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At least 1,153 records · Page 64

Derivative-free stochastic optimization via adaptive sampling strategies

In this paper, we present a novel derivative-free framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning to quantum computing involve settings where only stochastic function values are obtained via a zeroth-order oracle, which has no available gradient information and necessitates the usage of derivative-free optimization methodologies. Our approach includes estimating gradients using stochastic function evaluations and integrating adaptive sampling techniques to control the accuracy in these stochastic approximations. Our framework encapsulates several gradient estimation techniques, including standard finite-difference, Gaussian smoothing, sphere smoothing, randomized coordinate finite-difference, and randomized subspace finite-difference methods. We provide theoretical convergence guarantees for our framework and analyze the worst-case iteration and sample complexities associated with each gradient estimation method. Finally, we demonstrate the empirical performance of the methods on logistic regression and nonlinear least squares problems.

Adaptive sampling↗

Alpert multi-wavelets for functional inverse problems: direct optimization and deep learning

Computational engineering models often contain unknown entities (e.g. parameters, initial and boundary conditions) that require estimation from other measured observable data. Estimating such unknown entities is challenging when they involve spatio-temporal fields because such functional variables often require an infinite-dimensional representation. Here, we address this problem by transforming an unknown functional field using Alpert wavelet bases and truncating the resulting spectrum. Hence the problem reduces to the estimation of few coefficients that can be performed using common optimization methods. We apply this method on a one-dimensional heat transfer problem where we estimate the heat source field varying in both time and space. The observable data is comprised of temperature measured at several thermocouples in the domain. This latter is composed of either copper or stainless steel. The optimization using our method based on wavelets is able to estimate the heat source with an error between 5% and 7%. We analyze the effect of the domain material and number of thermocouples as well as the sensitivity to the initial guess of the heat source. Finally, we estimate the unknown heat source using a different approach based on deep learning techniques where we consider the input and output of a multi-layer perceptron in wavelet form. We find that this deep learning approach is more accurate than the optimization approach with errors below 4%.

97 MATHEMATICS AND COMPUTING↗

Multi-Fidelity Bayesian Optimization with Gaussian Processes for Double Shell Inertial Confinement Fusion Target Design

Reliable, secure access to energy is a major focus for national security efforts. One potential route to such energy is through fusion reactions in inertial confinement fusion (ICF) experiments. Such experiments are carried out at facilities such as the National Ignition Facility (NIF) in Livermore, California, where high powered lasers are used to compress a DT fuel-containing target to the necessary high temperature, high pressure conditions. These experiments are limited in number, which creates a heavy dependence on high fidelity predictive physics simulations and analysis performed “pre shot,” or before the experiment occurs. Many of these simulations in higher dimensions (2D and 3D) are computationally expensive, so finding optimal simulation-based designs presents its own challenges. In this work, we present our multi-fidelity Bayesian optimization with Gaussian processes (GPs) for ICF double shell targets, where a 1D surrogate model is used to help find a 2D surrogate model, enabling us to find optimal targets in the higher fidelity (2D), while saving computational cost.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Scenario optimization for the tokamak ramp-down phase in RAPTOR: Part B. safe termination of DEMO plasmas

An optimized plasma current ramp-down strategy is critical for safe and fast termination of plasma discharges in a tokamak demonstration fusion reactor (DEMO), both in planned and emergency scenarios, avoiding plasma disruptions and excessive heat loads to the first wall. Plasma stability limits and machine-specific technical requirements constrain the stable envelope through which the plasma must be navigated. Large amounts of auxiliary heating are required throughout the ramp-down phase, to avoid a radiative collapse in the presence of intrinsic tungsten and seeded xenon impurities, as quantitatively estimated in this work. As the plasma current is reduced, the current density becomes increasingly peaked, reflected by a growing value of the internal inductance $\ell$ $i3$ , resulting in reduced controllability of the vertical position of the plasma. The feasibility of different plasma current ramp-down rates is tested by applying an automated optimization framework embedding the RAPTOR core transport solver. Optimal time traces for plasma current $I$ $p$ $(t)$ and plasma elongation $κ(t)$ are proposed, to satisfy an $I$ $p$ -dependent upper limit on the plasma internal inductance, as obtained from vertical stability studies using the CREATE-NL code, as well as a constraint on the time evolution of $q$ 95 , to avoid an ideal MHD mode. A negative current density near the plasma edge is observed in our simulations, even for the most conservative $I$ $p$ ramp-down rate, indicating significant transient dynamics due to a large resistive time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fast physics-based launcher optimization for electron cyclotron current drive

With the increased urgency to design fusion pilot plants, fast optimization of electron cyclotron current drive (ECCD) launchers is paramount. Traditionally, this is done by coarsely sampling the 4D parameter space of possible launch conditions consisting of (1) the launch location (constrained to lie along the reactor vessel), (2) the launch frequency, (3) the toroidal launch angle, and (4) the poloidal launch angle. For each initial condition, a ray-tracing simulation is performed to evaluate the ECCD efficiency. Unfortunately, this approach often requires a large number of simulations (sometimes millions in extreme cases) to build up a dataset that adequately covers the plasma volume, which must then be repeated every time the design point changes. Here we adopt a different approach. Rather than launching rays from the plasma periphery and hoping for the best, we instead directly reconstruct the optimal ray for driving current at a given flux surface using a reduced physics model coupled with a commercial ray-tracing code. Repeating this throughout the plasma volume requires only hundreds of simulations, constituting a significant speedup. The new method is validated on two separate example tokamak profiles, and is shown to reliably drive localized current at the specified flux surface with the same optimal efficiency as obtained from the traditional approach.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Exploring the fusion power plant design space: comparative analysis of positive and negative triangularity tokamaks through optimization

The optimal configuration choice between positive triangularity (PT) and negative triangularity (NT) tokamaks for fusion power plants hinges on navigating different operational constraints rather than achieving specific plasma performance metrics. This study presents a systematic comparison using constrained multi-objective optimization with the integrated FUsion Synthesis Engine (FUSE) framework. Over 200 000 integrated design evaluations were performed exploring the trade-offs between capital cost minimization and operational reliability (maximizing q 95 ) while satisfying engineering constraints including 250 ± 50 MW net electric power, tritium breeding ratio > 1.1, power exhaust limits and an hour flattop time. Both configurations achieve similar cost-performance Pareto fronts through contrasting design philosophies. PT, while demonstrating resilience to pedestal degradation (compensating for up to 40% reduction), are constrained to larger machines (R 0 > 6.5 m) by the narrow operational window between L–H threshold requirements and the research-established power exhaust limit (P sol /R < 15 MW m –1 ). This forces optimization through comparatively reduced magnetic field (∼8 T). NT configurations exploit their freedom from these constraints to access compact, high-field designs (R 0 ~ 5.5 m, B 0 >12 T), creating natural synergy with advancing HTS technology. Sensitivity analyses reveal that PT’s economic viability depends critically on uncertainties in L–H threshold scaling and power handling limits. Notably, a 50% variation in either could eliminate viable designs or enable access to the compact design space. These results suggest configuration selection should be risk-informed: PT offers the lowest-cost path when operational constraints can be confidently predicted, while NT is robust to large variations in constraints and physics uncertainties.

FUSE framework↗

Wind Farm Layout Optimization with Loads Considerations

The objective of this paper is to improve the annual energy production of a wind farm by optimizing the layout of a wind farm, while considering fatigue loads on turbines. In this paper, the loads are estimated using the edgewise bending moment computed using CCBlade, a steady-state blade element momentum code. The edgewise bending moment is then used to calculate fatigue damage using Miner's rule. The fatigue damage is used to constrain the layout optimization problem. We show that our method can predict blade root damage with similar trends to damage calculated with other methods, such as a complex, computationally expensive large-eddy simulation and unsteady aeroelastic code. We also optimize wind farm layouts and show that, for a simple problem with two wind directions and ten turbines, the fatigue damage can be constrained without sacrificing wind farm power production.

17 WIND ENERGY↗

IEA Wind Task 32 and Task 37: Optimizing Wind Turbines with Lidar-Assisted Control Using Systems Engineering

Lidar-assisted control is a promising technology for reducing the levelized cost of energy from wind turbines, but quantifying its impact at the overall system level requires sophisticated systems engineering analysis and optimization frameworks. The joint workshop on Optimizing Wind Turbines with Lidar-Assisted Control Using Systems Engineering was held by the International Energy Agency Wind Task 32 (Lidar) and Task 37 (Systems Engineering) in October 2019 to address this challenge. This paper summarizes the outcome of the workshop and presents a road map for further research. The most promising applications of lidar-assisted control identified at the workshop and discussed here include 1) increasing annual energy production, 2) decreasing capital expenditure costs by reducing design loads, 3) extending turbine lifetime by reducing operating loads, and 4) enabling wind turbine class upgrades. For each application, we review the state of the art and highlight remaining research needs. Finally, we discuss strategies for addressing these research needs by conducting high-fidelity systems engineering optimizations.

17 WIND ENERGY↗

Serial-Refine Method for Fast Wake-Steering Yaw Optimization

In this paper we present the Serial-Refine method for quickly finding the optimal yaw angles in wake steering. The method optimizes turbine angles serially from upstream to downstream using a small number of candidate angles. The presented results show that Serial-Refine finds solutions that are at least as good as former conventional optimization approaches but that require much less computation time.

17 WIND ENERGY↗

Crystal generation using the fully differentiable pipeline and latent space optimization

We present a materials generation framework that couples a symmetry-conditioned variational autoencoder with a differentiable SO(3) power spectrum objective to steer candidates toward a specified local environment under the crystallographic constraints. In particular, we implement a fully differentiable pipeline that performs batch-wise optimization on both direct and latent crystallographic representations. Using the GPU acceleration, the implementation achieves about fivefold speed compared to our previous CPU workflow, while yielding comparable outcomes. In addition, we introduce the optimization strategy that alternatively performs optimization on the direct and latent crystal representations. This dual-level relaxation approach can effectively escape local minima defined by different objective gradients, thus increasing the success rate of generating complex structures satisfying the target local environments. This framework can be extended to systems consisting of multi-components and multi-environments, providing a scalable route to generate material structures with the target local environment.

conditional VAE↗

Finding diverse ways to improve algebraic connectivity through multi-start optimization

The algebraic connectivity, also known as the Fiedler value, is a spectral measure of network connectivity that can be increased through edge addition. We present an algorithm for producing many diverse ways to add a fixed number of edges to a network to achieve a near optimal Fiedler value. Previous Fielder value optimization algorithms (i.e. the greedy algorithm) output only one solution. Obtaining a single solution is rarely good enough for real-world network redesign problems, as practical constraints (political, physical or financial) may prevent implementation. Our algorithm takes a multi-start optimization approach, adding a random initial edge and then applies a greedy heuristic to improve the Fiedler value. The random choice moves us to a new region of the search space, enabling discovery of diverse solutions. Additionally, we present a Determinantal Point Process framework for quantifying diversity. We then apply a Markov chain Monte Carlo technique to sift through the large number of output solutions and locate a smaller, more manageable collection of highly diverse solutions that can be presented to network redesign engineers. We demonstrate the effectiveness of our algorithm on real-world graphs with varied structures.

97 MATHEMATICS AND COMPUTING↗

Codon Optimization Improves the Prediction of Xylose Metabolism from Gene Content in Budding Yeasts

Xylose is the second most abundant monomeric sugar in plant biomass. Consequently, xylose catabolism is an ecologically important trait for saprotrophic organisms, as well as a fundamentally important trait for industries that hope to convert plant mass to renewable fuels and other bioproducts using microbial metabolism. Although common across fungi, xylose catabolism is rare within Saccharomycotina, the subphylum that contains most industrially relevant fermentative yeast species. The genomes of several yeasts unable to consume xylose have been previously reported to contain the full set of genes in the XYL pathway, suggesting the absence of a gene–trait correlation for xylose metabolism. Here, we measured growth on xylose and systematically identified XYL pathway orthologs across the genomes of 332 budding yeast species. Although the XYL pathway coevolved with xylose metabolism, we found that pathway presence only predicted xylose catabolism about half of the time, demonstrating that a complete XYL pathway is necessary, but not sufficient, for xylose catabolism. We also found that XYL1 copy number was positively correlated, after phylogenetic correction, with xylose utilization. We then quantified codon usage bias of XYL genes and found that XYL3 codon optimization was significantly higher, after phylogenetic correction, in species able to consume xylose. Finally, we showed that codon optimization of XYL2 was positively correlated, after phylogenetic correction, with growth rates in xylose medium. We conclude that gene content alone is a weak predictor of xylose metabolism and that using codon optimization enhances the prediction of xylose metabolism from yeast genome sequence data.

59 BASIC BIOLOGICAL SCIENCES↗

SODAs: sparse optimization for the discovery of differential and algebraic equations

Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by time-scale separation, conservation laws and physical constraints. While sparse optimization has revolutionized model development by allowing data-driven discovery of parsimonious models from a library of possible equations, existing approaches for dynamical systems assume DAEs can be reduced to ODEs by eliminating variables before model discovery. This assumption limits the applicability of such methods for DAE systems with unknown constraints and time scales. We introduce sparse optimization for differential-algebraic systems (SODAs), a data-driven method for the identification of DAEs in their explicit form. By discovering the algebraic and dynamic components sequentially without prior identification of the algebraic variables, this approach leads to a sequence of convex optimization problems. It has the advantage of discovering interpretable models that preserve the structure of the underlying physical system. To this end, SODAs improves since SODAs is singular numerical stability when handling high correlations between library terms, caused by near-perfect algebraic relationships, by iteratively refining the conditioning of the candidate library. We demonstrate the performance of our method on biological, mechanical and electrical systems, showcasing its robustness to noise in both simulated time series and real-time experimental data.

DAE↗

Time-Varying Feedback Optimization for Quadratic Programs with Heterogeneous Gradient Step Sizes

Online feedback-based optimization has become a promising framework for real-time optimization and control of complex engineering systems. This tutorial paper surveys the recent advances in the field as well as provides novel convergence results for primal-dual online algorithms with heterogeneous step sizes for different elements of the gradient. The analysis is performed for quadratic programs and the approach is illustrated on applications for adaptive step-size and model-free online algorithms, in the context of optimal control of modern power systems.

gradient methods↗

Design and Optimization of High-frequency Transformer for Isolated Single-Stage Three-Phase AC/DC Converter using Bidirectional Switches

This paper presents the design and optimization of the high-frequency transformer for an isolated single-stage threephase AC/DC converter enabled by the 4H-SiC BiDirectional Field Effect Transistor (BiDFET). Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to perform a multiobjective optimization to minimize loss, weight, and volume. A 20 kW, 50 kHz hardware prototype based on the selected optimal point is characterized by a power amplifier. The finite element analysis simulation results are also presented to validate the core magnetic flux density and winding electric field strength. The experimental prototype was tested at 800 Vdc/480 Vrms at 10 kW rated power.

BiDFET, High-frequency transformer, Multiobjective↗

Joint Management and Optimization of Residential Natural Gas and Electricity Distribution Networks Coupled via Fuel Cells

The attractive features of natural gas as well as the growing electric power demand worldwide have created increasing interest in natural-gas-based distributed generation applications for electric distribution networks. Here, this paper investigates the interdependency between a residential natural gas network and an electric distribution network that are linked together via fuel cells. The modeling of the natural gas network is introduced first, and then the algorithm for gas flow study is presented. The optimal placement and sizing of fuel cell based distributed generation systems are formulated to minimize the losses in both the natural gas network and the electric distribution grid, subject to the constraints imposed by both networks. In addition, a probabilistic model for both gas and electricity demands is developed based on historical electricity and natural gas demand data. A K-means clustering method is used to determine the hourly load states to solve the joint probabilistic optimization problem. Simulation studies are carried out on an integrated system consisting of the IEEE 69-bus distribution network and a radial 27-node natural gas network to verify the developed optimization model and the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Design Optimization of Medium-Frequency Transformer for DAB Converters With DC Bias Capacity

Medium-frequency transformer (MFT) dc bias is critical for the safe operation of dual-active-bridge (DAB) converters. To analyze the dc bias, expressions of dc bias are derived for SiC MOSFET DAB converters. It shows that the dc bias is a current source in steady state; thus, a dc bias current capacity is defined and used as a design constraint in the optimization of MFT. The dc bias current capacity is related to core materials, geometric parameters, and flux density, which is analyzed with analytical expression. Optimization equations with geometric variables are derived, which can be solved theoretically or numerically for both interleaved winding (IW) and separated winding (SW) MFT without and/or with leakage inductance design. Based on the optimization equations, different MFT designs for a 150-kW SiC MOSFET DAB converter are compared on the aspects of core materials, winding structures, and without/with leakage inductance design. The combination of IW structure MFT with auxiliary phase shift inductors is chosen, and the assembled prototype is tested with the 150-kW DAB converter. Here, the designed dc bias capacity, temperature rise, and efficiency are verified.

42 ENGINEERING↗

Optimal Eco-Driving Control of Connected and Autonomous Vehicles Through Signalized Intersections

This article focuses on the speed planning problem for connected and automated vehicles (CAVs) communicating to traffic lights. The uncertainty of traffic signal timing for signalized intersections on the road is considered. The eco-driving problem is formulated as a data-driven chance-constrained robust optimization problem. Effective red-light duration (ERD) is defined as a random variable, and describes the feasible passing time through the signalized intersections. Usually, the true probability distribution for ERD is unknown. Consequently, a data-driven approach is adopted to formulate chance constraints based on empirical sample data. This incorporates robustness into the eco-driving control problem with respect to uncertain signal timing. Dynamic programming (DP) is employed to solve the optimization problem. The simulation results demonstrate that the proposed method can generate optimal speed reference trajectories with 40% less vehicle fuel consumption, while maintaining the arrival time at a similar level compared to a modified intelligent driver model (IDM). The proposed control approach significantly improves the controller's robustness in the face of uncertain signal timing, without requiring to know the distribution of the random variable a priori.

33 ADVANCED PROPULSION SYSTEMS↗