Inverse Design Problem Research Articles

Alignable Lamella Gridshells

Alignable lamella gridshells are 3D grid structures capable of collapsing into a planar strip. This feature significantly simplifies on-site assembly and also ensures compactness for efficient transport and storage. However, designing these structures still remains a challenge. This paper tackles the inverse design problem of alignable lamella gridshells leveraging concepts from differential geometry and Cartan's theory of moving frames. The study unveils that geodesic alignable gridshells, where lamellae are disposed tangentially to the surface, are limited to forming shapes isometric to surfaces of revolution. Furthermore, it demonstrates that alignable gridshells with lamellae arranged orthogonally to a surface can be realized only on a specific class of surfaces that meet a particular curvature condition along their principal curvature lines. Finally, drawing on these theoretical findings, this work introduces novel computational tools tailored for the design of these structures.

Inverse Garment and Pattern Modeling with a Differentiable Simulator

AbstractThe capability to generate simulation‐ready garment models from 3D shapes of clothed people will significantly enhance the interpretability of captured geometry of real garments, as well as their faithful reproduction in the digital world. This will have notable impact on fields like shape capture in social VR, and virtual try‐on in the fashion industry. To align with the garment modeling process standardized by the fashion industry and cloth simulation software, it is required to recover 2D patterns, which are then placed around the wearer's body model and seamed prior to the draping simulation. This involves an inverse garment design problem, which is the focus of our work here: Starting with an arbitrary target garment geometry, our system estimates its animatable replica along with its corresponding 2D pattern. Built upon a differentiable cloth simulator, it runs an optimization process that is directed towards minimizing the deviation of the simulated garment shape from the target geometry, while maintaining desirable properties such as left‐to‐right symmetry. Experimental results on various real‐world and synthetic data show that our method outperforms state‐of‐the‐art methods in producing both high‐quality garment models and accurate 2D patterns.

Airfoil Shape Generation and Feature Extraction Using the Conditional VAE-WGAN-gp

A machine learning method was applied to solve an inverse airfoil design problem. A conditional VAE-WGAN-gp model, which couples the conditional variational autoencoder (VAE) and Wasserstein generative adversarial network with gradient penalty (WGAN-gp), is proposed for an airfoil generation method, and then, it is compared with the WGAN-gp and VAE models. The VAEGAN model couples the VAE and GAN models, which enables feature extraction in the GAN models. In airfoil generation tasks, to generate airfoil shapes that satisfy lift coefficient requirements, it is known that VAE outperforms WGAN-gp with respect to the accuracy of the reproduction of the lift coefficient, whereas GAN outperforms VAE with respect to the smoothness and variations of generated shapes. In this study, VAE-WGAN-gp demonstrated a good performance in all three aspects. Latent distribution was also studied to compare the feature extraction ability of the proposed method.

Designing spongy-bone-like cellular materials: Matched topology and anisotropy

Bone is a natural material with properties such as high specific stiffness and strength. These exceptional mechanical properties are attributed to the meso-scale structure and elastic anisotropy of spongy bone. Replicating the topological traits and mechanical properties of spongy bone presents a novel opportunity to develop high-performance cellular materials. To achieve this, we propose an innovative framework for designing biomimetic cellular materials that match the trabecular structure and elastic anisotropy of spongy bone. This framework introduces a forward-flow design process that utilizes gradient-based feature tuning on a low-dimensional feature vector, transforming the complex inverse design problem into an efficient iterative process. A key innovation in our approach is the use of a pre-trained generative model, SliceGAN, to reconstruct 3D unit cells from 2D micro-CT images. This significantly reduces the cost and time associated with traditional layer-by-layer CT scans typically required for 3D training data. Numerical homogenization is then used to determine the effective elastic stiffness matrix, and a Fourier neural operator is trained to predict these matrices efficiently, greatly enhancing the computational efficiency of the design process. Using this framework, we successfully designed unit cells with topological traits and elastic anisotropy that closely approximate those of natural spongy bone. This opens new avenues for developing spongy-bone-mimetic cellular materials with exceptional mechanical properties. Moreover, the framework's versatility allows it to be extended to the design of other bio-inspired cellular materials.

Data-driven bio-mimetic composite design: Direct prediction of stress–strain curves from structures using cGANs

Designing high-performance composites requires integrating tasks, including material selection, structural arrangement, and mechanical property characterization. Accurate prediction of composite mechanical properties requires a comprehensive understanding of their mechanical response, particularly the failure mechanisms under high deformations. As traditional computational methods struggle to exhaustively explore every composite configuration in the vast design space for optimal design search, machine learning offers rapid identification of optimal composite designs. This study presents a cGAN-based deep learning model for predicting stress–strain curves directly from composite structures using an image-to-vector approach. The model incorporates fully connected layers within a U-Net generator for stress–strain curve generation and utilizes a PatchGAN discriminator for realism assessment. This end-to-end mapping from structures to mechanical response effectively eliminates the need for extensive simulations and labor-intensive post-analyses. Phase-field simulations were conducted to model the material failure process, generating stress–strain curves for various composite structures used as ground truth data to train and test the surrogate model. This study incorporates various composite structures in the dataset, including random (RS), layered (LS), chessboard-like (CS), soft-scaffold (SS), and hard-scaffold (HS), enhancing the representation of design diversity. Despite being trained on a limited dataset (approximately 1.5% for each bio-mimetic structure and 10−72% for RS composites), the model achieves highly accurate predictions in stress–strain curves, with MAE loss converging to 0.01 for training and 0.05 for testing after 2 million iterations. High evaluation scores on training data (R2>0.997, MAPE <1.08%) and testing data (R2>0.946, MAPE <5.53%) demonstrate the model’s accuracy in predicting mechanical properties such as Young’s modulus, strength, and toughness across all composite structures. Overall, the study provides a proof of concept for using machine learning to simplify the design process, demonstrating its potential for solving inverse composite design problems.

Nanophotonic structure inverse design for switching application using deep learning

Switching functionality is pivotal in advancing communication systems, serving as a paramount mechanism. Despite numerous innovations in this field, optical switch design, fabrication, and characterization have traditionally followed an iterative approach. Within this paradigm, the designer formulates an informed conjecture regarding the switch's structural configuration and subsequently resolves Maxwell's equations to ascertain its performance. Conversely, the inverse problem, which entails deriving a switch geometry to achieve a targeted electromagnetic response, continues to pose formidable challenges and necessitates substantial time and effort, particularly under the constraints of specific assumptions. In this work, we propose a deep neural network-based method to approximate the spectral transmittance of all-optical switches. The findings substantiate the efficacy of deep learning in the design of all-optical plasmonic switches, which are renowned as the fastest switches at the nanoscale. The nonlinear Kerr effect in square resonators is leveraged to demonstrate the switching performance. Juxtaposed with conventional simulations, the proposed model showcases a remarkable improvement in computational efficiency. Furthermore, deep learning can resolve nanophotonic inverse design problems without reliance on trial-and-error or empirical strategies. Compared to simulations, the mean squared error for both forward and inverse models is meager, with values of around 0.03 and 0.02, respectively. The deep learning-proposed switches exhibit excellent suitability for integration into photonic integrated circuits, substantially influencing the progression of all-optical signal processing.

Chirped apodized fiber Bragg gratings inverse design via deep learning

Overcoming inverse design problems in fiber Bragg gratings (FBGs) can be challenging due to the significant nonlinearity of the problem and the intricate relationship between structural properties and optical characteristics. Here, we present a novel artificial intelligence-based approach that effectively addresses these challenges. We introduce a methodology centered on applying deep learning (DL) to estimate the reflective spectrum of FBGs. The results highlight DL’s exceptional capability in designing chirped apodized FBGs, with our model demonstrating significantly enhanced computational efficiency relative to traditional numerical simulations. Notably, our DL-based approach exhibits the remarkable ability to tackle the inverse design challenges of FBGs, thereby eliminating the reliance on trial-and-error or empirical methodologies. The predictive losses for both the forward and inverse models are impressively minimal, with low loss values of 2.2 × 10-2 and 1.6 × 10-2, respectively. The FBG configurations derived via DL are ideally suited for optical communications, heralding significant advancements in all-optical signal processing.

Efficient inverse design optimization through multi-fidelity simulations, machine learning, and boundary refinement strategies

This paper introduces a methodology designed to augment the inverse design optimization process in scenarios constrained by limited compute, through the strategic synergy of multi-fidelity evaluations, machine learning models, and optimization algorithms. The proposed methodology is analyzed on two distinct engineering inverse design problems: airfoil inverse design and the scalar field reconstruction problem. It leverages a machine learning model trained with low-fidelity simulation data, in each optimization cycle, thereby proficiently predicting a target variable and discerning whether a high-fidelity simulation is necessitated, which notably conserves computational resources. Additionally, the machine learning model is strategically deployed prior to optimization to compress the design space boundaries, thereby further accelerating convergence toward the optimal solution. The methodology has been employed to enhance two optimization algorithms, namely Differential Evolution and Particle Swarm Optimization. Comparative analyses illustrate performance improvements across both algorithms. Notably, this method is adaptable across any inverse design application, facilitating a synergy between a representative low-fidelity ML model, and high-fidelity simulation, and can be seamlessly applied across any variety of population-based optimization algorithms.

A surrogate-assisted extended generative adversarial network for parameter optimization in free-form metasurface design

Metasurfaces have widespread applications in fifth-generation (5G) microwave communication. Among the metasurface family, free-form metasurfaces excel in achieving intricate spectral responses compared to regular-shape counterparts. However, conventional numerical methods for free-form metasurfaces are time-consuming and demand specialized expertise. Alternatively, recent studies demonstrate that deep learning has great potential to accelerate and refine metasurface designs. Here, we present XGAN, an extended generative adversarial network (GAN) with a surrogate for high-quality free-form metasurface designs. The proposed surrogate provides a physical constraint to XGAN so that XGAN can accurately generate metasurfaces monolithically from input spectral responses. In comparative experiments involving 20000 free-form metasurface designs, XGAN achieves 0.9734 average accuracy and is 500 times faster than the conventional methodology. This method facilitates the metasurface library building for specific spectral responses and can be extended to various inverse design problems, including optical metamaterials, nanophotonic devices, and drug discovery.

Pattern search algorithm-aided structural color Sb2S3-based dynamic hybrid all-dielectric metasurface

The versatility and dynamic tunability of reconfigurable photonic devices hold paramount significance in optics. Nevertheless, most such dynamically adjustable all-dielectric metasurfaces, particularly those utilized in structural color applications, are usually resonators made exclusively of phase-change materials. The elevated absorption coefficients exhibited by phase-change materials in the short-wavelength band (particularly within the blue light range) often culminate in suboptimal performance for generating colors. To address this challenge, we designed a hybrid all-dielectric metasurface that achieved reflectivities of 60%, 75%, and 96% across blue, green, and red-light bands, respectively and achieved dynamic tunability of the metasurface by generating chromatic aberrations of 19.626, 3.341, and 17.354 via the reversible phase transition of Sb2S3. The device exhibits good angular robustness, maintaining nearly constant color within a viewing angle range of ±20°. Meanwhile, we employ a pattern search algorithm to accelerate the inverse design process of metasurfaces. The algorithm can reduce the design time by a factor of at least two orders of magnitude relative to the genetic algorithm, substantially improving design efficiency. The algorithm applies to high degree-of-freedom inverse design problems for intricate physical systems with similar design relationships. It offers a promising avenue for rapid and dependable optical device design.

A random walk based methodology to calculate the sensitivity coefficients in inverse radiant boundary design problems

Radiative heating furnaces are widely used for heat treatment applications in manufacturing industries. Strict requirements on heat treatment characteristics of the workpieces require precise control of furnace heater temperatures. Numerical techniques for the solution of inverse heat transfer problems can be used for the optimization of the radiant heater temperatures. In gradient-based optimization techniques, the optimization is carried out using the sensitivity coefficients between the heater and workpiece temperatures. In this study, we present a methodology for calculating the sensitivity coefficients for the solution of inverse boundary design problems involving transient heating of solid workpieces in a three-dimensional radiant furnace. In our methodology, the sensitivity coefficients on the selected design points within the workpieces are calculated by analytical differentiation of design point temperature formulations derived utilizing the floating random walk method and radiative heat flux formulation with exchange factors. The methodology for calculating sensitivity coefficients has been verified through applications to both a one-dimensional scenario and the three-dimensional radiant furnace model. The developed methodology was integrated into a gradient-based optimization algorithm in two test cases, to determine the furnace heater temperatures required to achieve the desired temperature histories at design points within the workpieces. First test case focuses reconstruction of an assumed heater temperature and examines the impact of design point configuration and input data noise on convergence behavior and calculated estimation. The findings reveal that increasing the number of design points in the workpieces increases solution accuracy, with transverse positioning of the design points in the workpieces resulting in heater temperatures closest to the assumed values. Second test case focused on estimating required heater temperatures for spatially uniform heating pattern on the workpieces. With 72 transversely positioned design points, we achieved uniform heating at these points with a maximum relative temperature deviation of 0.26%.

Dynamic Inverse Design of Broadband Metasurfaces with Synthetical Neural Networks

AbstractFor over 35 years of research, the debate about the systematic compositionality of neural networks remains unchanged, arguing that existing artificial neural networks are inadequate cognitive models. Recent advancements in deep learning have significantly shaped the landscape of popular domains, however, the systematic combination of previously trained neural networks remains an open challenge. This study presents how to dynamically synthesize a neural network for the design of broadband electromagnetic metasurfaces. The underlying mechanism relies on an assembly network to adaptively integrate pre‐trained inherited networks in a transparent manner that corresponds to the metasurface assembly in physical space. This framework is poised to curtail data requirements and augment network flexibility, promising heightened practical utility in complex composition‐based tasks. Importantly, the intricate coupling effects between different metasurface segments are accurately captured. The approach for two broadband metasurface inverse design problems is exemplified, reaching accuracies of 96.7% and 95.5%. Along the way, the importance of suitably formatting the spectral data is highlighted to capture sharp spectral features. This study marks a significant leap forward in inheriting pre‐existing knowledge in neural‐network‐based inverse design, improving its adaptability for applications involving dynamically evolving tasks.

Data-Driven Nonintrusive Model-Order Reduction for Aerodynamic Design Optimization

Fast and accurate evaluation of aerodynamic characteristics is essential for aerodynamic design optimization because aircraft programs require many years of design and optimization. Therefore, it is imperative to develop sufficiently fast, robust, and accurate computational tools for industry routine analysis. This paper presents a nonintrusive machine-learning method for building reduced-order models (ROMs) using an autoencoder neural network architecture. An optimization framework was developed to identify the optimal solution by exploring the low-dimensional subspace generated by the trained autoencoder. To demonstrate the convergence, stability, and reliability of the ROM, a subsonic inverse design problem and a transonic drag minimization problem of the airfoil were studied and validated using two different parameterization strategies. The robustness and accuracy demonstrated by the method suggest that it is valuable in parametric studies, such as aerodynamic design and optimization, and requires only a small fraction of the cost of full-order modeling.

A graph neural network approach to the inverse design for thermal transparency with periodic interparticle system

Abstract Recent years have witnessed significant advancements in utilizing machine learningbased techniques for thermal metamaterial-based structures and devices to attain favorable thermal transport behavior. Among the various thermal transport behaviors, achieving thermal transparency stands out as particularly desirable and intriguing. Our earlier work demonstrated the use of a thermal metamaterial-based periodic interparticle system as the underlying structure for manipulating thermal transport behavior and achieving thermal transparency. In this paper, we introduce an approach based on graph neural network to address the complex inverse design problem of determining the design parameters for a thermal metamaterial-based periodic interparticle system with the desired thermal transport behavior. Our work demonstrates that combining graph neural network modeling and inference is an effective approach for solving inverse design problems associated with attaining desirable thermal transport behaviors using thermal metamaterials.

Inverse design of two-function transmission-type reconfigurable polarization control metasurfaces based on deep learning

Compared with single-function metasurfaces, the design difficulty of multi-function metasurfaces increases significantly. This paper introduces an inverse design method based on deep learning to address this challenge. By this method, a transmission-type reconfigurable polarization control metasurface (TRPCM) with two functions is rapidly designed. The network model used in the method consists of an electromagnetic parameter reconstruction network model and an inverse prediction network model. The combination of the two models can solve the problem of difficulty in defining high-dimensional inputs in traditional inverse design, and achieve accurate prediction of metasurface structure parameters under given design targets. To optimize the hyperparameters of the neural network model, a genetic algorithm was introduced. To solve the non-uniqueness problem of inverse design, a method for eliminating similar data by calculating Euclidean Distance was introduced. Both schemes further improve the predictive performance of the proposed network model. Finally, six design targets were set based on the TRPCM. The structural parameters of the metasurface were successfully predicted using two neural network models and achieved the required performance. On this basis, a set of parameters was selected for experimental validation. By controlling the ON or OFF of the PIN diodes, the fabricated metasurface achieves two functions: linear-to-circular polarization conversion and linear polarization maintenance in the range of 2–3.6 GHz. Study results show that the inverse design scheme proposed in the paper is feasible and practical for solving the rapid optimization design of complex multi-function metasurfaces.

Metamaterial-based realization for thermal transparency: A conditional variational autoencoder approach

The advances in thermal metamaterials and their applications have revolutionized how we can manipulate thermal transport behavior. The challenging inverse design problems of utilizing thermal metamaterial-based structures to achieve desired thermal transport behavior are increasingly being tackled by data-driven, machine learning-based approaches. The explosive progress in generative AI is permeating the field of material design by offering new perspectives to address the inverse design problems. In this paper, we propose a simple yet effective method of training a generative conditional variational autoencoder to find the design parameters for a thermal metamaterial-based system with a periodic interparticle arrangement to achieve thermal transparency, which is one of the most desirable and interesting thermal transport behaviors. Our work attests to the predictive power of a generative model with a relatively small number of parameters for the purpose of tackling inverse design problems to achieve thermal transport behavior manipulation.

Microstructure-Sensitive Deformation Modeling and Materials Design with Physics-Informed Neural Networks

Microstructure-sensitive materials design has become popular among materials engineering researchers in the last decade because it allows the control of material performance through the design of microstructures. In this study, the microstructure is defined by an orientation distribution function. A physics-informed machine learning approach is integrated into microstructure design to improve the accuracy, computational efficiency, and explainability of microstructure-sensitive design. When data generation is costly and numerical models need to follow certain physical laws, machine learning models that are domain-aware perform more efficiently than conventional machine learning models. Therefore, a new paradigm called the physics-informed neural network (PINN) is introduced in the literature. This study applies the PINN to microstructure-sensitive modeling and inverse design to explore the material behavior under deformation processing. In particular, we demonstrate the application of PINN to small-data problems driven by a crystal plasticity model that needs to satisfy the physics-based design constraints of the microstructural orientation space. For the first problem, we predict the microstructural texture evolution of copper during a tensile deformation process as a function of initial texturing and strain rate. The second problem aims to calibrate the crystal plasticity parameters of the Ti-7Al alloy by solving an inverse design problem to match the PINN-predicted final texture prediction and the experimental data.

Efficient Mapping Between Void Shapes and Stress Fields Using Deep Convolutional Neural Networks With Sparse Data

Abstract Establishing fast and accurate structure-to-property relationships is an important component in the design and discovery of advanced materials. Physics-based simulation models like the finite element method (FEM) are often used to predict deformation, stress, and strain fields as a function of material microstructure in material and structural systems. Such models may be computationally expensive and time intensive if the underlying physics of the system is complex. This limits their application to solve inverse design problems and identify structures that maximize performance. In such scenarios, surrogate models are employed to make the forward mapping computationally efficient to evaluate. However, the high dimensionality of the input microstructure and the output field of interest often renders such surrogate models inefficient, especially when dealing with sparse data. Deep convolutional neural network (CNN) based surrogate models have shown great promise in handling such high-dimensional problems. In this paper, a single ellipsoidal void structure under a uniaxial tensile load represented by a linear elastic, high-dimensional and expensive-to-query, FEM model. We consider two deep CNN architectures, a modified convolutional autoencoder framework with a fully connected bottleneck and a UNet CNN, and compare their accuracy in predicting the von Mises stress field for any given input void shape in the FEM model. Additionally, a sensitivity analysis study is performed using the two approaches, where the variation in the prediction accuracy on unseen test data is studied through numerical experiments by varying the number of training samples from 20 to 100.

Aerodynamic Exergy-Based Analysis and Optimization of the Generic Hypersonic Vehicle Using FUN3D

The development of future novel aircraft concepts requires a holistic approach to vehicle design, analysis, and optimization. Aircraft designers can no longer consider components individually as systems become more interconnected and multidisciplinary. Hence, a new approach to aircraft design and a new way to measure the performance of aircraft are needed. A novel approach to aircraft design is the use of exergy methods that can evaluate typically disparate systems using a universal measure of performance mapped to global system performance. This paper introduces a new functional and its adjoint gradient in FUN3D to determine aerodynamic exergy destruction rates. The functional is verified using the Oswatitsch relationship by comparing it to native, surface-based drag coefficients. The adjoint gradient is verified using the FUN3D native complex step method, and discrete agreement is demonstrated for flowfields and geometric derivatives. The new functional is then used for aerodynamic exergy-based analysis and optimization of the generic hypersonic vehicle. An inverse design problem is conducted first to verify the design optimization framework. Finally, a planform and airfoil aerodynamic inviscid exergy optimization of the GHV is conducted, improving exergy destruction rates by 7.1% while making substantial improvements to the cruise trim characteristics of the vehicle.

Automated resolution of the spiral torsion spring inverse design problem

Many mechanical applications take advantage of spiral torsion springs due to their robustness, compactness, and simplicity. Brand-new manufacturing methods allow to create spiral springs with unconventional geometries and materials that suit a wider range of uses demanding either linearity or nonlinearity. Designing a spiral torsion spring with a nonlinear desired torque curve may be a great challenge, due to their many degrees-of-freedom (length, width, thickness, arbor, and barrel diameters, etc.) and the complexity of the geometrical and mechanical requirements to ensure their manufacturability, system compatibility, operation safety and reliability; and the solution is never unique. This manuscript proposes and validates an innovative methodology for the resolution of this inverse design problem based on the application of a nonlinear restrained global optimization algorithm. This algorithm is adjusted to converge, out of the infinity of designs that match the desired torque curve and hold all the functional and manufacturing constraints, to a design solution that minimizes strip mass. The methodology is built on a formulation for the calculation of the torque curve of a generalized spiral spring, with or without coiling and with any along-the-length cross-section, already published by the authors.