arXiv subjects

Shaked Regev

Publications and source records attributed to Shaked Regev.

17 recordsLinked to original sources

arXiv2026

Fast and Accurate Hydro Unit Commitment

We introduce a fast novel algorithm to commit hydro-generators. We show that our algorithm can commit 56 generators for 200 days 10,000 times faster than Hexaly, the leading commercial solver for scheduling problems, without sacrificing solution quality. Our method can commit 1792 generators for an entire year in approximately 20 seconds on commodity hardware. Hexaly is unable to solve problems of this size in reasonable time. We attain this runtime improvement by introducing a greedy-heuristic tailored for hydro units. We provide a direction for a possible proof that the error our solver makes decreases with the problem size. This is supported by our experimental results. We prove that our solver's runtime scales log-linearly in the number of generators and time periods.

math.OC↗

arXiv2026

Fast Relax-and-Round Unit Commitment with Economic Horizons

The US energy system is under increasing pressure to serve expanding data centers loads and to accommodate a larger number of generating units with varying technologies and ownership structures. Therefore, developing new unit commitment (UC) methods remains a priority for reliable and affordable grid operations. We expand our novel computational method for UC to include ramping constraints and long-horizon planning, and provide a theoretical bound on its accuracy. We solve problems with thousands of generators at 5-minute market intervals. We show that our method can solve UC problems with over 20,000 generators in approximately 10 seconds on commodity hardware and that an increased planning horizon leads to sizable op- erational cost savings. This is twice as fast as the leading commercial solver, Gurobi. The gap increases when adding more constraints. Our method can be implemented using existing continuous optimization solvers and adapted for different applications. We prove a bound on the error of these solvers and show that it vanishes (in relative terms) as the problem becomes larger. Our novel algorithm could allow an operator to make horizon-aware economic decisions for large systems.

math.OC↗

arXiv2026

Reinforcement Learning-Based Pricing and Operation for Hybrid Electric and Hydrogen Vehicle Stations

Electric vehicles (EVs) and hydrogen fuel cell vehi- cles (HFCVs) are promising technologies in the efforts to reduce carbon emissions. Challenges such as limited infrastructure, con- sumer dissatisfaction, and electrical grid strain inhibit progress in the adoption of these technologies. A zero emission vehicle (ZEV) station, capable of handling EVs and HFCVs, addresses these challenges by focusing on maximizing station profit and consumer utility, while minimizing grid impacts. The purpose of this research is to develop a realistic simulation of a ZEV station that is capable of handling real-time pricing decisions enabled by reinforcement learning (RL) and to compare the performance of the RL agent to static pricing methods. After training, the RL agent gains 10.83% greater station profit than the baseline manual parameter search. This work serves as a useful tool for ZEV station owners when handling complex pricing and purchasing decisions.

cs.CE↗

arXiv2026

Two-Stage Quantum-Classical Distribution Network Reconfiguration via Cycle-Edge Encoding

Distribution network reconfiguration (DNR) is a combinatorial optimization problem that seeks a low-loss network topology subject to topological and electrical operating constraints. In this work, we propose a two-stage quantum-classical method for DNR. First, an iterative linear-ramp Quantum Alternating Operator Ansatz (LR-QAOA) searches topologically feasible subspaces constructed using a novel cycle-edge encoding. The encoding guarantees that every represented configuration is a spanning tree while allowing the size and coverage of each subspace to be adjusted to the available qubit budget. Second, the resulting sample distribution is used to guide a mixed-integer second-order-cone programming (MISOCP) solver. The method is evaluated on six distribution networks ranging from 33 to 417 buses through ideal simulation and execution on trapped-ion quantum hardware. For the 417-bus network, quantum hardware sampling identifies a configuration within approximately $1.4\%$ of the literature reference loss. Across all six test systems, the MISOCP solver guided by hardware-derived distributions reaches an incumbent within $1\%$ of the target with a lower median solver time than the corresponding unguided solver. These findings establish a concrete framework for applying current quantum hardware to DNR, with the potential to become increasingly competitive as hardware improves.

quant-ph↗

arXiv2026

Warm-Start Iterative QITE for Distribution Network Reconfiguration via Branch-Exchange Encoding

We present a hybrid quantum-classical algorithm for distribution network reconfiguration, a combinatorial optimization problem on power distribution networks, that combines a radiality preserving branch-exchange encoding with iterative warm-start quantum imaginary-time evolution to minimize active line losses. The encoding uses a fixed-width binary representation of sequential branch-exchange actions, ensuring that every register outcome decodes to a radial configuration. The quantum subroutine is informed by a surrogate model fit to classically-solved alternating current power flow (ACPF) labels. After a set budget of ACPF solves and circuit samples is exhausted, the algorithm returns the lowest-loss configuration seen. We employ our algorithm on ten test cases, including seven commonly-used benchmark cases and three cases we modified from these and similar standard systems. We include two methods to reduce problem size, which enable extensions of the algorithm to larger networks. We successfully reach minimal-loss configurations for six cases and find configurations with losses from 0.2 percent to 2.18 percent above the reported reference minimal loss for the other four.

quant-ph↗

arXiv2026

Closed form logical error rate approximations for surface codes

We propose a novel method to calculate logical error rates in surface codes, assuming independent and identically distributed physical errors. These results fit well known scaling laws for studied physical error rates and code distances, but break down in some other regimes. Increasing the code distance still reduces logical error rates, but returns diminish quickly beyond a certain point. We show how to use our method to analyze hypothetical quantum computers with various configurations and select designs with lower error rates. Currently, this requires expensive classical simulations of quantum decoders for various distances and physical error rates or inaccurate extrapolation from minimal experimental data. Instead, we use the symmetry of the problem to count the configurations that result in a logical error with our novel software. Given a physical error rate, we can deduce the probability of a logical error to provably good accuracy quickly. We include an analysis of measurement errors to allow for a more complete comparison of different surface code implementations. We extend this counting method to a particular locally-correlated error model and another globally-correlated error model.

quant-ph↗

arXiv2026

Fast Relax-and-Round Unit Commitment with Topological Constraints

Recent developments in the US knowledge economy have created a significant growth in datacenter loads, with two major consequences for power generation. First, to compensate for growth in load, datacenters are encouraged to bring their own generating units. Second, in search of the remaining pools of dispatchable generation, utilities are increasingly turning to subtransmission and distribution level generating assets. Coupled with increasing loads and the resulting tighter grid conditions, both trends are likely to create a need to commit a large number of localized generating units under grid constraints. We propose an extension of Relax-and- Round Unit Commitment (RRUC) that is capable of committing generating units for larger problems faster than conventional methods, while staying within intertemporal and spatial MVA constraints. We demonstrate the performance of RRUC using synthetic congestible test systems ranging from 100 to 20,000 buses. RRUC consistently finds low cost solutions, independent of the problem size, and its run time increases sub-quadratically in the number of buses. RRUC can solve the 100 bus system in less than a second and the 20,000 bus system 7 minutes. In contrast, a leading state of the art solver cannot find a feasible solution to the 100 bus system in 15 minutes.

math.OC↗

arXiv2026

Dynamic Operational Reserve Margin Assessment from Risk-Constrained Unit Commitment States

We propose Dynamic Reserve Margin (DRM) as a time-varying operational adequacy metric derived from risk-constrained unit commitment (RCUC) states. DRM quantifies reserve adequacy using the additional generation capacity that committed generators can provide within a 5-minute response window relative to uncertainty and contingency reserve requirements. We introduce a complementary Reserve Risk Envelope (RRE) metric to quantify operational reserve headroom in directly interpretable MW terms. A low-margin duration metric is further developed to quantify the persistence of reserve stress over an operating horizon. We use an IEEE 14-bus example to illustrate these concepts, followed by large-scale RCUC case studies under multiple operating scenarios. Results demonstrate that reserve requirements and ramp-accessible reserve capability can vary substantially across operating conditions, and that commitment decisions adapt to maintain reserve adequacy under changing system conditions. The proposed DRM and RRE metrics provide an interpretable operational characterization of reserve adequacy, reveal reserve accessibility and stress persistence that are not captured by conventional reserve margin metrics.

eess.SY↗

arXiv2026

Accelerating the Conjugate Gradient Method by Solving Multiple GPU-Parallelized Duplicate Systems

We propose a method to accelerate the conjugate gradient method (CG) on parallel computing hardware by performing block conjugate gradient on one linear system. We aim to reduce the number of iterations until convergence by solving several copies of the system to explore multiple regions of the solution space at once. Although solving multiple systems requires more floating point operations than solving one, these computations are highly parallelizable, even without additional hardware resources. Our method does not replace preconditioning and can be used with any preconditioner. We developed linear regression models to predict iteration reduction and speedup as functions of the coefficient matrix's size, its number of nonzeros, and the solve time with CG. Our experiments show that our method can reduce solve time by up to 6 times in dense systems and up to 5 times in sparse systems that require long solve times with CG relative to their size.

math.NA↗

arXiv2026

Fast Relax-and-Round Unit Commitment with Sub-hourly Mechanical and Ramp Constraints

We propose a novel computational method for unit commitment UC, which does not require linearized approximation and provides several orders of magnitude performance improvement over current state-of-the-art. The performance improvement is achieved by introducing a heuristic tailored for UC problems. The method can be implemented using existing continuous optimization solvers and adapted for different applications. We demonstrate value of the new method in examples of advanced UC analyses at the scale where use of current state-of-the-art tools is infeasible. We expect that the capability demonstrated in this paper will be critical to address emerging power systems challenges with more volatile large loads, such as data centers, and generation that is composed of larger number of smaller units, including significant behind-the-meter generation.

math.OC↗

arXiv2026

Memory-Guided Trust-Region Bayesian Optimization (MG-TuRBO) for High Dimensions

Traffic simulation and digital-twin calibration is a challenging optimization problem with a limited simulation budget. Each trial requires an expensive simulation run, and the relationship between calibration inputs and model error is often nonconvex, and noisy. The problem becomes more difficult as the number of calibration parameters increases. We compare a commonly used automatic calibration method, a genetic algorithm (GA), with Bayesian optimization methods (BOMs): classical Bayesian optimization (BO), Trust-Region BO (TuRBO), Multi-TuRBO, and a proposed Memory-Guided TuRBO (MG-TuRBO) method. We compare performance on 2 real-world traffic simulation calibration problems with 14 and 84 decision variables, representing lower- and higher-dimensional (14D and 84D) settings. For BOMs, we study two acquisition strategies, Thompson sampling and a novel adaptive strategy. We evaluate performance using final calibration quality, convergence behavior, and consistency across runs. The results show that BOMs reach good calibration targets much faster than GA in the lower-D problem. MG-TuRBO performs comparably in our 14D setting, it demonstrates noticeable advantages in the 84D problem, particularly when paired with our adaptive strategy. Our results suggest that MG-TuRBO is especially useful for high-D traffic simulation calibration and potentially for high-D problems in general.

cs.LG↗

arXiv2026

A Fast Relax-and-Round Approach to Unit Commitment for Data Center Own Generation

The rapid growth of data centers increasingly requires data center operators to "bring own generation" to complement the available utility power plants to supply all or part of data center load. This practice sharply increases the number of generators on the bulk power system and shifts operational focus toward fuel costs rather than traditional startup and runtime constraints. Conventional mixed-integer unit commitment formulations are not well suited for systems with thousands of flexible, fast-cycling units. We propose a unit commitment formulation that relaxes binary commitment decisions by allowing generators to be fractionally on, enabling the use of algorithms for continuous solvers. We then use a rounding approach to get a feasible unit commitment. For a 276-unit system, solution time decreases from 10 hours to less than a second, with no accuracy degradation. Our approach scales with no issues to tens of thousands of generators, which allows solving problems on the scale of the major North America interconnections. The bulk of computation is parallel and GPU compatible, enabling further acceleration in future work.

math.OC↗

arXiv2024

Iterative Methods in GPU-Resident Linear Solvers for Nonlinear Constrained Optimization

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra methods are often inefficient. For example, methods for solving ill-conditioned linear systems have relied on conditional branching, which degrades performance on hardware accelerators such as graphical processing units (GPUs). To improve the efficiency of solving ill-conditioned systems, our computational strategy separates computations that are efficient on GPUs from those that need to run on traditional central processing units (CPUs). Our strategy maximizes the reuse of expensive CPU computations. Iterative methods, which thus far have not been broadly used for ill-conditioned linear systems, play an important role in our approach. In particular, we extend ideas from [1] to implement iterative refinement using inexact LU factors and flexible generalized minimal residual (FGMRES), with the aim of efficient performance on GPUs. We focus on solutions that are effective within broader application contexts, and discuss how early performance tests could be improved to be more predictive of the performance in a realistic environment

cs.CE↗

arXiv2021

A Hybrid Direct-Iterative Method for Solving KKT Linear Systems

We propose a solution strategy for linear systems arising in interior method optimization, which is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for solving these systems is the LDL^T factorization. However, LDL^T requires pivoting during factorization, which substantially increases communication cost and degrades performance on GPUs. Our novel approach solves a large indefinite system by solving multiple smaller positive definite systems, using an iterative solve for the Schur complement and an inner direct solve (via Cholesky factorization) within each iteration. Cholesky is stable without pivoting, thereby reducing communication and allowing reuse of the symbolic factorization. We demonstrate the practicality of our approach and show that on large systems it can efficiently utilize GPUs and outperform LDL^T factorization of the full system.

math.OC↗

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↗

arXiv2018

Application of underdamped Langevin dynamics simulations for the study of diffusion from a drug-eluting stent

We use a one-dimensional two layer model with a semi-permeable membrane to study the diffusion of a therapeutic drug delivered from a drug-eluting stent (DES). The rate of drug transfer from the stent coating to the arterial wall is calculated by using underdamped Langevin dynamics simulations. Our results reveal that the membrane has virtually no delay effect on the rate of delivery from the DES. The work demonstrates the great potential of underdamped Langevin dynamics simulations as an easy to implement, efficient, method for solving complicated diffusion problems in systems with a spatially-dependent diffusion coefficient.

cond-mat.stat-mech↗

arXiv2016

Isothermal Langevin dynamics in systems with power-law spatially-dependent friction

We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function (PDF) is calculated both analytically, by solving Fick's diffusion equation, and from numerical simulations of the underdamped Langevin equation. At large times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for $c<0$, and superdiffusion for $0 1$, the diffusion equation predicts that the particles accelerate. Here, we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially-dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit ($\left\langle x^2\right\rangle \sim t^2$). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin, and is correctly captured by Langevin's equation.

cond-mat.stat-mech↗