arXiv subjects

Wesley Jones

Publications and source records attributed to Wesley Jones.

10 recordsLinked to original sources

arXiv2026

A hard-constrained NN learning framework for rapidly restoring AC-OPF from DC-OPF

This paper proposes a hard-constrained unsupervised learning framework for rapidly solving the non-linear and non-convex AC optimal power flow (AC-OPF) problem in real-time operation. Without requiring ground-truth AC-OPF solutions, feasibility and optimality are ensured through a properly designed learning environment and training loss. Inspired by residual learning, the neural network (NN) learns the correction mapping from the DC-OPF solution to the active power setpoints of the generators through re-dispatch. A subsequent optimization model is utilized to restore the optimal AC-OPF solution, and the resulting projection difference is employed as the training loss. A replay buffer is utilized to enhance learning efficiency by fully leveraging past data pairs. The optimization model is cast as a differentiable optimization layer, where the gradient is derived by applying the implicit function theorem to the KKT conditions at the optimal solution. Tested on IEEE-118 and PEGASE-9241 bus systems, numerical results demonstrate that the proposed NN can obtain strictly feasible and near-optimal solutions with reduced computational time compared to conventional optimization solvers. In addition, aided by the updated DC-OPF solution under varying topologies, the trained NN, together with the PF solver, can rapidly find the corresponding AC solution. The proposed method achieves a $40\times$ time speedup, while maintaining an average constraint violation on the order of $10^{-4}$ and an optimization gap below $1\%$.

eess.SY↗

arXiv2024

Dynamic, Symmetry-Preserving, and Hardware-Adaptable Circuits for Quantum Computing Many-Body States and Correlators of the Anderson Impurity Model

We present a hardware-reconfigurable ansatz on $N_q$-qubits for the variational preparation of many-body states of the Anderson impurity model (AIM) with $N_{\text{imp}}+N_{\text{bath}}=N_q/2$ sites, which conserves total charge and spin z-component within each variational search subspace. The many-body ground state of the AIM is determined as the minimum over all minima of $O(N_q^2)$ distinct charge-spin sectors. Hamiltonian expectation values are shown to require $\omega(N_q) < N_{\text{meas.}} \leq O(N_{\text{imp}}N_{\text{bath}})$ symmetry-preserving, parallelizable measurement circuits, each amenable to post-selection. To obtain the one-particle impurity Green's function we show how initial Krylov vectors can be computed via mid-circuit measurement and how Lanczos iterations can be computed using the symmetry-preserving ansatz. For a single-impurity Anderson model with a number of bath sites increasing from one to six, we show using numerical emulation that the ease of variational ground-state preparation is suggestive of linear scaling in circuit depth and sub-quartic scaling in optimizer complexity. We therefore expect that, combined with time-dependent methods for Green's function computation, our ansatz provides a useful tool to account for electronic correlations on early fault-tolerant processors. Finally, with a view towards computing real materials properties of interest like magnetic susceptibilities and electron-hole propagators, we provide a straightforward method to compute many-body, time-dependent correlation functions using a combination of time evolution, mid-circuit measurement-conditioned operations, and the Hadamard test.

quant-ph↗

arXiv2024

Calculating the expected value function of a two-stage stochastic optimization program with a quantum algorithm

Two-stage stochastic programming is a problem formulation for decision-making under uncertainty. In the first stage, the actor makes a best "here and now" decision in the presence of uncertain quantities that will be resolved in the future, represented in the objective function as the expected value function. This function is a multi-dimensional integral of the second stage optimization problem, which must be solved over all possible future scenarios. This work uses a quantum algorithm to estimate the expected value function with a polynomial speedup. Our algorithm gains its advantage through the two following observations. First, by encoding the probability distribution as a quantum wavefunction in an auxilliary register, and using this register as control logic for a phase-separation unitary, Digitized Quantum Annealing (DQA) can converge to the minimium of each scenario in the random variable in parallel. Second, Quantum Amplitude Estimation (QAE) on DQA can calculate the expected value of this per-scenario optimized wavefunction, producing an estimate for the expected value function. Quantum optimization is theorized to have a polynomial speedup for combinatorial optimization problems, and estimation error from QAE is known to converge inverse-linear in the number of samples (as opposed to the best case inverse of a square root in classical Monte Carlo). Therefore, assuming the probability distribution wavefunction can be prepared efficiently, we conclude our method has a polynomial speedup (of varying degree, depending on the optimization problem) over classical methods for estimating the expected value function. We conclude by demonstrating this algorithm on a stochastic programming problem inspired by operating the power grid under weather uncertainty.

quant-ph↗

arXiv2022

Curriculum-based Reinforcement Learning for Distribution System Critical Load Restoration

This paper focuses on the critical load restoration problem in distribution systems following major outages. To provide fast online response and optimal sequential decision-making support, a reinforcement learning (RL) based approach is proposed to optimize the restoration. Due to the complexities stemming from the large policy search space, renewable uncertainty, and nonlinearity in a complex grid control problem, directly applying RL algorithms to train a satisfactory policy requires extensive tuning to be successful. To address this challenge, this paper leverages the curriculum learning (CL) technique to design a training curriculum involving a simpler steppingstone problem that guides the RL agent to learn to solve the original hard problem in a progressive and more effective manner. We demonstrate that compared with direct learning, CL facilitates controller training to achieve better performance. To study realistic scenarios where renewable forecasts used for decision-making are in general imperfect, the experiments compare the trained RL controllers against two model predictive controllers (MPCs) using renewable forecasts with different error levels and observe how these controllers can hedge against the uncertainty. Results show that RL controllers are less susceptible to forecast errors than the baseline MPCs and can provide a more reliable restoration process.

eess.SY↗

arXiv2021

A Comparison of Model-Free and Model Predictive Control for Price Responsive Water Heaters

We present a careful comparison of two model-free control algorithms, Evolution Strategies (ES) and Proximal Policy Optimization (PPO), with receding horizon model predictive control (MPC) for operating simulated, price responsive water heaters. Four MPC variants are considered: a one-shot controller with perfect forecasting yielding optimal control; a limited-horizon controller with perfect forecasting; a mean forecasting-based controller; and a two-stage stochastic programming controller using historical scenarios. In all cases, the MPC model for water temperature and electricity price are exact; only water demand is uncertain. For comparison, both ES and PPO learn neural network-based policies by directly interacting with the simulated environment under the same scenarios used by MPC. All methods are then evaluated on a separate one-week continuation of the demand time series. We demonstrate that optimal control for this problem is challenging, requiring more than 8-hour lookahead for MPC with perfect forecasting to attain the minimum cost. Despite this challenge, both ES and PPO learn good general purpose policies that outperform mean forecast and two-stage stochastic MPC controllers in terms of average cost and are more than two orders of magnitude faster at computing actions. We show that ES in particular can leverage parallelism to learn a policy in under 90 seconds using 1150 CPU cores.

eess.SY↗

arXiv2021

Linear solvers for power grid optimization problems: a review of GPU-accelerated linear solvers

The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite and become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frameworks based on sparse LU or LDL^T decompositions. We benchmark five well known direct linear solver packages using matrices extracted from power grid optimization problems. The achieved solution accuracy varies greatly among the packages. None of the tested packages delivers significant GPU acceleration for our test cases.

math.NA↗

arXiv2020

K-spin Hamiltonian for quantum-resolvable Markov decision processes

The Markov decision process is the mathematical formalization underlying the modern field of reinforcement learning when transition and reward functions are unknown. We derive a pseudo-Boolean cost function that is equivalent to a K-spin Hamiltonian representation of the discrete, finite, discounted Markov decision process with infinite horizon. This K-spin Hamiltonian furnishes a starting point from which to solve for an optimal policy using heuristic quantum algorithms such as adiabatic quantum annealing and the quantum approximate optimization algorithm on near-term quantum hardware. In proving that the variational minimization of our Hamiltonian is equivalent to the Bellman optimality condition we establish an interesting analogy with classical field theory. Along with proof-of-concept calculations to corroborate our formulation by simulated and quantum annealing against classical Q-Learning, we analyze the scaling of physical resources required to solve our Hamiltonian on quantum hardware.

quant-ph↗

arXiv2020

On the Computational Viability of Quantum Optimization for PMU Placement

Using optimal phasor measurement unit placement as a prototypical problem, we assess the computational viability of the current generation D-Wave Systems 2000Q quantum annealer for power systems design problems. We reformulate minimum dominating set for the annealer hardware, solve the reformulation for a standard set of IEEE test systems, and benchmark solution quality and time to solution against the CPLEX Optimizer and simulated annealing. For some problem instances the 2000Q outpaces CPLEX. For instances where the 2000Q underperforms with respect to CPLEX and simulated annealing, we suggest hardware improvements for the next generation of quantum annealers.

quant-ph↗

arXiv2018

Advanced Scenario Creation Strategies for Stochastic Economic Dispatch with Renewables

Real-time dispatch practices for operating the electric grid in an economic and reliable manner are evolving to accommodate higher levels of renewable energy generation. In particular, stochastic optimization is receiving increased attention as a technique for handling the inherent uncertainty in wind and solar generation. The typical two-stage stochastic optimization formulation relies on a sample average approximation with scenarios representing errors in forecasting renewable energy ramp events. Standard Monte Carlo sampling approaches can result in prohibitively high-dimensional systems for optimization, as well as a poor representation of extreme events that challenge grid reliability. We propose two alternative scenario creation strategies, importance sampling and Bayesian quadrature, that can reduce the estimator's variance. Their performance is assessed on a week's worth of 5 minute stochastic economic dispatch decisions for realistic wind and electrical system data. Both strategies yield more economic solutions and improved reliability compared to Monte Carlo sampling, with Bayesian quadrature being less computationally intensive than importance sampling and more economic when considering at least 20 scenarios.

math.OC↗

arXiv2012

Keeping greed good: sparse regression under design uncertainty with application to biomass characterization

In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated measurements on both the design and dependent variables may be leveraged to enhance a sparse regression algorithm. Specifically, we estimate the variance and use it to scale our design variables. We demonstrate the efficacy of scaling from several points of view and validate it empirically with a biomass characterization data set using two of the most widely used sparse algorithms: least angle regression (LARS) and the Dantzig selector (DS).

stat.AP↗