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At least 325 records · Page 18

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DOE OSTI2025

On optimal control of hybrid dynamical systems using complementarity constraints

Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas–liquid tank model and an optimal control problem with a sliding mode solution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Decomposition and Algorithmic Approaches for Solving Large-Scale Process Family Design Problems

Our most recent work expands the water desalination case study from 76 variants to 10,897 variants using the equation-oriented model built in Pyomo as part of the PARETO project. Using the discretization formulation presented in Stinchfield (2024a), rather than solving for all 10,897 variants simultaneously, we decompose the formulation into subproblems containing subsets of variants from the process family. We solve the overall problem with Progressive Hedging (PH) deployed in parallel on a distributed HPC cluster using the open-source Python package mpi-sppy (Knueven et al., 2023). This approach allowed us to solve this process family design problem to ~1.5% relative optimality gap in about 5 hours; in comparison, Gurobi reached ~50% relative optimality gap in about 6 hours (Stinchfield et al., 2024b). However, this approach still requires discretization of the common unit module design ranges; additionally, PH acts as a heuristic for MILP’s with gap-closing capabilities. Ideally, we would not have to use ML surrogates or discretization to solve this problem, instead solving the process family design problem with the equation-oriented model directly to achieve the most accurate results. However, recall that we did not consider solving the MINLP directly due to complexity and size. In this work, we aim to decompose and solve this large-scale MINLP using a Structured Nonlinear Global Optimization algorithm presented by Cao and Zavala (2019).

Stinchfield, Georgia↗

DOE OSTI2024

Bayesian optimization scheme for the design of a nanofibrous high power target

High Power Targetry (HPT) R&D is critical in the context of increasing beam intensity and energy for next generation accelerators. Many target concepts and novel materials are being developed and tested for their ability to withstand extreme beam environments; the HPT R&D Group at Fermilab is developing an electrospun nanofiber material for this purpose. The performance of these nanofiber targets is sensitive to their construction parameters, such as the packing density of the fibers. Lowering the density improves the survival of the target, but reduces the secondary particle yield. Optimizing the lifetime and production efficiency of the target poses an interesting design problem, and in this paper we study the applicability of Bayesian optimization to its solution. We first describe how to encode the nanofiber target design problem as the optimization of an objective function, and how to evaluate that function with computer simulations. We then explain the optimization loop setup. Thereafter, we present the optimal design parameters suggested by the algorithm, and close with discussions of limitations and future refinements.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Bayesian Optimization Scheme for the Design of a Nanofibrous High Power Target

High Power Targetry (HPT) R\&D is critical in the context of increasing beam intensity and energy for next generation accelerators. Many target concepts and novel materials are being developed and tested for their ability to withstand extreme beam environments; the HPT R\&D Group at Fermilab is developing an electrospun nanofiber material for this purpose. The performance of these nanofiber targets is sensitive to their construction parameters, such as the packing density of the fibers. Lowering the density improves the survival of the target, but reduces the secondary particle yield. Optimizing the lifetime and production efficiency of the target poses an interesting design problem, and in this paper we study the applicability of Bayesian optimization to its solution. We first describe how to encode the nanofiber target design problem as the optimization of an objective function, and how to evaluate that function with computer simulations. We then explain the optimization loop setup. Thereafter, we present the optimal design parameters suggested by the algorithm, and close with discussions of limitations and future refinements.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗

DOE OSTI2025

Efficient shallow Ritz method for 1D diffusion problems

This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or nearly optimal order of the shallow Ritz approximation, we develop a damped block Newton (dBN) method that alternates between updates of the linear and non-linear parameters. Per each iteration, the linear and the non-linear parameters are updated by exact inversion and one step of a modified, damped Newton method applied to a reduced non-linear system, respectively. The computational cost of each dBN iteration is $\mathcal{O}$(n). Starting with the non-linear parameters as a uniform partition of the interval, numerical experiments show that the dBN is capable of efficiently moving mesh points to nearly optimal locations. In conclusion, to improve the efficiency of the dBN further, we propose an adaptive damped block Newton (AdBN) method by combining the dBN with the adaptive neuron enhancement (ANE) method [28].

Diffusion problems↗

DOE OSTI2025

Robust Optimal Control of Inverter-Based Resources Under Grid-Forming Operation

In this paper, we propose and solve a robust control problem for inverter-based resources under grid-forming operation to regulate the voltage and frequency. One major challenge is to mitigate the effect of unmeasurable load current disturbance, grid and load parametric uncertainties. Moreover, strong coupling between the state variables on both the AC and DC sides, as well as between the modulating control input and the frequency impose additional challenges. To address these challenges, first, a robust control problem is solved at the high level via transformation into an equivalent, but more tractable, optimal control problem. Then, in the middle layer a voltage control law is designed on the one side, and a frequency control law on the other side. Finally, an inverter filter current controller is designed to complete the controller design. Theoretical results are derived to provide stability guarantees for the resulting closed-loop system. Specifically, we show that the inverter current injection error is dissipative, the frequency error is semi-globally asymptotically stable, and the inverter terminal voltage error is globally asymptotically stable, all with provided sufficient conditions. Here, numerical simulation experiments are used to validate the theoretical claims. Furthermore, the developed controller is compared with existing work in literature to show the efficacy of the proposed approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Core Design Optimization of the Westinghouse Lead Fast Reactor

Westinghouse is pursuing an advanced Nuclear Power Plant design based on Lead Fast Reactor (LFR) technology for global commercialization. To achieve an optimal combination of key attributes, such as safety, sustainability, and economic competitiveness, Westinghouse and ANL partnered in developing and applying a formalized core design optimization strategy. An LFR analysis workflow was developed to automate a suite of reactor physics, fuels performance, safety, and economics simulations on a selected LFR concept. The workflow streamlines analysis of a wide range of LFR designs with different dimensions and fuel types to assess their viability and economic performance, significantly reducing human processing time and risks of processing errors. The LFR optimization exercise was defined, resulting in selection of the design constraints (geometric, neutronics, thermo-mechanical, safety, thermal-hydraulics, and economics) and performance metrics researched (minimization of both the fuels LCOE and the first core inventory cost). A total of 14 varied design parameters were considered, including assembly dimensions, coolant temperature, and enrichment distribution throughout the core. The LFR analysis workflow was connected to DAKOTA for sensitivity and optimization analyses. Due to the extremely large size of the potential LFR optimization solution space relative to the computing time required to characterize one LFR solution, a multi-stage optimization approach was proposed to breakdown the problem into several stages with more reasonable sizes. This optimization approach enabled finding various viable core solutions with different cost tradeoffs that were considered by Westinghouse and justify selection of a smaller core with multi-batch 2-year cycle length.

Stauff, Nicolas E.↗

DOE OSTI2025

A tri-level distribution locational marginal price-based demand response framework

Here, in this paper, we propose a tri-level, nested, two-stage price-based demand response (PBDR) framework that considers distribution locational marginal price (DLMP) as DR enabler between load-serving entities (LSE), demand response providers (DRPs), and customers in the day-ahead distribution market. It enables LSE and customer interactions by using multiple DRPs, positioned in-between, and independently optimizes their objectives. The problem is formulated using linear power flow with approximated power losses and its application in DLMP as DR pricing. The tri-level problem is solved using a nested reformulation & decomposition (R&D) method and tested on the real Indian-108 bus distribution system under various dynamic pricings. Further, the temporal–spatial variations in DLMPs are assessed using fairness criteria. Numerical analyses demonstrate that DLMP applications can effectively improve economic efficiency, and transparency in DR programs valuation with a favorable fairness margin. The results show that DLMP as DR pricing signal induces (0-2) % variation in DLMP for DR participation up to 10 %. Further, it gives over 90 % fairness over temporal–spatial variation for all the customers.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Sensitivity-based voltage constraints for optimal power flow in low-voltage distribution feeders

The optimal power flow (OPF) problem for distribution systems can include network details down to the low-voltage (LV) points of interconnection of individual customers. This paper addresses the implementation of voltage magnitude constraints, and sets forth a practicable approach for capturing the effects on voltage from the switching behavior of loads (e.g., heat pumps, air conditioners, water heaters, or pool pumps) and from the variability of renewable generation (e.g., rooftop solar). The proposed method adjusts the OPF voltage constraints based on forecasts of load and generation upper and lower bounds, in conjunction with sensitivity factors derived from the power flow equations. An illustrative OPF formulation is also provided, which incorporates transformer models that include core loss. We demonstrate that accurate modeling of these LV network components is critical to avoid voltage violations at customer points of interconnection. Furthermore, the ideas are validated through numerical case studies on a realistic distribution feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Optimal Polynomial Smoothers and One‐Sided V‐Cycles for Poisson Problems

The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier‐Stokes equations needs robust preconditioning strategies. One such strategy is multigrid. To realize the potential of multigrid methods, effective smoothing strategies are needed. Chebyshev polynomial smoothers, in conjunction with pointwise Jacobi or additive Schwarz methods (ASMs), prove to be an effective smoother. Other polynomial smoothers, however, may provide superior convergence to the multigrid preconditioner. The authors compare the standard Chebyshev polynomial smoothers to both the novel fourth‐kind Chebyshev polynomial smoothers proposed by Lottes as well as smoothers based on the polynomial of best uniform approximation to as proposed by Kraus, Vassilevski, and Zikatanov. At the cost of symmetry, further improvements may be made. For example, a order polynomial smoother on both sides of the V‐cycle may be substituted with an order polynomial smoother on one side at no additional cost. The choice of omitting the postsmoother in favor of higher‐order polynomial presmoothing is advantageous in cases where the multigrid approximation property constant is large. The authors consider a 2D model problem based on finite differences to motivate the choice of polynomial smoother, order, and whether to apply postsmoothing for the target application of high‐order ‐geometric multigrid methods for GPU architectures. Results from both domains demonstrate the substantial improvement of these approaches over the standard Chebyshev polynomial smoother with a symmetric V‐cycle.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Massively parallel axisymmetric fluid model for streamer discharges

A highly parallelizable fluid plasma simulation tool based upon the first-order drift-diffusion equations is discussed. Atmospheric pressure plasmas have densities and gradients that require small element sizes in order to accurately simulate the plasm resulting in computational meshes on the order of millions to tens of millions of elements for realistic size plasma reactors. To enable simulations of this nature, parallel computing is required and must be optimized for the particular problem. Here, a finite-volume, electrostatic drift-diffusion implementation for low-temperature plasma is discussed. The implementation is built upon the Message Passing Interface (MPI) library in C++ using Object Oriented Programming. The underlying numerical method is outlined in detail and benchmarked against simple streamer formation from other streamer codes. Electron densities, electric field, and propagation speeds are compared with the reference case and show good agreement. Convergence studies are also performed showing a minimal space step of approximately 4 μm required to reduce relative error to below 1% during early streamer simulation times and even finer space steps are required for longer times. Additionally, strong and weak scaling of the implementation are studied and demonstrate the excellent performance behavior of the implementation up to 100 million elements on 1024 processors. Lastly, different advection schemes are compared for the simple streamer problem to analyze the influence of numerical diffusion on the resulting quantities of interest.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Xyce™ Parallel Electronic Simulator Users' Guide (V.7.9)

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: • Capability to solve extremely large circuit problems by supporting large-scale parallel computing platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. • A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. • Device models that are specifically tailored to meet Sandia’s needs, including some radiation-aware devices (for Sandia users only). • Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase — a message passing parallel implementation — which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows.

42 ENGINEERING↗

DOE OSTI2024

MatCal Users Guide: Release 1.3.0

Any continuum mechanics model will require three components: (1) a discretized geometry of the boundary value problem being studied, (2) the partial differential equations to be solved, and (3) the initial conditions and boundary conditions for the problem. To describe material behavior in these computational models, material models contribute to (2) the underlying equations and, occasionally, to (3) the initial conditions for the simulation. These material models can exhibit a mathematical form that is empirically based, based on first principles, or developed from both empirical observations and known physics. In general, these models are meant to represent a class of materials with well understood behavior. As a result, material models have parameters that must be tuned or calibrated so that the model response matches characterization data available for the specific material it is intended to represent when used to simulate a specific system. For simple models, such as isotropic, linear elastic materials in solid mechanics, this calibration process can be a simple analytical calculation directly extracting the parameters from experimental measurements. For complex models that have many inputs and require many characterization datasets to adequately identify the material behavior, the model calibration process can require an inverse problem approach where an optimization is performed to tune the model parameters to the available data.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Xyce™ Parallel Electronic Simulator Users’ Guide, Version 7.10

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

DistOPF: Advanced Solutions for Distribution Optimal Power Flow Analysis - DistOPF v0.2 Documentation

To achieve an affordable and reliable energy system, research on power distribution system is often focused on integration of distributed generators, energy storage solution, EV charging, smart meters, and other advanced assets that may benefit from or require more advanced control and optimization techniques. Despite this focus on advanced distribution system topics, early researchers and grid scientists often start from scratch when developing optimization programs for power distribution systems. This report introduces DistOPF, a Python package that consolidates years of research into a versatile and modular tool. DistOPF provides researchers with essential capabilities to solve distribution system Optimal Power Flow (OPF) problems using standard network models. Additionally, it offers a platform to benchmark both new and existing algorithms against established test systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Third-integer Resonant Extraction Regulation System for Mu2e

A third-integer resonant slow extraction system is being developed for Fermilab's Delivery Ring to deliver protons to the upcoming Mu2e experiment. The timescale of the extraction (or spill) duration is 43 milliseconds, which is extremely short and unprecedented. Additionally, the experiment's strict and challenging requirements on the quality of the spill at this time scale has led to the development of a new Spill Regulation System (SRS) design. The SRS primarily consists of three components - slow regulation, fast regulation, and harmonic content suppressor. Contributions to the first two components of the SRS, i.e., Slow Regulation and Fast Regulation subsystems, will be presented in which new adaptive learning algorithm schemes for the slow regulation of the spill -- validated using particle tracking simulations -- shall be described. In addition to these novel methods for the enhancement of the spill regulation system, results of employing Machine Learning in enhancing the performance of the resonant extraction are also presented. At the forefront of applying ML techniques to solve non-linear accelerator control problems, this work includes optimizing the PID gains as well as the replacement of the traditional PID controller using Recurrent Neural Networks and Gated Recurrent Unit (GRU) ML models to achieve efficiencies greater than a PID controller. Cutting-edge on-going Reinforcement Learning efforts, including an actor-critic family of learning algorithms, to regulate the spill rate will be reviewed, as well as present analytical calculations pertaining the transit time of particles in a third-integer resonant extraction. Detailed numerical investigations and validations of such calculations, the model of which could be exported and reliably used in future analytical modeling of any resonant extraction, are discussed.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits

In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits and proof-of-principle error-correction on a single logical qubit. Nevertheless, despite significant progress and excitement, the path toward a full-stack scalable technology is largely unknown. There are significant outstanding quantum hardware, fabrication, software architecture, and algorithmic challenges that are either unresolved or overlooked. These issues could seriously undermine the arrival of utility-scale quantum computers for the foreseeable future. Here, we provide a comprehensive review of these scaling challenges. We show how the road to scaling could be paved by adopting existing semiconductor technology to build much higher-quality qubits, employing system engineering approaches, and performing distributed quantum computation within heterogeneous high-performance computing infrastructures. These opportunities for research and development could unlock certain promising applications, in particular, efficient quantum simulation/learning of quantum data generated by natural or engineered quantum systems. To estimate the true cost of such promises, we provide a detailed resource and sensitivity analysis for classically hard quantum chemistry calculations on surface-code error-corrected quantum computers given current, target, and desired hardware specifications based on superconducting qubits, accounting for a realistic distribution of errors. Furthermore, we argue that, to tackle industry-scale classical optimization and machine learning problems in a cost-effective manner, heterogeneous quantum-probabilistic computing with custom-designed accelerators should be considered as a complementary path toward scalability.

Mohseni, Masoud↗