Exploring Optimization and Robust Control Techniques for use in Control Design of Nonlinear Dynamic Systems.
Abstract not provided.
Wilbanks, James↗
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Results for “Nonlinear optimization”
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Multi-objective Bayesian active learning for MeV-ultrafast electron diffraction
Ultrafast electron diffraction using MeV energy beams(MeV-UED) has enabled unprecedented scientific opportunities in the study of ultrafast structural dynamics in a variety of gas, liquid and solid state systems. Broad scientific applications usually pose different requirements for electron probe properties. Due to the complex, nonlinear and correlated nature of accelerator systems, electron beam property optimization is a time-taking process and often relies on extensive hand-tuning by experienced human operators. Algorithm based efficient online tuning strategies are highly desired. Here, we demonstrate multi-objective Bayesian active learning for speeding up online beam tuning at the SLAC MeV-UED facility. The multi-objective Bayesian optimization algorithm was used for efficiently searching the parameter space and mapping out the Pareto Fronts which give the trade-offs between key beam properties. Such scheme enables an unprecedented overview of the global behavior of the experimental system and takes a significantly smaller number of measurements compared with traditional methods such as a grid scan. This methodology can be applied in other experimental scenarios that require simultaneously optimizing multiple objectives by explorations in high dimensional, nonlinear and correlated systems.
43 PARTICLE ACCELERATORS↗
A Surrogate-Based Asynchronous Decomposition Technique for Realistic Security-Constrained Optimal Power Flow Problems
Here we present a decomposition approach for obtaining good feasible solutions for the security-constrained, alternating-current, optimal power flow (SC-AC-OPF) problem at an industrial scale and under real-world time and computational limits. The approach was designed while preparing and participating in ARPA-E’s Grid Optimization Competition (GOC) Challenge 1. The challenge focused on a near-real-time version of the SC-AC-OPF problem, where a base operating point is optimized, taking into account possible single-element contingencies, after which the system adapts its operating point following the response of automatic frequency droop controllers and voltage regulators. Our solution approach for this problem relies on state-of-the-art nonlinear programming algorithms, and it employs nonconvex relaxations for complementarity constraints, a specialized two-stage decomposition technique with sparse approximations of recourse terms and contingency ranking and prescreening. The paper describes and justifies our approach and outlines the features of its implementation, including functions and derivatives evaluation, warm-starting strategies, and asynchronous parallelism. We discuss the results of the independent benchmark of our approach by ARPA-E’s GOC team in Challenge 1, where it was found to consistently produce high-quality solutions across a wide range of network sizes and difficulty, and conclude by outlining future extensions of the approach.
97 MATHEMATICS AND COMPUTING↗
Spatiotemporal control of laser intensity using differentiable programming
Optical techniques for spatiotemporal control can produce laser pulses with custom amplitude, phase, or polarization structure. In nonlinear optics and plasma physics, the use of structured pulses typically follows a forward design approach, in which the efficacy of a known structure is analyzed for a particular application. Inverse approaches, in contrast, enable the discovery of new structures with the potential for superior performance. Here, an implementation of the unidirectional pulse propagation equation that supports automatic differentiation is combined with gradient-based optimization to design structured pulses with features that are advantageous for a range of nonlinear optical and plasma-based applications: (1) a longitudinally uniform intensity over an extended region, (2) a superluminal intensity peak that travels many Rayleigh ranges with constant duration, spot size, and amplitude, and (3) a laser pulse that ionizes a gas to form a uniform column of plasma. In the final case, optimizing the full spatiotemporal structure improves the performance by a factor of 15 compared to optimizing only spatial or only temporal structure, highlighting the advantage of spatiotemporal control.
automatic differentiation↗
Software Verification and Validation Guidelines for Non-Linear Soil-Structure Interaction Analysis
Seismic analysis of structures, systems, and components (SSCs), including the consideration of soil-structure interaction (SSI) effects, is an important and required step in the design and licensing of nuclear power plant SSCs important to safety. Historically, the SSI analysis of nuclear structures has been performed using equivalent linear methods. However, there has been considerable industry investment in alternative seismic design and analysis approaches to reduce the construction cost of new reactors. Toward that goal and in alignment with the Licensing Modernization Project (LMP) framework, the Nuclear Regulatory Commission (US NRC) has proposed a risk-informed, performance-based approach to seismic design that allows inelastic response in those nuclear plant structures not required for confinement. As a complementary effort, reactor designers are exploring nonlinear seismic analysis methods to optimize structural designs and reduce construction costs.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
PETSc/TAO Users Manual V.3.21
This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations (PDEs) and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for implementing large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication. PETSc/TAO includes a large suite of parallel linear solvers, nonlinear solvers, time integrators, and optimizers that may be used in application codes written in Fortran, C, C++, and Python (via petsc4py; see Getting Started ). The library is organized hierarchically, enabling users to employ the abstraction level most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users.
97 MATHEMATICS AND COMPUTING↗
Optimal Energy Scheduling and Sensitivity Analysis for Integrated Power-Water-Heat Systems
The conventionally independent power, water, and heating networks are becoming more tightly connected, which motivates their joint optimal energy scheduling to improve the overall efficiency of an integrated energy system. However, such a joint optimization is known as a challenging problem with complex network constraints and couplings of electric, hydraulic, and thermal models that are nonlinear and nonconvex. We formulate an optimal power-water-heat flow (OPWHF) problem and develop a computationally efficient heuristic to solve it. The proposed heuristic decomposes OPWHF into subproblems, which are iteratively solved via convex relaxation and convex-concave procedure. Simulation results validate that the proposed framework can improve operational flexibility and social welfare of the integrated system, wherein the water and heating networks respond as virtual energy storage to time-varying energy prices and solar photovoltaic generation. Moreover, we perform sensitivity analysis to compare two modes of heating network control: by flow rate and by temperature. Our results reveal that the latter is more effective for heating networks with a wider space of pipeline parameters.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Optimizing the optimizer for physics-informed neural networks and Kolmogorov-Arnold networks
Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network’s training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly nonlinear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self- Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers – using both PINNs and PIKANs – on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs. More broadly, our work reveal insights into the effectiveness of quasi-Newton optimization strategies in significantly improving the convergence and accurate generalization of PINNs and PIKANs.
97 MATHEMATICS AND COMPUTING↗
Economic NMPC for a Reversible Solid Oxide Cell
Reversible solid oxide fuel cells (rSOCs) offer the flexibility to operate in tandem with the electric grid by switching between fuel cell and electrolysis modes based on real-time electricity prices. However, their complex, tightly coupled dynamic behavior poses significant challenges in determining optimal operating strategies. In this work, we present an economic nonlinear model predictive control (E-NMPC) framework to optimize the operation of rSOCs. The proposed E-NMPC is applied to a detailed rSOC flowsheet model that includes a utility scale rSOC module as well as balance-of-plant equipment necessary for thermal management. Our results demonstrate that in fuel cell mode, the E-NMPC strategy reduces hydrogen consumption compared to conventional set-point tracking NMPC, while maintaining the same level of electricity output. Also, in electrolysis mode, the E-NMPC yields a marginal improvement in hydrogen production. In addition, we explore the integration of a battery with the rSOC system to enhance flexibility in meeting electricity production and consumption targets.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Tandem neural network-based controller for x-ray bimorph mirrors
Nanometer-scale shape control of x-ray mirrors is crucial for coherent x-ray beam experiments at low-emittance synchrotron beamline instruments. Piezoelectric bimorph mirrors offer adaptive control but are hindered by nonlinearities such as cross talk, creep, and hysteresis. To overcome these limitations, we present a novel feedback-free control solution, inspired by the proportional–integral–derivative (PID) scheme, driven by tandem neural networks (TNNs). Using task-specific datasets, the TNN-based system predicts actuator voltages with greater speed, accuracy, and stability than a single NN-based model. This approach is ideal for real-time applications, such as adapting beam focus to dynamic sample sizes while maintaining precise wavefront quality. Our findings highlight the potential of artificial intelligence in rapidly optimizing adaptive optics and managing nonlinear control systems.
Zhang, Runyu↗
Relaxations of the steady optimal gas flow problem for a non-Ideal gas
Natural gas ranks second in U.S. primary energy consumption. Because most production sites are remote, gas must be transported through pipeline networks equipped with compressors, valves, and other components. For both economic efficiency and system reliability, it is desirable to operate these networks optimally. The governing physics across pipeline components entails nonlinear, non-convex equality and inequality constraints, and the most general steady-flow operations problem is a Mixed-Integer Nonlinear Program (MINLP).This work focuses on one such steady-flow problem-the Optimal Gas Flow (OGF) for a natural gas pipeline network-which minimizes production cost subject to the steady-flow physics. For day-to-day operations, the ability to quickly compute a globally optimal solution and a strong lower bound for varying demand profiles is crucial. A promising strategy is to build tight relaxations of the OGF’s nonlinear constraints. However, many nonlinearities arising from non-ideal equations of state either lack relaxations or have relaxations that do not scale to realistic network sizes. We address this gap by combining recent advances in polyhedral relaxations for univariate functions to construct tight, computationally efficient relaxations of the OGF with a non-ideal equation of state. These relaxations solve within seconds on a standard laptop. In conclusion, we demonstrate their quality through extensive numerical experiments on very large-scale test networks from the literature and find that the proposed approach proves optimality in 92% of tested instances.
03 NATURAL GAS↗
A Flexible Quasi-Static Mooring Design Optimization Method for Floating Structures
This paper presents a flexible and efficient design method for optimizing the mooring systems of floating structures. Mooring system optimization is challenging because of the strong nonlinearity of mooring system behavior and the many technical constraints that must be satisfied. Furthermore, different mooring configurations can have very different design spaces. While some successful examples of mooring design optimization exist in the literature, developing an optimization approach that can work across various mooring design problems is a larger challenge. We present such a method based on a flexible parameterization that allows a wide variety of mooring designs to be described by a list of variables, a quasi-static mooring model that provides efficient evaluation of a mooring design without directly considering mooring system dynamics, and an optimization framework that generates, evaluates, and adjusts the mooring design while considering user-specified constraints such as offset limits, strength safety factors, and seabed contact limits. We demonstrate the design optimization framework on four mooring design problems, each for a different type of mooring system. We compare the use of different design modes to simplify the optimization problem, showing that they can reduce the computation time by up to 75%. We also compare different optimization algorithms and find that the resulting computational speed can vary by up to 51 times. We perform a sensitivity study on one design and find that the local sensitivity of anchoring radius to water depth has a positive correlation of 0.29, but the global sensitivity shows large nonlinearities. Lastly, we perform a coupled dynamic analysis on one of the optimized designs and find that the predicted mean platform motions and mooring line tensions are within 1% of dynamic results and the extreme motions and tensions are within 14%. Lastly, we show that a DEA-Chain-Polyester mooring configuration is cost-optimal for the given design problem of the demonstrations, which aligns with general industry practice.
16 TIDAL AND WAVE POWER↗
Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum
This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. As a result, we use the convex ι 1 and the nonconvex ι 1 – ι 2 functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.
97 MATHEMATICS AND COMPUTING↗
Uncertain characterization of reservoir fluids due to brittleness of equation of state regression
Equations of state (EoS) play a central role in modeling the phase equilibrium of fluid mixtures. Their parameterization involves fitting a model to experimental data, i.e., solving a nonlinear, non-convex, multivariate optimization problem. The latter requires one to select design variables, domains of definition for each variable, and weights assigned to individual measurements. We demonstrate that subjective choices of an optimization algorithm and an initial guess also impact the regression process. Consequently, EoS predictions are fundamentally uncertain even after the EoS tuning to a limited set of experimental data points. We demonstrate this observation for two hydrocarbon reservoir fluids, in which five properties of the heaviest carbon fraction are treated as design variables. While all the optimization algorithms and initial guesses match experimental data for the gas and liquid properties, the resulting EoS parameterizations lead to dramatically different predictions of the fluid’s thermophysical behavior in the unsampled pressure and temperature regions. In conclusion, we propose the probabilistic treatment of design variables to quantify the predictive uncertainty of the resulting fluid models.
15 GEOTHERMAL ENERGY↗
Genetic algorithm-based geometry calibration for dynamic compression x-ray diffraction experiments
An important component of dynamic compression x-ray diffraction (XRD) experiment analysis is geometry calibration: proper data interpretation requires knowledge of the precise detector position and orientation and, if the experiment involves a single-crystal sample, knowledge of the lattice orientation. The determination of these parameters in the arbitrary three-dimensional (3D) scattering geometries often present in dynamic compression facilities is challenging, as the associated optimization problem can be highly nonlinear, nonsmooth, and discontinuous. We present a genetic algorithm-based approach for performing dynamic compression XRD calibrations that overcomes these obstacles. We provide details regarding the image processing, algorithm implementation, and open-source software deployment and demonstrate the capability of the approach to calibrate the detector and crystal parameters in 3D geometries. Notably, we demonstrate the solver’s capacity to find the crystal orientation without a priori rotation constraints.
Brown, Nathan P. [Sandia National Laboratories (SN↗
Improving the performance of cryogenic calorimeters with nonlinear multivariate noise cancellation algorithms
Abstract State-of-the-art physics experiments require high-resolution, low-noise, and low-threshold detectors to achieve competitive scientific results. However, experimental environments invariably introduce sources of noise, such as electrical interference or microphonics. The sources of this environmental noise can often be monitored by adding specially designed “auxiliary devices” (e.g. microphones, accelerometers, seismometers, magnetometers, and antennae). A model can then be constructed to predict the detector noise based on the auxiliary device information, which can then be subtracted from the true detector signal. Here, we present a multivariate noise cancellation algorithm which can be used in a variety of settings to improve the performance of detectors using multiple auxiliary devices. To validate this approach, we apply it to simulated data to remove noise due to electromagnetic interference and microphonic vibrations. We then employ the algorithm to a cryogenic light detector in the laboratory and show an improvement in the detector performance. Finally, we motivate the use of nonlinear terms to better model vibrational contributions to the noise in thermal detectors. We show a further improvement in the performance of a particular channel of the CUORE detector when using the nonlinear algorithm in combination with optimal filtering techniques.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Per-Phase and 3-Phase Optimal Coordination of Directional Overcurrent Relays Using Genetic Algorithm
Penetration of the power grid by renewable energy sources, distributed storage, and distributed generators is becoming increasingly common. Increased utilization of these distributed energy resources (DERs) has given rise to additional protection coordination concerns, particularly where they are utilized in an unbalanced manner or where loading among phases is unbalanced. Digital relays such as the SEL-751 (produced by Schweitzer Engineering Laboratories, Pullman, WA, USA) series have the capability of being set on a per-phase basis. This capability is underutilized in common practice. Additionally, in optimization algorithms for determining relay settings, the time-overcurrent characteristics (TOCs) of relays are generally not treated as variables and are assigned before running the optimization algorithm. In this paper, TOC options themselves are treated as discrete variables to be considered in the optimization algorithm. A mixed integer nonlinear programming problem (MINLP) is set up where the goal is to minimize relay operating times. A genetic algorithm (GA) approach is implemented in MATLAB where two cases are considered. In the first case, the TOC and Time dial setting (TDS) of each relay is set on a three-phase basis. In the second case, per-phase settings are considered. Relay TDSs and TOCs are both considered as simultaneous discrete control variables. Despite the stochastic nature of using per-phase settings for unbalanced systems is found to generally allow for shorter operating times. However, for relatively balanced systems, it is best to use three-phase settings if computation time is of importance.
Matthews, Ronald C.↗
Prediction of Dielectric Constant in Series of Polymers by Quantitative Structure-Property Relationship (QSPR)
This work is devoted to the investigation of dielectric permittivity which is influenced by electronic, ionic, and dipolar polarization mechanisms, contributing to the material’s capacity to store electrical energy. In this study, an extended dataset of 86 polymers was analyzed, and two quantitative structure–property relationship (QSPR) models were developed to predict dielectric permittivity. From an initial set of 1273 descriptors, the most relevant ones were selected using a genetic algorithm, and machine learning models were built using the Gradient Boosting Regressor (GBR). In contrast to Multiple Linear Regression (MLR)- and Partial Least Squares (PLS)-based models, the gradient boosting models excel in handling nonlinear relationships and multicollinearity, iteratively optimizing decision trees to improve accuracy without overfitting. The developed GBR models showed high R2 coefficients of 0.938 and 0.822, for the training and test sets, respectively. An Accumulated Local Effect (ALE) technique was applied to assess the relationship between the selected descriptors—eight for the GB_A model and six for the GB_B model, and their impact on target property. ALE analysis revealed that descriptors such as TDB09m had a strong positive effect on permittivity, while MLOGP2 showed a negative effect. These results highlight the effectiveness of the GBR approach in predicting the dielectric properties of polymers, offering improved accuracy and interpretability.
Ascencio-Medina, Estefania↗