Solving inverse problems via neural network flow map approximation
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Dramatic disruptions in technologies can result in the creation of new markets, the emergence of new paradigms, and the displacement of entrenched approaches and business models. This can be especially pronounced when multiple technologies converge to create something new. Today, artificial intelligence (“AI”) is acting as an accelerant for such technology transformations. Still, the scope and depth of its impact will depend in part on our ability to address challenging problems that are surfacing without solutions. Industries will pursue AI for their corporate missions and to create shareholder value. But the timescales and applications can be incongruent with important public needs and with the longer research horizons required to make real progress. Public-Private partnerships are an important mechanism for tackling these rapidly emerging new, complex, challenging problems. Finally, this paper examines our experience gained by creating a unique public-private partnership to apply AI to one example of a hard problem that is particularly timely today-- dramatically accelerating drug discovery.
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A low-energy medium-luminosity Muon Collider (MC) is being studied as a possible Higgs Factory (HF). Electrons from muon decays will deposit more than 300 kW in superconducting magnets of the HF collider ring. This imposes significant challenges to superconducting (SC) magnets used in the MC storage ring (SR) and interaction regions (IR). Magnet designs are proposed which provide high operating gradient and magnetic field in a large aperture to accommodate the large size of muon beams (due to low beta*), as well as a cooling system to intercept the large heat deposition from the showers induced by decay electrons. The distribution of heat deposition in the MC SR lattice elements requires large-aperture magnets in order to accommodate thick high-Z absorbers to protect the SC coils. Based on the developed MARS15 model and intensive simulations, a sophisticated radiation protection system was designed for the collider SR and IR to bring the peak power density in the superconducting coils below the quench limit and reduce the dynamic heat deposition in the cold mass by a factor of 100. The system consists of tight tungsten masks in the magnet interconnect regions and elliptical tungsten liners in the magnet aperture optimized individually for each magnet. These also reduce the background particle fluxes in the collider detector.
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Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for solving such a problem using a classical algorithm exceeds that required by a quantum algorithm. Reducing the power flow (PF) problem into a linear system of equations allows for the formulation of quantum PF (QPF) algorithms, which are based on solving methods for quantum linear systems such as the Harrow-Hassidim-Lloyd (HHL) algorithm. Speedup from using QPF algorithms is often claimed to be exponential when compared to classical PF solved by state-of-the-art algorithms. Here, we investigate the potential for practical quantum advantage in solving QPF compared to classical methods on gate-based quantum computers. Notably, this paper does not present a new QPF solving algorithm but scrutinizes the end-to-end complexity of the QPF approach, providing a nuanced evaluation of the purported quantum speedup in this problem. Our analysis establishes a best-case bound for the HHL-based quantum power flow complexity, conclusively demonstrating that the HHL-based method has higher runtime complexity compared to the classical algorithm for solving the direct current power flow (DCPF) and fast decoupled load flow (FDLF) problem. Notably, our analysis and conclusions can be extended to any quantum linear system solver with rigorous performance guarantees, based on the known complexity lower bounds for this problem. Additionally, we establish that for potential practical quantum advantage (PQA) to exist it is necessary to consider DCPF-type problems with a very narrow range of condition number values and readout requirements.
SAND2024-03236O Orca2 is a trajectory design and optimization code for constructing and solving problems numerically defined on homogeneous manifolds. Orca2 solves numerical trajectory design and optimization problems defined on Lie-type domains and operates primarily as a library requiring a user to write additional C++ code to leverage it. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.
Quantum information science is a growing field that promises to take computing into a new age of higher performance and larger scale computing as well as being capable of solving problems classical computers are incapable of solving. The outstanding issue in practical quantum computing today is scaling up the system while maintaining interconnectivity of the qubits and low error rates in qubit operations to be able to implement error correction and fault-tolerant operations. Trapped ion qubits offer long coherence times that allow error correction. However, error correction algorithms require large numbers of qubits to work properly. We can potentially create many thousands (or more) of qubits with long coherence states in a storage ring. For example, a circular radio-frequency quadrupole, which acts as a large circular ion trap and could enable larger scale quantum computing. Such a Storage Ring Quantum Computer (SRQC) would be a scalable and fault tolerant quantum information system, composed of qubits with very long coherence lifetimes. With computing demands potentially outpacing the supply of high-performance systems, quantum computing could bring innovation and scientific advances to particle physics and other DOE supported programs. Increased support of R$\&$D in large scale ion trap quantum computers would allow the timely exploration of this exciting new scalable quantum computer. The R$\&$D program could start immediately at existing facilities and would include the design and construction of a prototype SRQC. We invite feedback from and collaboration with the particle physics and quantum information science communities.
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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.
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.
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.
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.