Open-source implementations of the methods developed in this manuscript can be found at https://github.com/POptUS/ IBCDFO/.
We represent a selection of early career staff at LANL with backgrounds in mathematics. There are many possible paths to a position at LANL. The lab has very active graduate research and postdoctoral programs, and it is not uncommon for graduate students to become postdocs, who can then be “converted” to staff. Conversion from being a postdoc is not the only route to a position at LANL, nor is it a guarantee, but most of us did postdocs here before becoming staff. Being a postdoc here also gives you an idea of whether you’d like living in northern New Mexico, a rugged, beautiful, and somewhat remote area. It is important to say here that citizenship is not a requirement for many of the positions at the lab. The lab historically and currently welcomes investigators from all over the world. LANL offers a broad spectrum of mathematical challenges that are largely problem driven. Particularly to those who feel that academic mathematics can be stove-piped, with a focus on deep but not necessarily broad expertise, the LANL environment gives the flexibility to move and grow in many different directions. The lab encourages a team-based approach to problems, which not only enhances the breadth of our approach to solving problems, but also gives team members access to new fields. From the outside (academia), however, it can be difficult to see how fields map between academia and the lab. This is one of the reasons that having interaction with the lab as a graduate student or postdoc can be helpful in understanding if the environment would be a good match for you. An important advantage of working at the lab is our high visibility both in academia, as well as in industry and the government. Because of its mission-driven projects, LANL, and more broadly the Department of Energy Laboratories, help set research directions that are picked up by researchers in academia. For this reason, many lab staff have worked at LANL for a number of years, then have transferred into academia after having set the agenda for their field of expertise. Below, we will share some of our experiences, opinions, and reflections in order to give the reader a feel for our own early career experiences.
We propose a stochastic gradient descent based optimization algorithm to solve the analytic continuation problem in which we extract real frequency spectra from imaginary time Quantum Monte Carlo data. The procedure of analytic continuation is an ill-posed inverse problem which is usually solved by regularized optimization methods, such like the Maximum Entropy method, or stochastic optimization methods. The main contribution of this work is to improve the performance of stochastic optimization approaches by introducing a supervised stochastic gradient descent algorithm to solve a flipped inverse system which processes the random solutions obtained by a type of Fast and Efficient Stochastic Optimization Method.
Abstract In this paper, inhomogeneous chemical kinetics are simulated by describing the concentrations of interacting chemical species by a linear expansion of basis functions in such a manner that the coupled reaction and diffusion processes are propagated through time efficiently by tailor-made numerical methods. The approach is illustrated through modelling $$\alpha$$ α - and $$\gamma$$ γ -radiolysis in thin layers of water and at their solid interfaces from the start of the chemical phase until equilibrium was established. The method’s efficiency is such that hundreds of such systems can be modelled in a few hours using a single core of a typical laptop, allowing the investigation of the effects of the underlying parameter space. Illustrative calculations showing the effects of changing dose-rate and water-layer thickness are presented. Other simulations are presented which show the approach’s capability to solve problems with spherical symmetry (an approximation to an isolated radiolytic spur), where the hollowing out of an initial Gaussian distribution is observed, in line with previous calculations. These illustrative simulations show the generality and the computational efficiency of this approach to solving reaction-diffusion problems. Furthermore, these example simulations illustrate the method’s suitability for simulating solid-fluid interfaces, which have received a lot of experimental attention in contrast to the lack of computational studies.
While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex non-linear embeddings, but do not naturally quantify uncertainty and are often data-inefficient to train. GPs infer posterior distributions over functions, but popular kernels exhibit limited expressivity on complex and high-dimensional data. Fortunately, recently discovered conjugate and neural tangent kernel functions encode the behavior of overparameterized neural networks in the kernel domain. We demonstrate that these kernels can be efficiently applied to regression and reinforcement learning problems by analyzing a baseline case study.We apply GPs with neural network dual kernels to solve reinforcement learning tasks for the first time. We demonstrate, using the well understood mountain-car problem, that GPs empowered with dual kernels perform at least as well as those using the conventional radial basis function kernel. Finally, we conjecture that by inheriting the probabilistic rigor of GPs and the powerful embedding properties of DNNs, GPs using NN dual kernels will empower future reinforcement learning models on difficult domains.
Shear localization is a damage mechanism characterized by the concentration of plastic deformation within thin bands of materials, often observed as a precursor to failure in metals. In this study, we present a three-dimensional explicit finite element formulation with embedded weak discontinuities for the treatment of shear localization under dynamic loading conditions. In this formulation, the onset of localization is detected via a material stability analysis suitable for rate-sensitive materials, and the continuity of propagating shear bands is ensured using a global tracking strategy involving a heat-conduction type boundary value problem, solved for a scalar level set function over the global domain of the problem. In addition, we propose a modified quadrature rule that is used to compute the contribution of an individual element to the global finite element arrays, taking into account the position of the embedded shear band within that element.
Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.