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Near-Optimal Performance of Stochastic Model Predictive Control

Here, this article presents a regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem can be cast as a finite-dimensional quadratic program, but the problem becomes quickly intractable as the problem size grows exponentially in the horizon length. SMPC aims to compute approximate solutions by solving a sequence of problems with truncated prediction horizons and committing the solution in a receding-horizon fashion. Although this approach is widely used in practice, its performance relative to the optimal solution is not well understood. This article reports for the first time a rigorous near-optimal performance guarantee of SMPC: under stabilizability and detectability conditions, the regret of SMPC is exponentially small in the prediction horizon length, allowing SMPC to achieve near-optimal performance at a substantially reduced computational expense.

93E20, 93B45

Exact block encoding of imaginary time evolution with universal quantum neural networks

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.

97 MATHEMATICS AND COMPUTING

An Introduction to the Federated Architecture for Secure and Transactive Distributed Energy Management Solutions (FAST-DERMS)

Deployment and capability of distributed energy resources (DER) in power systems is growing rapidly. These resources present an opportunity for low-cost provision of energy and grid services. The Federal Energy Regulatory Commission recently provided rulings to enable market participation of these distribution-connected resources, but the prevailing strategies for their management may not scale well to meet future needs. This paper introduces the Federated Architecture for Secure and Transactive Distributed Energy Management Solutions (FAST-DERMS) which was designed to address this need. In it we describe the architectural features of the approach, and a reference controls implementation employing a hierarchical coordination that includes stochastic optimization, model predictive control, and a simple real-time management scheme. Sample results from simulation show firm transmission-level service provision measured at the distribution substation.

grid architecture

Advanced Computing is at the Forefront of a New “Moonshot” Revolutionizing the North American Power Grid

In the 50+ years since the first humans landed on the moon, computing has grown at breakneck speed. We are faced with another challenge that is just as daunting, and just as important to overcome-modernizing the North American electric power grid-and high-performance computing (HPC) systems with specialized software will be an important element in rising to this challenge. We describe at a high level how software developed in the ExaSGD project addresses this "moonshot" goal by utilizing exascale computing and a novel high performance solver software stack to support the mission of decarbonizing power grid operations in an environment of uncertain weather and climate. To reach the exascale benchmark the team has made a number of first-of-their-kind innovations, including novel method for stochastic optimization, fine grained parallel methods for modeling power systems, and GPU resident sparse numerical linear solvers.

17 WIND ENERGY

MDLoader: A Hybrid Model-Driven Data Loader for Distributed Graph Neural Network Training

Scalable data management is essential for processing large scientific dataset on HPC platforms for distributed deep learning. In-memory distributed storage is preferred for its speed, enabling rapid, random, and frequent data access required by stochastic optimizers. Processes use one-sided or collective communication to fetch remote data, with optimal performance depending on (i) dataset characteristics, (ii) training scale, and (iii) interconnection network. Empirical analysis shows collective communication excels with larger mini-batch sizes and/or fewer processes, whereas one-sided communication outperforms at larger scales. We propose MDLoader, a hybrid in-memory data loader for distributed graph neural network training. MDLoader features a model-driven performance estimator that dynamically selects between one-sided and collective communication at the beginning of training using Tree of Parzen Estimators (TPE). Evaluations on NERSC Perlmutter and OLCF Summit show MDLoader outperforms single-backend loaders by up to 2.83 × and predicts the suitable communication method with 96.3% (Perlmutter) and 94.3% (Summit) success rate.

Bae, Jonghyun

Flexible Resource Scheduler for FAST-DERMS (FRS-FASTDERMS) v0.9

The Flexible Resource Scheduler is a hierarchical controller that manages the distributed energy resources in a distribution substation or distribution feeder to provide a firm commitment of power flow at the substation or feeder head to be scheduled in transmission-level markets as an aggregated demand resource. It is the reference controller for the FAST-DERMS Architecture, developed in tandem with the architecture under the DOE FAST-DERMS project. It is comprised of a day-ahead stochastic optimization, which schedules substation power flow and reserves, a intra-hour MPC, which generates dispatch base points for DER, and a real-time PID controller maintaining that dispatches DER to maintain the substation power around the base points. The repository also includes a representative aggregator controller, and all of the necessary components to run a simulation using PNNL's GridAPPS-D software with the controller.

MacDonald, Jason [Lawrence Berkeley National Labor

Hybrid Energy Resources Bidding Model (HERB) v1.0

The HERB Model provides a stochastic optimization framework for hybrid power plants (Storage plus Renewables) participating in day-ahead electricity markets. It considers uncertainty in market prices and renewable energy generation and generated risk-constrained price-quantity bid curves with limited, non-decreasing price steps.

Heleno, Miguel [Lawrence Berkeley National Laborat

An Introduction to the Federated Architecture for Secure and Transactive Distributed Energy Management Solutions (FAST-DERMS): Preprint

Deployment and capability of distributed energy resources (DER) in power systems is growing rapidly. These resources present an opportunity for low-cost provision of energy and grid services. The Federal Energy Regulatory Commission recently provided rulings to enable market participation of these distribution-connected resources, but the prevailing strategies for their management may not scale well to meet future needs. This paper introduces the Federated Architecture for Secure and Transactive Distributed Energy Management Solutions (FASTDERMS) which was designed to address this need. In it we describe the architectural features of the approach, and a reference controls implementation employing a hierarchical coordination that includes stochastic optimization, model predictive control, and a simple real-time management scheme. Sample results from simulation show firm transmission-level service provision measured at the distribution substation.

DERMS

A Distributionally Robust Optimization Framework for Stochastic Assessment of Power System Flexibility in Economic Dispatch

Given the complexity of power systems, particularly the high-dimensional variability of net loads, accurately depicting the entire operational range of net loads poses a challenge. To address this, recent methodologies have sought to gauge the maximum range of net load uncertainty across all buses. In this paper, we consider the stochastic nature of the net load and introduce a distributionally robust optimization framework that assesses system flexibility stochastically, accommodating a minimal extent of system violations. We verify the proposed method by solving the flexibility of the economic dispatch problem on four distinct IEEE standard test systems. Compared to traditional deterministic flexibility evaluations, our approach consistently yields less conservative flexibility outcomes.

distributionally robust optimization

SPAROW: Stochastic Programming and Related Optimization Workflows

SAND2026-16703O SPAROW: Stochastic Programming and Related Optimization Workflows is a Python library tool that facilitates the development and solution of stochastic programming problems. It provides a user-friendly class structure for defining stochastic programs through scenario-based representations of uncertainties. SPAROW incorporates multiple optimization strategies, including integer programming with all scenarios, progressive hedging, Benders decomposition, and Snoglode, a novel technique developed by Carnegie Mellon University. It also features interfaces to external solvers and functions that are commonly used in analysis workflows, making it applicable to a wide range of scientific and engineering design challenges, particularly in power grid planning. 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.

Hart, William [Sandia National Lab. (SNL-NM), Albu

Binary Quantum Control Optimization with Uncertain Hamiltonians

Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum controls under uncertainties. In this paper, we consider a stochastic discrete optimization formulation of a discretized binary optimal quantum control problem involving Hamiltonians with predictable uncertainties. We propose a sample-based reformulation that optimizes both risk-neutral and risk-averse measurements of control policies, and solve these with two gradient-based algorithms using sum-up-rounding approaches. Furthermore, we discuss the differentiability of the objective function and prove upper bounds of the gaps between the optimal solutions to binary control problems and their continuous relaxations. We conduct numerical simulations on various sized problem instances based on two applications of quantum pulse optimization; we evaluate different strategies to mitigate the impact of uncertainties in quantum systems. In conclusion, we demonstrate that the controls of our stochastic optimization model achieve significantly higher quality and robustness compared with the controls of a deterministic model.

conditional value-at-risk (CVaR)

Multistage economic MPC for systems with a cyclic steady state: A gas network case study

Multistage model predictive control (MPC) provides a robust control strategy for dynamic systems with uncertainties and a setpoint tracking objective. Moreover, extending MPC to minimize an economic cost instead of tracking a pre-calculated optimal setpoint improves controller performance. This paper presents a novel multistage economic nonlinear model predictive control (E-NMPC) framework for dynamic systems operating under uncertainty, with specific application to natural gas transmission networks. A key innovation lies in the integration of cyclic steady-state (CSS) constraints within the multistage MPC formulation, enabling the controller to manage periodic operating conditions commonly observed in energy systems. A Lyapunov-based descent condition is enforced to ensure robust stability of the controller. The multistage economic MPC framework is validated on two gas pipeline case studies, where it successfully minimizes net energy consumption, respects operational constraints under uncertain demand profiles, and guides the network to optimal cyclic operation. The Lyapunov function remains bounded in both case studies, validating the robust stability of multistage E-NMPC.

03 NATURAL GAS

Stochastic Trust-Region Algorithm in Random Subspaces with Convergence and Expected Complexity Analyses

Here, this work proposes a framework for large-scale stochastic derivative-free optimization (DFO) by introducing STARS, a trust-region method based on iterative minimization in random subspaces. This framework is both an algorithmic and theoretical extension of a random subspace derivative-free optimization (RSDFO) framework, and an algorithm for stochastic optimization with random models (STORM). Moreover, like RSDFO, STARS achieves scalability by minimizing interpolation models that approximate the objective in low-dimensional affine subspaces, thus significantly reducing per-iteration costs in terms of function evaluations and yielding strong performance on largescale stochastic DFO problems. The user-determined dimension of these subspaces, when the latter are defined, for example, by the columns of so-called Johnson-Lindenstrauss transforms, turns out to be independent of the dimension of the problem. For convergence purposes, inspired by the analyses of RSDFO and STORM, both a particular quality of the subspace and the accuracies of random function estimates and models are required to hold with sufficiently high, but fixed, probabilities. Using martingale theory under the latter assumptions, an almost sure global convergence of STARS to a first-order stationary point is shown, and the expected number of iterations required to reach a desired first-order accuracy is proved to be similar to that of STORM and other stochastic DFO algorithms, up to constants.

97 MATHEMATICS AND COMPUTING

Performant Optimization Strategies for Multifidelity Stochastic Power Grid Models

This talk goes into the algorithmic work done under the Forest project in order to solve expensive power grid models. We explore multiple fidelities of models that balance accuracy and computational expense. We use bundling strategies and progressive hedging in order to parallelize large stochastic programs.

Alfant, Rachael May [Sandia National Laboratories

A large-scale benchmarking of deterministic and stochastic derivative-free optimization algorithms

This presentation summarizes our work in the PrOMMiS project on benchmarking of data-driven optimization algorithms and their applications in self-driving laboratories. This work supports the broader project goal of accelerating the identification of promising separation methods and operating conditions for critical minerals separation processes. We present a systematic benchmarking study of 42 data-driven optimization algorithms on a broad collection of 502 test problems. The results identify BAM, GLCCLUSTER, and MULTIMIN as the most effective optimization solvers, with BAM showing the highest overall performance and solving more than 80% of the benchmark problems. The study also shows that no single solver consistently outperforms the others across all problem types, indicating that our future laboratory applications may benefit from using a small set of strong solvers rather than relying on a single method. The presentation also illustrates an in-silico chemical reactor case study showing that data-driven optimization methods can guide autonomous experimentation in a self-driving laboratory and identify optimal operating conditions within a small number of experiments. Overall, the results provide a basis for selecting efficient optimization methods and demonstrate the practical use of data-driven optimization in self-driving laboratory workflows.

36 MATERIALS SCIENCE

Assimilating partial observation to enhance feedback control of stochastic dynamical systems

Here, in this paper, we present a novel methodology to tackle feedback optimal control problems in scenarios where the exact state of the controlled process is unknown. It integrates data assimilation techniques and optimal control solvers to manage partial observation of the state process, a common occurrence in practical scenarios. Traditional stochastic optimal control methods assume full state observation, which is often not feasible in real-world fluid dynamics control problems. Our approach underscores the significance of utilizing observational data to inform control policy design. Specifically, we introduce a kernel learning backward stochastic differential equation (SDE) filter to enhance data assimilation efficiency and propose a sample-wise stochastic optimization method within the stochastic maximum principle framework. We demonstrate the efficacy and accuracy of our method in the control of advection-diffusion-reaction flow problem and the Dubins airplane maneuvering problem with model uncertainty.

data driven

A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.

97 MATHEMATICS AND COMPUTING