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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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Tabulation of high accuracy gamma function values for some rational arguments, noting applications to Gaussian quadrature formulas, fractional Bessel functions and Airy functions
Two point boundary value problems of quasi- differential equations, discussing conditions for continuous and increasing lower bounds of functions
Finite-temperature quantum field theories are formulated in terms of Green's functions and self-energies on the Matsubara axis. In multiorbital systems, these quantities are related to positive semidefinite matrix-valued functions of the Carathéodory and Schur class. Analysis, interpretation, and evaluation of derived quantities such as real-frequency response functions requires analytic continuation of the off-diagonal elements to the real axis. Here we derive the criteria under which such functions exist for given Matsubara data and present an interpolation algorithm that intrinsically respects their mathematical properties. For small systems with precise Matsubara data, we find that the continuation exactly recovers all off-diagonal and diagonal elements. In real-materials systems, we show that the precision of the continuation is sufficient for the analytic continuation to commute with the Dyson equation, and we show that the truncation of the off-diagonal self-energy elements leads to considerable approximation artifacts.
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A self-contained theory of extrema (viz., suprema, maxima, minima, and infima) of differentiable functions of several (possibly infinitely many) variables mapping into finite-dimensional integrally closed directed partially ordered linear spaces is reported. The applicability of the theory to the analysis of linear least squares vector estimation problem is demonstrated.
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Let F(z) be a vector-valued function, F: C yields C(sup N), which is analytic at z = 0 and meromorphic in a neighborhood of z = 0, and let its Maclaurin series be given. In this work we developed vector-valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyzed some of the algebraic and analytic properties of the rational approximations thus obtained, and showed that they were akin to Pade approximations. In particular, we proved a Koenig type theorem concerning their poles and a de Montessus type theorem concerning their uniform convergence. We showed how optical approximations to multiple poles and to Laurent expansions about these poles can be constructed. Extensions of the procedures above and the accompanying theoretical results to functions defined in arbitrary linear spaces was also considered. One of the most interesting and immediate applications of the results of this work is to the matrix eigenvalue problem. In a forthcoming paper we exploited the developments of the present work to devise bona fide generalizations of the classical power method that are especially suitable for very large and sparse matrices. These generalizations can be used to approximate simultaneously several of the largest distinct eigenvalues and corresponding eigenvectors and invariant subspaces of arbitrary matrices which may or may not be diagonalizable, and are very closely related with known Krylov subspace methods.
Finding the inverse of a continuous function can be challenging and computationally expensive when the inverse function is multi-valued. Difficulties may be compounded when the function itself is difficult to evaluate. We show that we can use fuzzy-logic approximators such as Sugeno inference systems to compute the inverse on-line. To do so, a fuzzy clustering algorithm can be used in conjunction with a discriminating function to split the function data into branches for the different values of the forward function. These data sets are then fed into a recursive least-squares learning algorithm that finds the proper coefficients of the Sugeno approximators; each Sugeno approximator finds one value of the inverse function. Discussions about the accuracy of the approximation will be included.
Existence theorems for optimal control problems with vector valued cost function
Noninferior set for static optimization of systems with vector valued objective function using dual linear inequality
We introduce a class of variational actor-critic algorithms based on a variational formulation over both the value function and the policy. The objective function of the variational formulation consists of two parts: one for maximizing the value function and the other for minimizing the Bellman residual. Besides the vanilla gradient descent with both the value function and the policy updates, we propose two variants, the clipping method and the flipping method, in order to speed up the convergence. We also prove that, when the prefactor of the Bellman residual is sufficiently large, the fixed point of the algorithm is close to the optimal policy.
Abstract Materials development is slow and expensive, taking decades from inception to fielding. For materials research at extremes, the situation is even more demanding, as the desired property combinations such as strength and oxidation resistance can have complex interactions. Here, we explore the role of AI and autonomous experimentation (AE) in the process of understanding and developing materials for extreme and coupled environments. AI is important in understanding materials under extremes due to the highly demanding and unique cases these environments represent. Materials are pushed to their limits in ways that, for example, equilibrium phase diagrams cannot describe. Often, multiple physical phenomena compete to determine the material response. Further, validation is often difficult or impossible. AI can help bridge these gaps, providing heuristic but valuable links between materials properties and performance under extreme conditions. We explore the potential advantages of AE along with decision strategies. In particular, we consider the problem of deciding between low-fidelity, inexpensive experiments and high-fidelity, expensive experiments. The cost of experiments is described in terms of the speed and throughput of automated experiments, contrasted with the human resources needed to execute manual experiments. We also consider the cost and benefits of modeling and simulation to further materials understanding, along with characterization of materials under extreme environments in the AE loop. Graphical abstract AI sequential decision-making methods for materials research: Active learning, which focuses on exploration by sampling uncertain regions, Bayesian and bandit optimization as well as reinforcement learning (RL), which trades off exploration of uncertain regions with exploitation of optimum function value. Bayesian and bandit optimization focus on finding the optimal value of the function at each step or cumulatively over the entire steps, respectively, whereas RL considers cumulative value of the labeling function, where the latter can change depending on the state of the system (blue, orange, or green).
Abstract The ability to efficiently load functions on quantum computers with high fidelity is essential for many quantum algorithms, including those for solving partial differential equations and Monte Carlo estimation. In this work, we introduce the Fourier series loader (FSL) method for preparing quantum states that exactly encode multi-dimensional Fourier series using linear-depth quantum circuits. Specifically, the FSL method prepares a (Dn)-qubit state encoding the 2 Dn -point uniform discretization of aD-dimensional function specified by aD-dimensional Fourier series. A free parameter,m, which must be less thann, determines the number of Fourier coefficients, 2 D ( m + 1 ) , used to represent the function. The FSL method uses a quantum circuit of depth at most 2 ( n − 2 ) + ⌈ log 2 ( n − m ) ⌉ + 2 D ( m + 1 ) + 2 − 2 D ( m + 1 ) , which is linear in the number of Fourier coefficients, and linear in the number of qubits (Dn) despite the fact that the loaded function’s discretization is over exponentially many (2 Dn ) points. The FSL circuit consists of at most D n + 2 D ( m + 1 ) + 1 − 1 single-qubit and D n ( n + 1 ) / 2 + 2 D ( m + 1 ) + 1 − 3 D ( m + 1 ) − 2 two-qubit gates; we present a classical compilation algorithm with runtime O ( 2 3 D ( m + 1 ) ) to determine the FSL circuit for a given Fourier series. The FSL method allows for the highly accurate loading of complex-valued functions that are well-approximated by a Fourier series with finitely many terms. We report results from noiseless quantum circuit simulations, illustrating the capability of the FSL method to load various continuous 1D functions, and a discontinuous 1D function, on 20 qubits with infidelities of less than 10 −6 and 10 −3 , respectively. We also demonstrate the practicality of the FSL method for near-term quantum computers by presenting experiments performed on the Quantinuum H1-1 and H1-2 trapped-ion quantum computers: we loaded a complex-valued function on 3 qubits with a fidelity of over 95 % , as well as various 1D real-valued functions on up to 6 qubits with classical fidelities ≈99%, and a 2D function on 10 qubits with a classical fidelity ≈94%.
Inaccuracies in the length of members and the diameters of joints of large truss reflector backup structures may produce unacceptable levels of surface distortion and member forces. However, if the member lengths and joint diameters can be measured accurately it is possible to configure the members and joints so that root-mean-square (rms) surface error and/or rms member forces is minimized. Following Greene and Haftka (1989) it is assumed that the force vector f is linearly proportional to the member length errors e(sub M) of dimension NMEMB (the number of members) and joint errors e(sub J) of dimension NJOINT (the number of joints), and that the best-fit displacement vector d is a linear function of f. Let NNODES denote the number of positions on the surface of the truss where error influences are measured. The solution of the problem is discussed. To classify, this problem was compared to a similar combinatorial optimization problem. In particular, when only the member length errors are considered, minimizing d(sup 2)(sub rms) is equivalent to the quadratic assignment problem. The quadratic assignment problem is a well known NP-complete problem in operations research literature. Hence minimizing d(sup 2)(sub rms) is is also an NP-complete problem. The focus of the research is the development of a simulated annealing algorithm to reduce d(sup 2)(sub rms). The plausibility of this technique is its recent success on a variety of NP-complete combinatorial optimization problems including the quadratic assignment problem. A physical analogy for simulated annealing is the way liquids freeze and crystallize. All computational experiments were done on a MicroVAX. The two interchange heuristic is very fast but produces widely varying results. The two and three interchange heuristic provides less variability in the final objective function values but runs much more slowly. Simulated annealing produced the best objective function values for every starting configuration and was faster than the two and three interchange heuristic.
An industrial asset may have monitoring nodes that generate current monitoring node values. An abnormality detection computer may determine that an abnormal monitoring node is currently being attacked or experiencing fault. A dynamic, resilient estimator constructs, using normal monitoring node values, a latent feature space (of lower dimensionality as compared to a temporal space) associated with latent features. The system also constructs, using normal monitoring node values, functions to project values into the latent feature space. Responsive to an indication that a node is currently being attacked or experiencing fault, the system may compute optimal values of the latent features to minimize a reconstruction error of the nodes not currently being attacked or experiencing a fault. The optimal values may then be projected back into the temporal space to provide estimated values and the current monitoring node values from the abnormal monitoring node are replaced with the estimated values.
Weighting factors combined with individual value functions for 350 candidate orbits for Voyager Mars missions to develop computer-determined overall value functions for optimum orbits
We present a scalable unsupervised learning-based method for obtaining explicit control policies for model predictive control problems for stochastic linear systems with additive uncertainties subject to nonlinear chance constraints. We call the proposed method stochastic parametric differentiable predictive control (SP-DPC), which extends the recently proposed deterministic DPC policy optimization algorithm. We formulate the SP-DPC as a deterministic approximation to the stochastic parametric constrained optimal control problem via independent sampling of the problem's parameters and uncertainties. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the problem's value function is backpropagated through the finite-time closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy. We also provide theoretical probabilistic guarantees on closed-loop stability and chance constraints satisfaction for systems controlled by learned neural policies. We demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.
We study multiagent reinforcement learning (MARL) with constraints. This setting is gaining importance as MARL algorithms find new applications in real-world systems ranging from power grids to drone swarms. Most constrained MARL (C-MARL) algorithms use a primal-dual approach to enforce constraints through a penalty function added to the reward. In this paper, we study the structural effects of the primal-dual approach on the constraints and value function. First, we show that using the constraint evaluation as the penalty leads to a weak notion of safety, but by making simple modifications to the penalty function, we can enforce meaningful probabilistic safety constraints. Second, we show that the penalty term changes the value function in a way that is easy to model, and demonstrate the consequences of not doing so. We conclude with simulations in a simple constrained multiagent environment to back up the theoretical results.