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At least 703 records · Page 39

A Novel Noise-Aware Classical Optimizer for Variational Quantum Algorithms

A key component of variational quantum algorithms (VQAs) is the choice of classical optimizer employed to update the parameterization of an ansatz. It is well recognized that quantum algorithms will, for the foreseeable future, necessarily be run on noisy devices with limited fidelities. Thus, the evaluation of an objective function (e.g., the guiding function in the quantum approximate optimization algorithm (QAOA) or the expectation of the electronic Hamiltonian in variational quantum eigensolver (VQE)) required by a classical optimizer is subject not only to stochastic error from estimating an expected value but also to error resulting from intermittent hardware noise. Model-based derivative-free optimization methods have emerged as popular choices of a classical optimizer in the noisy VQA setting, based on empirical studies. However, these optimization methods were not explicitly designed with the consideration of noise. In this work we adapt recent developments from the “noise-aware numerical optimization” literature to these commonly used derivative-free model-based methods. We introduce the key defining characteristics of these novel noise-aware derivative-free model-based methods that separate them from standard model-based methods. In conclusion, we study an implementation of such noise-aware derivative-free model-based methods and compare its performance on demonstrative VQA simulations to classical solvers packaged in scikit-quant.

classical optimizers↗

Parameter-induced stochastic resonance based on spectral entropy and its application to weak signal detection

The parameter-induced stochastic resonance based on spectral entropy (PSRSE) method is introduced for the detection of a very weak signal in the presence of strong noise. The effect of stochastic resonance on the detection is optimized using parameters obtained in spectral entropy analysis. Upon processing employing the PSRSE method, the amplitude of the weak signal is enhanced and the noise power is reduced, so that the frequency of the signal can be estimated with greater precision through spectral analysis. While the improvement in the signal-to-noise ratio is similar to that obtained using the Duffing oscillator algorithm, the computational cost reduces from O(N{sup 2}) to O(N). The PSRSE approach is applied to the frequency measurement of a weak signal made by a vortex flow meter. The results are compared with those obtained applying the Duffing oscillator algorithm.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Higher-order time integration of Coulomb collisions in a plasma using Langevin equations

The extension of Langevin-equation Monte-Carlo algorithms for Coulomb collisions from the conventional Euler–Maruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the fixed-frame spherical-coordinate velocity variables. Results from the numerical implementation show the expected improvement [O(Δt) vs. O(Δt{sup 1/2})] in the strong convergence rate both for the speed |v| and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the “area-integral” terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multi-time-level schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional Monte-Carlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the Euler–Maruyama algorithm. A new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy. This method, while being useful in its own right because of its relative simplicity, is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration.

97 MATHEMATICS AND COMPUTING↗

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗

A Distributionally Robust Resilience Enhancement Strategy for Distribution Networks Considering Decision-Dependent Contingencies

When performing the resilience enhancement for distribution networks, there are two obstacles to reliably model the uncertain contingencies: 1) decision-dependent uncertainty (DDU) due to various line hardening decisions, and 2) distributional ambiguity due to limited outage information during extreme weather events (EWEs). Here, to address these two challenges, this paper develops scenario-wise decision-dependent ambiguity sets (SWDD-ASs), where the DDU and distributional ambiguity inherent in EWE-induced contingencies are simultaneously captured for each possible EWE scenario. Then, a two-stage tri-level decision-dependent distributionally robust resilient enhancement (DD-DRRE) model is formulated, whose outputs include the optimal line hardening, distributed generation (DG) allocation, and proactive network reconfiguration strategy under the worst-case distributions in SWDD-ASs. Subsequently, the DD-DRRE model is equivalently recast to a mixed-integer linear programming (MILP)-based master problem and multiple scenario-wise subproblems, facilitating the adoption of a customized column-and-constraint generation (C&CG) algorithm. Finally, case studies demonstrate a remarkable improvement in the out-of-sample performance of our model, compared to its prevailing stochastic and robust counterparts. Moreover, the potential values of incorporating the ambiguity and distributional information are quantitatively estimated, providing a useful reference for planners with different budgets and risk-aversion levels.

decision-dependent uncertainty↗

Convergence Analysis for an Online Data-Driven Feedback Control Algorithm

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings.

97 MATHEMATICS AND COMPUTING↗

Characterization of single-shot attosecond pulses with angular streaking photoelectron spectra

Most of the traditional attosecond pulse retrieval algorithms are based on a so-called attosecond streak camera technique, in which the momentum of the electron is shifted by an amount depending on the relative time delay between the attosecond pulse and the streaking infrared pulse. Thus, temporal information of the attosecond pulse is encoded in the amount of momentum shift in the streaked photoelectron momentum spectrogram S(p,τ), where p is the momentum of the electron along the polarization direction and τ is the time delay. An iterative algorithm is then employed to reconstruct the attosecond pulse from the streaking spectrogram. This method, however, cannot be applied to attosecond pulses generated from free-electron x-ray lasers where each single shot is different and stochastic in time. However, using a circularly polarized infrared laser as the streaking field, a two (or three)-dimensional angular streaking electron spectrum can be used to retrieve attosecond pulses for each shot, as well as the time delay with respect to the circularly polarized IR field. Here we show that a retrieval algorithm previously developed for the traditional streaking spectrogram can be modified to efficiently characterize single-shot attosecond pulses. The methods have been applied to retrieve 188 single shots from recent experiments. We analyze the statistical behavior of these 188 pulses in terms of pulse duration, bandwidth, pulse peak energy, and time delay with respect to the IR field. Furthermore, the retrieval algorithm is efficient and can be easily used to characterize a large number of shots in future experiments for attosecond pulses at free-electron x-ray laser facilities.

74 ATOMIC AND MOLECULAR PHYSICS↗

Quantum-assisted associative adversarial network: applying quantum annealing in deep learning

Abstract Generative models have the capacity to model and generate new examples from a dataset and have an increasingly diverse set of applications driven by commercial and academic interest. In this work, we present an algorithm for learning a latent variable generative model via generative adversarial learning where the canonical uniform noise input is replaced by samples from a graphical model. This graphical model is learned by a Boltzmann machine which learns low-dimensional feature representation of data extracted by the discriminator. A quantum processor can be used to sample from the model to train the Boltzmann machine. This novel hybrid quantum-classical algorithm joins a growing family of algorithms that use a quantum processor sampling subroutine in deep learning, and provides a scalable framework to test the advantages of quantum-assisted learning. For the latent space model, fully connected, symmetric bipartite and Chimera graph topologies are compared on a reduced stochastically binarized MNIST dataset, for both classical and quantum sampling methods. The quantum-assisted associative adversarial network successfully learns a generative model of the MNIST dataset for all topologies. Evaluated using the Fréchet inception distance and inception score, the quantum and classical versions of the algorithm are found to have equivalent performance for learning an implicit generative model of the MNIST dataset. Classical sampling is used to demonstrate the algorithm on the LSUN bedrooms dataset, indicating scalability to larger and color datasets. Though the quantum processor used here is a quantum annealer, the algorithm is general enough such that any quantum processor, such as gate model quantum computers, may be substituted as a sampler.

Wilson, Max (ORCID:0000000207983391)↗

Field Testing of LIDAR-Assisted Feedforward Control Algorithms for Improved Speed Control and Fatigue Load Reduction on a 600-kW Wind Turbine: Preprint

A severe challenge in controlling wind turbines is ensuring controller performance in the presence of a stochastic and unknown wind field, relying on the response of the turbine to generate control actions. Recent technologies such as LIDAR, allow sensing of the wind field before it reaches the rotor. In this work a field-testing campaign to test LIDAR Assisted Control (LAC) has been undertaken on a 600-kW turbine using a fixed, five-beam LIDAR system. The campaign compared the performance of a baseline controller to four LACs with progressively lower levels of feedback using 35 hours of collected data.

17 WIND ENERGY↗

A hybrid robust-stochastic optimization approach for day-ahead scheduling of cascaded hydroelectric system in restructured electricity market

Uncertainties arising from complicated natural and market environments pose great challenges for the efficient operation of cascaded hydroelectric systems. To overcome these challenges, this paper studies the day-ahead scheduling of cascaded hydroelectric systems in a restructured electricity market with the presence of uncertainties in electricity price and natural water inflow. To properly model the uncertainty, we consider the unique characteristics of these two types of uncertainties and capture them via the uncertainty set and stochastic scenarios, respectively. Further, a hybrid robust-stochastic optimization model is developed to simultaneously hedge against these two types of uncertainties, which is formulated as a large-scale non-convex optimization problem with mixed integer recourse. After introducing linearization of nonlinear terms, a tailored hybrid decomposition scheme combining Lagrangian relaxation and Dantzig-Wolfe decomposition is adopted to achieve efficient computation of the proposed model. Two real-world cases are conducted to demonstrate the capability and characteristics of the proposed model and algorithms.

13 HYDRO ENERGY↗

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.

Derivative-free Optimization↗

New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

A novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems is proposed and it considers a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen’s inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improves upon the standard Benders’ algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen’s inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. But, the decomposition phase is required to attain optimality gaps. Moreover, use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately.

97 MATHEMATICS AND COMPUTING↗

Non-adiabatic dynamics around a conical intersection with surface-hopping coupled coherent states

A surface-hopping extension of the coupled coherent states-method [D. Shalashilin and M. Child, Chem. Phys. 304, 103-120 (2004)] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schrödinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully’s fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronic wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both interference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [A. Ferretti, J. Chem. Phys. 104, 5517 (1996)], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and interferes with itself. These interference effects are absent in classical trajectory-based molecular dynamics but can be fully incorpo rated if trajectories are replaced by surface hopping coupled coherent states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

dfnWorks, Version 1.0

DFNWorks is a suite of software for generating and solving flow and transport physics on a Discrete Fracture Network (DFN). The suite is composed of three components: DFNGen: Stochastic fracture generation, mesh generation, model setup; DFNFlow: Flow solution using PFLOTRAN or FEHM control volume formulation solver; DFNTrans: Particle tracking transport; DFNGen Algorithm Description: This is a workflow that uses Mathematica software, Python scripts written by the authors and the LaGriT software to generate; DFNFlow; The solution of flow in porous media is accomplished by coupling DFNGen output with the existing software packages FEHM and PFLOTRAN. The DFNWorks workflow involves modules and scripts that translate DFNGen output to formats compatible with FEHM and PFLOTRAN input. FEHM LA-CC-2012-083 PFLOTRAN LA-CC-09-047 LaGriT LA-CC-07-38 DFNTrans Stand alone particle tracking algorithm that takes FEHM/PFLOTRAN flow solution as output and computes velocity field and advects particles.

Makedonska, Nataliia↗

dfnWorks, Version 2.0

DFNWorks is a suite of software for generating and solving flow and transport physics on a Discrete Fracture Network (DFN). The suite is composed of three components: DFNGen: Stochastic fracture generation, mesh generation, model setup; DFNFlow: Flow solution using PFLOTRAN or FEHM control volume formulation solver; DFNTrans: Particle tracking transport; DFNGen Algorithm Description: This is a workflow that uses C++ software version for fracture generation, Python scripts written by the authors and the LaGriT software to generate computational mesh. DFNFlow The solution of flow in porous media is accomplished by coupling DFNGen output with the existing software packages FEHM and PFLOTRAN. The DFNWorks workflow involves modules and scripts that translate DFNGen output to formats compatible with FEHM and PFLOTRAN input. FEHM LA-CC-2012-083 PFLOTRAN LA-CC-09-047 LaGriT LA-CC-07-38 DFNTrans Stand-alone particle tracking algorithm that takes FEHM/PFLOTRAN flow solution as output and computes velocity field and advects particles.

Makedonska, Nataliia↗

dfnWorks, Version 1.0

DFNWorks is a suite of software for generating and solving flow and transport physics on a Discrete Fracture Network (DFN). The suite is composed of three components: DFNGen: Stochastic fracture generation, mesh generation, model setup; DFNFlow: Flow solution using PFLOTRAN or FEHM control volume formulation solver; DFNTrans: Particle tracking transport; DFNGen Algorithm Description: This is a workflow that uses Mathematica software, Python scripts written by the authors and the LaGriT software to generate; DFNFlow; The solution of flow in porous media is accomplished by coupling DFNGen output with the existing software packages FEHM and PFLOTRAN. The DFNWorks workflow involves modules and scripts that translate DFNGen output to formats compatible with FEHM and PFLOTRAN input. FEHM LA-CC-2012-083 PFLOTRAN LA-CC-09-047 LaGriT LA-CC-07-38 DFNTrans Stand alone particle tracking algorithm that takes FEHM/PFLOTRAN flow solution as output and computes velocity field and advects particles.

Makedonska, Nataliia↗

dfnWorks, Version 2.0

DFNWorks is a suite of software for generating and solving flow and transport physics on a Discrete Fracture Network (DFN). The suite is composed of three components: DFNGen: Stochastic fracture generation, mesh generation, model setup; DFNFlow: Flow solution using PFLOTRAN or FEHM control volume formulation solver; DFNTrans: Particle tracking transport; DFNGen Algorithm Description: This is a workflow that uses C++ software version for fracture generation, Python scripts written by the authors and the LaGriT software to generate computational mesh. DFNFlow The solution of flow in porous media is accomplished by coupling DFNGen output with the existing software packages FEHM and PFLOTRAN. The DFNWorks workflow involves modules and scripts that translate DFNGen output to formats compatible with FEHM and PFLOTRAN input. FEHM LA-CC-2012-083 PFLOTRAN LA-CC-09-047 LaGriT LA-CC-07-38 DFNTrans Stand-alone particle tracking algorithm that takes FEHM/PFLOTRAN flow solution as output and computes velocity field and advects particles.

Makedonska, Nataliia↗