Inverse Design Method Research Articles

Mean Squared Error May Lead You Astray When Optimizing Your Inverse Design Methods

Abstract When performing time-intensive optimization tasks, such as those in Topology or Shape Optimization, researchers have turned to machine-learned (ML) Inverse Design methods i.e., predicting the optimized geometry from input conditions to replace or warm start traditional optimizers. Such methods are often optimized to reduce the Mean Squared Error (MSE) or Binary Cross-Entropy between the output and a training dataset of optimized designs. While convenient, we show that this choice may be myopic. Specifically, we compare two methods of optimizing the hyper-parameters of easily reproducible Machine Learning models including random forest (RF), k-nearest neighbors (KNN), and Deconvolutional Neural Network (DeCNN) model for predicting the three optimal topology problems. We show that under both direct Inverse Design and when warm starting further Topology Optimization (TO), using MSE metrics to tune hyper-parameters produces less performant models than directly evaluating the objective function, though both produce designs that are almost one order of magnitude better than using the common uniform initialization. We also illustrate how warm starting impacts both the convergence time, the type of solutions obtained during optimization, and the final designs. Overall, our initial results portend that researchers may need to revisit common choices for evaluating ID methods that subtly trade-off factors in how an ID method will actually be used. We hope our open-source dataset and evaluation environment will spur additional research in those directions.

Inverse-design laser-infrared compatible stealth with thermal management enabled by wavelength-selective thermal emitter

With the fast development of multi-band detection technology, the demand for multi-band stealth technology with thermal management in military and civilian fields is increasing. Although the metasurfaces can achieve multi-band stealth and thermal management, their fabrication is complex and costly. In this paper, a simple multilayer structure is used to realize laser-infrared compatible stealth with thermal management. More importantly, the traditional method of optimizing metasurface structures by manually scanning parameters consumes a lot of computational time and resources. In order to speed up design of nanostructures, we propose a wavelength-selective thermal emitter (WSTE) composed of ZnS/Ge3Sb2Te6 (GST) multilayer films and a Ni reflector using inverse design method. The simulation results show that, in the crystalline phase, the WSTE has low spectral emissivity (ε3-5μm = 0.12, ε8-14μm = 0.22) in the mid-wave infrared (MWIR) and long-wave infrared (LWIR), high spectral emissivity (ε5-8μm = 0.72) in the non-atmospheric window and high absorptivity (A1.06μm = 0.90, A1.55μm = 0.97, A10.6μm = 0.91) in the laser wavelengths, which indicates that the WSTE can simultaneously achieve MWIR, LWIR and laser stealth with radiative heat dissipation. The method proposed in this paper overcomes the problems of single-band stealth and inefficient. Moreover, by varying the crystallization fraction of the GST, the WSTE can achieve dynamic control of thermal radiation in the wavelength range of 3–14 µm. The simulated infrared images verify that WSTE has good infrared stealth performance. Finally, the effects of incidence angle and polarization angle on the emission spectrum of WSTE are studied, which can demonstrate the infrared stealth is insensitive to both. In conclusion, the WSTE is attractive in advanced photonics applications, such as radiative cooling and infrared stealth.

Experiment and numerical investigation on beetle elytra inspired lattice structure: Enhanced mechanical properties and customizable responses

The elytra of the ironclad beetles possess very strong and toughness performance, to protect the body from catastrophic physical damage, owing to its unique curved geometry and layered microstructure. In this paper, inspired by the elytra of ironclad beetles, a novel configuration of lattice structure (IBCC) was developed. The digital light processing (DLP) with hard-tough resin was used to fabricate the lattice structures. The compression experiment and simulation were performed to investigate the mechanical response and deformation mechanism. The response surface model (RSM) was adopted to build a forward relationship between structure parameters and mechanical properties. A numerical method was developed to inversely design structure parameters of IBCC with “target” mechanical properties using genetic algorithm. The novel lattice structure exhibits superior stiffness and energy absorption than conventional BCC (body-centered cubic) and OCT (Octet) structures, under the same relative density. For example, IBCC shows a maximum 59% improvement (at ρ¯=9.60%) of stiffness, and a maximum 25% improvement (at ρ¯=7.40%) of SEA, with respect to OCT. Besides, the stress plateau of IBCC is more stable than OCT, even at relatively large compression strain. The superior mechanical response of the IBCC lattice structure is mainly ascribed to bio-inspired topological design and interaction effects of curved rods in the “V-shaped” region. Besides, the effectiveness of the proposed inverse design method is verified by three numerical cases. The proposed bio-inspired design strategy, mechanical enhancement mechanism, and customizable method will be helpful in expanding the prospects of lattice structures in future multifunctional application fields.

Curvature programming of freestanding 3D mesostructures and flexible electronics based on bilayer ribbon networks

Three-dimensional (3D) buckling assembly of flexible electronics from strategically designed two-dimensional (2D) precursor structures has enabled important applications in a variety of areas, owing to its versatile applicability to a broad range of length scales and high-performance materials, as well as to a rich diversity of 3D topologies. Rational design methods that allow direct mapping of 3D mesostructures onto unknown 2D precursor structures and loading parameters are foundational to these assembly technologies, but face scientific challenges, such as the high nonlinearity of spatial deformations and tricky bifurcation behaviors. While a few inverse design methods based on the beam theory, topology optimization and machine learning algorithms have been reported, the shape programming of freestanding 3D mesostructures/electronics with highly complex curvature distributions remains elusive. In this work, we propose a curvature programming method based on bilayer ribbon networks, along with a mold-assisted assembly strategy, as a new route to customizable freestanding 3D mesostructures and electronics. Combined mechanics modeling, finite element analyses and experimental measurements allow a clear understanding of nonlinear bending-stretching coupled deformations of bilayer ribbon networks during the 2D-to-3D transformation. A parameter domain with one-to-one mapping of the dimensionless curvature and the bending stiffness ratio is identified, offering a theoretical basis of the curvature programming. By introducing a discretization strategy, a variety of regular (e.g., circles, ellipses, spirals and toroids) and biomimetic 3D curved ribbons and mesosurfaces (e.g., mimicking wavy vines, diatoms and arbitrarily curled leaves) were inversely designed and experimentally realized. A device demonstration capable of strain/temperature sensing and micro-LEDs indication suggests application opportunities in bioelectronics and microelectromechanical systems.

Ultra-high density and ultra-efficient TiO2-based chip-integrated wavelength beam splitters with an inverse design method

Wavelength beam splitter (WBS) is an important element for integrated photonic circuits. Conventional WBSs usually are based on conventional structures. However, the sizes of conventional WBSs are too large to be suitable for integrated photonic circuits. Motivated by this, the sequence quadratic program (SQP) is introduced combining with the finite element method (FEM) to realize ultra-high density and ultra-efficient chip-integrated WBSs. The SQP is used to generate iterative architectures and the FEM is adopted to monitor the optical fields of the generated architectures. And ultra-compact four-, five-, and six-channel WBSs have been implemented on TiO2 substrates of size 1.5 μm × 1.5 μm with this method. The transmission efficiencies of the four-channel WBS are 84.4%, 81.3%, 80.6%, and 81.3% at the splitting wavelengths of 504 nm, 540 nm, 578 nm, and 622 nm, and their extinction ratios (ERs) range from 11.1 dB to 24.6 dB. While those of the five-channel WBS are 89.0%, 87.6%, 81.3%, 85.1% and 87.3% at the splitting wavelengths of 478 nm, 520 nm, 556 nm, 600 nm and 678 nm, respectively. Those of the six-channel WBS are 91.9%, 88.7%, 91.2%, 86.1%, 81.4% and 86.4% at the splitting wavelengths of 502 nm, 534 nm, 564 nm, 594 nm, 620 nm and 658 nm, respectively. Our designed six-channel WBS achieves smaller size and higher efficiency than the reported chip-integrated WBSs. It is expected that it can provide a new idea to design ultra-compact integrated devices and more possibility for photonic circuits structure.

Polarization-controlled metasurface design based on deep ResNet

The accuracy of metasurface inverse design depends on the input dimension of the target light field and the output dimension of the unit structure parameters. When the two light field targets are simultaneously controlled, the designed unit structure often cannot satisfy the simultaneous directional control of the two light field target parameters due to the existence of coupling. This greatly limits the completeness of the function of metasurfaces in applications. In this paper, we apply the designed 13-layer residual network (ResNet) to the inverse design of wavefront control of dielectric metasurfaces. After the neural network training is completed, the correspondence between any amplitude, phase and the element structure parameters within a certain error range can be realized, which greatly saves the time cost in the metasurface design process. As a verification of the inverse design method, we arranged two focusing metasurfaces of different sizes. Their focusing efficiencies are more than 53%. The nanounit structure and its inverse design method proposed in this paper provide a new idea for the design of the metasurface to control the polarized light field. At the same time, it will have important applications in the intelligent design of metasurfaces.

Tailoring Phonon Dispersion of a Genetically Designed Nanophononic Metasurface.

Phonon engineering at the nanoscale holds immense promise for a myriad of applications. However, the design of phononic devices continues to rely on regular shapes chosen according to long-established simple rules. Here, we demonstrate an inverse design approach to create a two-dimensional phononic metasurface exhibiting a highly anisotropic phonon dispersion along the main axes of the Brillouin zone. A partial hypersonic bandgap of approximately 3.5 GHz is present along one axis, with gap closure along the orthogonal axis. Such a level of control is achieved through genetically optimized unit cells, with shapes exceeding conventional intuition. We experimentally validated our theoretical predictions using Brillouin light scattering, confirming the effectiveness of the inverse design method. Our approach unlocks the potential for automated engineering of phononic metasurfaces with on-demand functionalities, thus leading toward innovative phononic devices beyond the limitations of traditional design paradigms.

Full‐Phase Parameter Modulation with Arbitrary Polarization Combination via Bidirectional Asymmetric Transmission Meta‐Devices

AbstractThe bidirectional asymmetric transmission (BAT) meta‐devices have attracted widespread attention as an emerging display, encryption, and information storage platform. Generally, the multiplexing capability of BAT meta‐devices determines the upper limit of the loading capacity of multi‐task integrated systems. However, existing BAT meta‐devices still depend on structural properties and the arrangement of meta‐atoms, limiting the number of manipulated channels, operating frequency, and polarization combinations. Herein, a universal BAT meta‐device, enabling bidirectional eight‐phase‐channel asymmetric transmission, composed of bilayer spatially cascaded birefringent metasurfaces (BMs) is proposed to allow for arbitrary polarization combination via the inverse design method and validated in the microwave region. In addition, the polarization multiplexing capabilities of BAT meta‐devices are further extended via a Lego‐like physical mechanism. The proposed design strategy may facilitate BAT meta‐devices functional innovation and advanced application deployment in holographic images, duplex communication, and secret‐key‐sharing data encryption.

Topological and conventional nanophotonic waveguides for directional integrated quantum optics

Directionality in integrated quantum photonics has emerged as a promising route towards achieving scalable quantum technologies with nonlinearities at the single-photon level. Topological photonic waveguides have been proposed as a novel approach to harnessing such directional light-matter interactions on-chip. However, uncertainties remain regarding the strength of the directional coupling of embedded quantum emitters to topological waveguides in comparison to conventional line defect waveguides. In this work we present an investigation of directional coupling in a range of waveguides using a combination of experimental, theoretical, and numerical analyses. We quantitatively characterize the position dependence of the light-matter coupling on several topological photonic waveguides and benchmark their directional coupling performance against conventional line defect waveguides. We conclude that topological waveguides underperform in comparison to conventional line defect waveguides, casting their directional optics credentials into doubt. To demonstrate this is not a question of the maturity of the field; we show that state-of-the-art inverse design methods, while capable of improving the directional emission of these topological waveguides, still place them significantly behind the operation of a conventional (glide-plane) photonic crystal waveguide. Our results and conclusions pave the way towards improving the implementation of quantitatively predicted quantum nonlinear effects on-chip. Published by the American Physical Society 2024

A theoretical method for oblique and curved detonation waves

In this paper, a theoretical solution method for the post-wave parameters of detonation is proposed and developed with a series of analyses and applications. Based on Newton's method, the objective function for shock-coupled chemical reactions is constructed along with its derivative. Two verification examples demonstrate that the method can calculate accurate post-wave parameters quickly and is suitable for single-step and detailed mechanistic chemical reactions. In addition, the method provides sensitivities between various aerodynamic parameters to offer a fresh perspective for detonation, polar analysis with sensitivity is built as a result. Moreover, the method can predict the transition pattern of the detonation, and the validity is supported by the comparison of different examples. Rather than being limited to oblique detonation, the post-wave parameters of the curved detonation can also be calculated correctly, which indicates the excellent applicability of the method. This method can also be applied to the thermodynamic efficiency of detonation combustion and its sensitivity, which demonstrates the unique advantages of this method. Furthermore, the method can be rewritten as a solution for wedge angle under the given wave angle by changing the independent variable. This solution is validated by the simulation results, which implies that the method can be used as a simple inverse design method in oblique detonation engines. In general, the proposed method is an effective theoretical solution, analytical tool, and inverse design method for detonation.

Design method and flow analysis of a mixed flow pump based on blade load control

Abstract Mixed flow pumps are commonly used due to their wide operating range. Load distribution is the key parameter of the inverse design of mixed flow pumps. In this study, an inverse design method using a quadratic function to control the blade load distribution is introduced to design a mixed flow pump. The hydraulic performance of the pump is calculated using numerical simulation, and then the internal flow is analyzed. The results show that the pump designed by this method has a high efficiency at the designed point and a wide operating range. The flow field is symmetrical along the circumference and varies uniformly along the impeller inlet to the impeller outlet. No flow separation and no unfavourable low-pressure area appear.

Merging automatic differentiation and the adjoint method for photonic inverse design

Optimizing the shapes and topology of physical devices is crucial for both scientific and technological advancements, given their wide-ranging implications across numerous industries and research areas. Innovations in shape and topology optimization have been observed across a wide range of fields, notably structural mechanics, fluid mechanics, and more recently, photonics. Gradient-based inverse design techniques have been particularly successful for photonic and optical problems, resulting in integrated, miniaturized hardware that has set new standards in device performance. To calculate the gradients, there are typically two approaches: namely, either by implementing specialized solvers using automatic differentiation (AD) or by deriving analytical solutions for gradient calculation and adjoint sources by hand. In this work, we propose a middle ground and present a hybrid approach that leverages and enables the benefits of AD for handling gradient derivation while using existing, proven but black-box photonic solvers for numerical solutions. Utilizing the adjoint method, we make existing numerical solvers differentiable and seamlessly integrate them into an AD framework. Further, this enables users to integrate the optimization environment seamlessly with other autodifferentiable components such as machine learning, geometry generation, or intricate post-processing which could lead to better photonic design workflows. We illustrate the approach through two distinct photonic optimization problems: optimizing the Purcell factor of a magnetic dipole in the vicinity of an optical nanocavity and enhancing the light extraction efficiency of a µLED.

A mechanically robust and facile shape morphing using tensile-induced buckling.

Inspired by the adaptive mechanisms observed in biological organisms, shape-morphing soft structures have emerged as promising platforms for many applications. In this study, we present a shape-morphing strategy to overcome existing limitations of the intricate fabrication process and the lack of mechanical robustness against mechanical perturbations. Our method uses tensile-induced buckling, achieved by attaching restraining strips to a stretchable substrate. When the substrate is stretched, the stiffness mismatch between the restraining strips and the substrate, and the Poisson's effect on the substrate cause the restraining strips to buckle, thereby transforming initially flat shapes into intricate three-dimensional (3D) configurations. Guided by an inverse design method, we demonstrate the capability to achieve complicated and diverse 3D shapes. Leveraging shape morphing, we further develop soft grippers exhibiting outstanding universality, high grasping efficiencies, and exceptional durability. Our proposed shape-morphing strategy is scalable and material-independent, holding notable potential for applications in soft robotics, haptics, and biomedical devices.

Interactive inverse design of periodic non-uniform/inhomogeneous rod structures based on q-learning method

The existing researches on controlling the longitudinal waves through periodic rods with frequency bands mainly focus on the analysis of band structures together with their influences by various geometrical/material parameters and on the corresponding forward design via passive/active modulations. This paper originally proposes the interactive inverse design method by virtue of the Q-Learning algorithm for catering required objectives with introducing the cross-sectional nonuniformity and material inhomogeneity to the constituent components in periodic rods. Firstly, theoretically analyzing the frequency bands of periodic non-uniform/inhomogeneous rods with linear variations to the cross-sectional area and to the Young’s modulus and material density, is presented using transfer matrix method (TMM). After verifying the analysis method by comparing it with the finite element method (FEM) for obtaining band structures in three kinds of exemplified periodic rods with non-uniform/inhomogeneous components, the effects of non-uniformity and inhomogeneity of components on the frequency bands are discussed. These effects provide qualitative judgment criteria to the results of inverse design. Secondly, the inverse design method by the Q-learning algorithm for periodic non-uniform/inhomogeneous rods is proposed as the optimization objective is the maximum of the first bandgap width. The optimization results of the periodic rods with only non-uniformity, with only inhomogeneity or with both non-uniformity and inhomogeneity are provided to validate the accuracy and efficiency of the proposed Q-Learning algorithm that has the advantages of obtaining the optimal result from any initial states and giving the evolutionary path along the gradient to the objective. It should be pointed out that our proposed inverse design method can actually be extended for other optimization objectives and to other kinds of periodic structures for controlling diversified elastic waves.

Theoretical design and experimental verification of high-entropy carbide ablative resistant coating

Composition design of high-entropy carbides is a topic of great scientific interest for the hot-end parts in the aerospace field. A novel theoretical method through an inverse composition design route, i.e. initially ensuring the oxide scale with excellent anti-ablation stability, is proposed to improve the ablation resistance of the high-entropy carbide coatings. In this work, the (Hf0.36Zr0.24Ti0.1Sc0.1Y0.1La0.1)C1-δ (HEC) coatings were prepared by the inverse design concept and verified by the ablation resistance experiment. The linear ablation rate of the HEC coatings is −1.45 ​μm/s, only 4.78 % of the pristine HfC coatings after the oxyacetylene ablation at 4.18 ​MW/m2. The HEC possesses higher toughness with a higher Pugh's ratio of 1.55 in comparison with HfC (1.30). The in-situ formed dense (Hf0.36Zr0.24Ti0.1Sc0.1Y0.1La0.1)O2-δ oxide scale during ablation benefits to improve the anti-ablation performance attributed to its high structural adaptability with a lattice constant change not exceeding 0.19 % at 2000–2300 ​°C. The current investigation demonstrates the effectiveness of the inverse theoretical design, providing a novel optimization approach for ablation protection of high-entropy carbide coatings.

Single-etched fiber-chip coupler with a metal mirror on a 220-nm silicon-on-insulator platform for perfectly vertical coupling.

Vertical couplers play a pivotal role as essential components supporting interconnections between fibers and photonic integrated circuits (PICs). In this study, we propose and demonstrate a high-performance perfectly vertical coupler based on a three-stage inverse design method, realized through a single full etching process on a 220-nm silicon-on-insulator (SOI) platform with a backside metal mirror. Under surface-normal fiber placement, experimental results indicate a remarkable 3-dB bandwidth of 99 nm with a peak coupling efficiency of -1.44 dB at the wavelength of 1549 nm. This achievement represents the best record to date, to the best of our knowledge, for a perfectly vertical coupler fabricated under similar process conditions.

Frequency-extended inverse design of transmission-type linear-to-circular polarization control metasurface based on deep learning

Due to the parameter range limitations of the training dataset, traditional inverse prediction network models can only predict structure parameters of the metasurface within a limited frequency range. When the given design targets exceed the prediction range of network models, the predicted results will not match the actual results. This paper proposes a frequency-extended inverse design method (FEIDM) based on deep learning to address the problem. The method can automatically collect the required data and train the network model based on the center working frequency of the design targets, thereby achieving accurate prediction of metasurface structural parameters and effectively reducing labor and computational costs. Taking the transmission-type linear-to-circular polarization control metasurface as an example, the unit cell of the metasurface is first established in the paper. The structural parameters and corresponding electromagnetic parameters are collected without changing the unit size of the metasurface, and an initial inverse prediction network model (IIPNM) is constructed. The research results indicate that its predictable center working frequency range is 3–5.5 GHz. Using the design concept proposed in this paper, a program is constructed, it can automatically achieve data collection, target extraction, network model training, and prediction. Four given design targets are predicted. Among them, the center working frequencies of the three design targets are outside the initial predictable range. The predicted results meet the requirements of the given target, verifying the effectiveness of the proposed scheme. Finally, a set of parameters is selected to fabricate, and the experimental results are consistent with the simulation results. The research results can provide a reference for the efficient prediction of metasurface structural parameters over a wide frequency band.

On the Feasibility of Particle Swarm Optimization Method for Inverse Design of High-Performance SPR Biosensor

On the Feasibility of Particle Swarm Optimization Method for Inverse Design of High-Performance SPR Biosensor

Inverse design of dual-bandpass metasurface filters empowered by the multi-objective genetic algorithm

Multi-band metasurface filters are becoming increasingly pivotal in high-capacity communication technologies. Traditional methods for designing metasurface structures, to date, have relied on empirical approaches to obtain target electromagnetic responses, thereby suffering from low efficiency. Here, we demonstrate an advanced approach for the inverse design of a multi-band metasurface filter, which consists of a multi-objective genetic algorithm (MOGA) in tandem with equivalent circuit model (ECM) analysis. This integration converts specific frequency response requirements into ECM parameter constraints, significantly streamlining the metasurface design and optimization process and offering superior solutions. Using this inverse design method, we theoretically propose a dual-bandpass metasurface filter which can exhibit transmission passbands in any two adjacent frequency ranges among the X-, Ku-, and K-bands. Further, numerical simulations validate the performances of the proposed device, which show great agreement with MOGA-based predictions. Our results pave the way to the effective inverse design of multi-passband metasurface filters which are useful in many applications, such as microwave filters, radar and satellite communication systems, and radio frequency identification devices.

Dual-parameter controlled reconfigurable metasurface for enhanced terahertz beamforming via inverse design method

Recently, reconfigurable metasurfaces have emerged as a promising solution for wavefront manipulation in the terahertz (THz) region, providing enhanced beamforming capabilities. However, traditional single-parameter control methods fail to achieve independent phase and amplitude modulation, constraining their modulation capabilities. Meanwhile, forward design methods based on phase matching ignore the structural responses of the non-ideal unit, leading to degraded beamforming performance. Here, we introduce an electrically reconfigurable metasurface composed of bilayer graphene strips based on dual-parameter control. Full-wave simulations demonstrate independent amplitude and phase modulation, achieving the full 360° phase coverage and an adjustable amplitude range from 0 to 0.8 at 2.6 THz. To optimize beamforming performance, particularly for the responses of the non-ideal unit away from the designed frequency, we employed an inverse design method based on a hybrid evolutionary algorithm. This novel approach significantly enhances beam steering, achieving a maximum 60% increase in beam directivity and maintaining over 90% of ideal directivity across a broad frequency range from 1.6 THz to 5 THz. Especially, it achieves a maximum deflection angle of 75°. Meanwhile, the adaptability of the inverse design method is further demonstrated to various optimized objectives. For beam focusing, even with limited phase control (below 210°), this method significantly enhances the focusing quality (up to 150% enhancement) and increases the focusing efficiency from 25% to 40%. Additionally, it effectively mitigates the impact of quantized phase errors on beamforming. This research not only demonstrates potential applications in high-speed THz wireless communication and compact imaging systems but also paves the way for innovative designs in reconfigurable metasurfaces.