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Benchmark case for the inverse determination of adsorption parameters using lattice Boltzmann methods and gradient-based optimization

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CHEMICAL ENGINEERING SCIENCE 2025年 309卷

作者： Ito, Shota Grossmann, Simon Bukreev, Fedor Jessberger, Julius Krause, Mathias J. Karlsruhe Inst Technol Lattice Boltzmann Res Grp Karlsruhe Germany Karlsruhe Inst Technol Inst Mech Proc Engn & Mech Karlsruhe Germany Karlsruhe Inst Technol Inst Appl & Numer Math Karlsruhe Germany

This work proposes a parameter identification framework for determining adsorption model parameters from given concentration curves. Therein, an inverse problem involving a coupled system of partial differential equations is solved numerically by combining lattice Boltzmann methods and gradient-based optimization. The framework is validated for a constructed benchmark case where the concentration data for a batch reactor is obtained via the analytical solution or through simulations. Utilizing the benchmark case, we demonstrate the grid independence of the optimization problem when using simulation data and second order convergence of the identified parameters when the analytical solution is used as the input. From simulation data, the framework recovered the isotherm constant with an initial relative error from 67% to machine precision accuracy in 13 optimization steps. When artificial noise signals are imposed onto the input data with an intensity of SNR = 2, the final relative error regarding the parameters yields 2%.

关键词： Inverse problems Lattice Boltzmann method Computational fluid dynamics gradient-based optimization

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Efficient gradient-based Metasurface optimization toward the Limits of Wavelength-Polarization Multiplexing

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NANO LETTERS 2025年第15期25卷 6340-6347页

作者： Bao, Yanjun Shi, Hongsheng Wei, Rui Wang, Boyou Zhou, Zhou Chen, Yizhen Qiu, Cheng-Wei Li, Baojun Jinan Univ Inst Nanophoton Coll Phys & Optoelect Engn Guangdong Prov Key Lab Nanophoton Manipulat Guangzhou 511443 Peoples R China Natl Univ Singapore Dept Elect & Comp Engn Singapore 117583 Singapore Lanzhou Univ Technol Sch Sci Lanzhou 730050 Peoples R China

Polarization and wavelength multiplexing are the two widely employed techniques to improve capacity in metasurfaces. While previous studies have pushed the channel numbers of each technique to its individual limits, achieving simultaneous limits of both techniques still presents challenges. Furthermore, current multiplexing methods often suffer from computational inefficiencies, hindering their applicability in computationally intensive tasks. In this work, we introduce and experimentally validate a gradient-based optimization algorithm using deep neural network (DNN) to achieve the limits of polarization and wavelength multiplexing with high computational efficiency. By leveraging the computational efficiency of the DNN-based method, we further implement nine multiplexed channels (three wavelengths x three polarizations) for large-scale image recognition tasks with a total of 36 classes in the single-layer metasurface. The classification accuracy reaches 96% in simulations and 91.5% in experiments. Our work sets a new benchmark for high-capacity multiplexing with gradient-based inverse design for advanced optical elements.

关键词： metasurface gradient-based optimization polarization-wavelengthmultiplexing deep neural network

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Equivalent plate formulation of Double-Double laminates for the gradient-based design optimization of composite structures

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COMPOSITE STRUCTURES 2025年 354卷

作者： Zerbst, David Toenjes, Lennart Daehne, Sascha Werthen, Edgar Kappel, Erik Huehne, Christian Inst Lightweight Syst German Aerosp Ctr DLR Lilienthalpl 7 D-38108 Braunschweig Germany

The Double-Double concept of composite laminates suggests huge simplifications in aerospace structural design and manufacturing. This work presents a homogenized composite formulation introducing an analytical DD equivalent plate. Additionally, an optimization strategy is proposed using the DD parameterization as design variables to derive an optimized thickness and stiffness distribution on the basis of gradient-based numerical sensitivities. The method is applied to a simple wing box benchmark model for composite design applications. based on this model, the usage of gradients is verified for the newly implemented DD formulation with a global optimum and a robust convergence. Furthermore, the DD design is compared to a lamination parameter- based optimization of conventional Quad laminates. The DD optimized wing box shows small weight gains, due to the fact that one building block is distributed to an assembly of panels, whereas the Quad design provides individual optimality for each design region. At the same time, the proposed DD optimization process shows lower computational efforts, due to a lower amount of variables and constraints, while all laminate manufacturing constraints are implicitly fulfilled. Thus, the introduced DD formulation provides an efficient option to obtain a feasible structural design and therefore improve the maturity level for early aircraft design phases.

关键词： Composite design gradient-based optimization Double-Double laminates Lamination parameter

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gradient-based optimization of PCFM Radar Waveforms

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2021年第2期57卷 935-956页

作者： Mohr, Charles A. McCormick, Patrick M. Topliff, Charles A. Blunt, Shannon D. Baden, J. Michael Univ Kansas Radar Syst & Remote Sensing Lab Lawrence KS 66045 USA Air Force Res Lab Sensors Directorate Wright Patterson AFB OH 45433 USA Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30313 USA Georgia Tech Res Inst Sensors & Electromagnet Applicat Lab Smyrna GA 30080 USA

While a number of signal structures have been proposed for radar, frequency modulation (FM) remains the most common in practice because it is well-suited to high-power transmitters, which tend to introduce significant distortion to other waveform classes. That said, various forms of coding provide useful parameterizations for which a variety of optimization methods can be readily applied to accomplish different operational goals. To that end, the polyphase-coded FM (PCFM) implementation was previously devised as a means to bridge this gap between optimizable parameters and physically realizable waveforms. However, the original method employed to optimize PCFM waveforms involved a piecewise greedy search that, while relatively effective, was rather slow and cumbersome. Here, the continuous nature of this framework is leveraged to formulate a gradient-based optimization approach that updates all parameters simultaneously and can be efficiently performed using fast Fourier transforms, thus facilitating a general design methodology for practical waveforms that is directly extensible to myriad waveform-diverse arrangements. Results include a large number of optimization assessments to discern performance trends in aggregate and detailed analysis of specific cases, as well as both loopback and free-space experimental measurements to demonstrate practical efficacy.

关键词： Frequency modulation (FM) gradient-based optimization radar waveform design waveform diversity

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gradient-based optimization of micro-scale pressurized volumetric receiver geometry and flow rate

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RENEWABLE ENERGY 2023年第1期203卷 741-752页

作者： Akba, Tufan Baker, Derek Menguc, M. Pinar Ozyegin Univ Dept Mech Engn Istanbul Turkiye Ozyegin Univ Ctr Energy Environm & Econ CEEE Istanbul Turkiye Middle East Tech Univ Dept Mech Engn Ankara Turkiye Middle East Tech Univ Ctr Solar Energy Res & Applicat GUNAM Ankara Turkiye Turkish Aerosp Ind Inc Ankara Turkiye

This study focuses on the design optimization of a micro-scale pressurized volumetric receiver by changing geometry and flow rate constrained by the volume, outlet air temperature, and outer surface temperature. The pressurized volumetric receiver model is replicated from an existing model, which assumes constant air pressure and neglects the convection loss from the cavity. The existing model is revised from a solver to a design optimizer. The replicated model is restructured using OpenMDAO (Open-source MultiDisciplinary Analysis and optimization) framework, and analytical derivatives are implemented for efficient derivative calculation to increase optimization performance. The replicated model is verified, and the maximum outlet air temperature difference is less than 0.05%. optimization performance, selection of optimizers, the effect of the domain size, and radiative methods are discussed. The combined impact of the design variables is observed by selecting SLSQP (Sequential Least SQuares Programming) and trust-region optimizers. optimization performance is tested in different domain sizes and compared with a design of experiments analysis. For testing the impact of radiative heat transfer methods to design optimization, the Rosseland approximation, and P1 method are selected. Depending on the design domain, a solution methodology is suggested for future receiver design optimizations applicable for macro-scale pressurized volumetric receivers.

关键词： Concentrating solar thermal gradient-based optimization OpenMDAO Thermal radiation Volumetric receiver

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gradient-based bilevel optimization for multi-penalty Ridge regression through matrix differential calculus

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EUROPEAN JOURNAL OF CONTROL 2025年 81卷

作者： Maroni, Gabriele Cannelli, Loris Piga, Dario IDSIA Dalle Molle Inst Artificial Intelligence Res SUPSI Via Santa 1 CH-6900 Lugano Switzerland

Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the trade-off between minimizing the fitting error and the norm of the learned model coefficients. As this hyperparameter is scalar, it can be easily selected via random or grid search optimizing a cross-validation criterion. However, using a scalar hyperparameter limits the algorithm's flexibility and potential for better generalization. In this paper, we address the problem of linear regression with l(2)-regularization, where a different regularization hyperparameter is associated with each input variable. We optimize these hyperparameters using a gradient-based approach, wherein the gradient of a cross-validation criterion with respect to the regularization hyperparameters is computed analytically through matrix differential calculus. Additionally, we introduce two strategies tailored for sparse model learning problems aiming at reducing the risk of overfitting to the validation data. Numerical examples demonstrate that the proposed multi-hyperparameter regularization approach outperforms LASSO, Ridge, and Elastic Net regression in terms of R-2 score both in a static regression and in a system identification problem. Moreover, the analytical computation of the gradient proves to be more efficient in terms of computational time compared to automatic differentiation, especially when handling a large number of input variables, with an improvement of more than an order of magnitude. Application to the identification of over-parameterized Linear Parameter-Varying models is also presented.

关键词： Regularization Regularized least-squares Ridge regression gradient-based optimization Multi-hyperparameter optimization Bilevel optimization Multi-penalty Ridge regression

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A gradient-based optimization Method for the Design of Layered Phononic Band-Gap Materials

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Acta Mechanica Solida Sinica 2016年第4期29卷 429-443页

作者： Yu Huang Shutian Liu Jian Zhao State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering MechanicsDalian University of Technology

Phononic materials with specific band-gap characteristics at desired frequency ranges are in great demand for vibration and noise isolation, elastic wave filters, and acoustic devices. The attenuation coefficient curve depicts both the frequency range of band gap and the attenuation of elastic wave, where the frequency ranges corresponding to the none-zero attenuation coefficients are band gaps. Therefore, the band-gap characteristics can be achieved through maximizing the attenuation coefficient at the corresponding frequency or within the corresponding frequency range. Because the attenuation coefficient curve is not smooth in the frequency domain, the gradient-based optimization methods cannot be directly used in the design optimization of phononic band-gap materials to achieve the maximum attenuation within the desired frequency range. To overcome this difficulty, the objective of maximizing the attenuation coefficient is transformed into maximizing its Cosine, and in this way, the objective function is smoothed and becomes differentiable. based on this objective function, a novel gradient-based optimization approach is proposed to open the band gap at a prescribed frequency range and to further maximize the attenuation efficiency of the elastic wave at a specific frequency or within a prescribed frequency range. Numerical results demonstrate the effectiveness of the proposed gradient-based optimization method for enhancing the wave attenuation properties.

关键词： optimization band gap gradient-based optimization two-step optimization approach

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Online Trajectory Replanning for Avoiding Moving Obstacles Using Fusion Prediction and gradient-based optimization

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APPLIED SCIENCES-BASEL 2024年第18期14卷 8339页

作者： Fu, Qianyi Zhao, Wenjie Fang, Shiyu Zhu, Yiwen Li, Jun Chen, Qili Zhejiang Univ Sch Aeronaut & Astronaut Hangzhou 310014 Peoples R China Huanjiang Lab Ctr Unmanned Aerial Vehicles Zhuji 311800 Peoples R China Beijing Informat Sci & Technol Univ Sch Automat Beijing 100192 Peoples R China

In this study, we introduce a novel method for an online trajectory replanning approach for fixed-wing Unmanned Aerial Vehicles (UAVs). Our method integrates moving obstacle predictions within a gradient-based optimization framework. The trajectory is represented by uniformly discretized waypoints, which serve as the optimization variables within the cost function. This cost function incorporates multiple objectives, including obstacle avoidance, kinematic and dynamic feasibility, similarity to the reference trajectory, and trajectory smoothness. To enhance prediction accuracy, we combine physics-based and pattern-based methods for predicting obstacle movements. These predicted movements are then integrated into the online trajectory replanning framework, significantly enhancing the system's safety. Our approach provides a robust solution for navigating dynamic environments, ensuring both optimal and secure UAV operation.

关键词： trajectory replanning UAVs motion prediction gradient-based optimization

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ROBUST-CONTROL DESIGN VIA EIGENSTRUCTURE ASSIGNMENT, GENETIC ALGORITHMS AND gradient-based optimization

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IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS 1994年第3期141卷 202-208页

作者： PATTON, RJ LIU, GP Dept. of Electron. York Univ. UK

The paper presents a new approach for robust control design of multivariable systems via eigenstructure assignment, genetic algorithms and gradient-based optimisation. It takes the combination of the sensitivity and the complementary sensitivity functions of the closed-loop system as the robust control performance index. The gradient calculation of the performance index is described in detail for the closed-loop system with real and complex eigenvalues. The paper makes full use of the freedom provided by eigenstructure assignment to find a controller which stabilises the closed-loop system and minimises the performance index via the combination of genetic algorithms and gradient-based optimisation. The simulation results for the design of a lateral flight control system provide a tutorial demonstration of the power of the method.

关键词： ROBUST CONTROL DESIGN EIGENSTRUCTURE ASSIGNMENT GENETIC ALGORITHMS gradient-based optimization

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Geometrically exact beam theory for gradient-based optimization

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COMPUTERS & STRUCTURES 2024年 298卷

作者： McDonnell, Taylor Ning, Andrew Brigham Young Univ Dept Mech Engn Provo UT 84602 USA

Decades of research have progressed geometrically exact beam theory to the point where it is now an invaluable resource for analyzing and modeling highly flexible slender structures. Large-scale optimization using geometrically exact beam theory remains nontrivial, however, due to the inability of gradient -free optimizers to handle large numbers of design variables in a computationally efficient manner and the difficulties associated with obtaining smooth, accurate, and efficiently calculated design sensitivities for gradient -based optimization. To overcome these challenges, this paper presents a finite -element implementation of geometrically exact beam theory which has been developed specifically for gradient -based optimization. A key feature of this implementation of geometrically exact beam theory is its compatibility with forward and reverse -mode automatic differentiation. Another key feature is its support for both continuous and discrete adjoint sensitivity analysis. Other features are also presented which build upon previous implementations of geometrically exact beam theory, including a singularity -free rotation parameterization based on Wiener-Milenkovic parameters, an implementation of stiffness -proportional structural damping using a discretized form of the compatibility equations, and a reformulation of the equations of motion for geometrically exact beam theory as a semi -explicit system. Several examples are presented which verify the utility and validity of each of these features.

关键词： Geometrically exact beam theory gradient-based optimization Automatic differentiation Structural damping Continuous adjoint Discrete adjoint

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