Inverse Design Method Research Articles

Reverse design of metamaterial absorbers based on an equivalent circuit

We present a reverse design method useful for designing and analyzing metamaterial absorbers; we demonstrate its power by designing both a narrowband absorber and a wideband absorber. The method determines the structure of the absorber using an equivalent-circuit model. The narrowband metamaterial absorber structures were based on the equivalent-circuit model, and the narrowband metamaterial absorber designed using the method has an absorption fraction greater than 90% in a bandwidth of 500 nm centered at about 1450 nm. In order to extend the absorption bandwidth for the absorber, the narrowband absorber structure is adjusted based on the equivalent-circuit model, and the broadband metamaterial absorber structure is investigated. The numerical results show that the absorption bandwidth is substantially increased; the absorbance is greater than 90% for a band nearly reaching the limits of our experiment, from about 400 nm (near-ultraviolet) to about 2800 nm (deep infrared). The absorption spectrum of the wideband absorber is more sensitive to the angle of incident polarization due to the asymmetric structure, but the whole band shows polarization independence. For a large angle of 60° (TM polarization) oblique incidence, the average absorption of the broadband metamaterial absorber reaches 81%. The physical mechanism of the wideband high absorption is analyzed, which is mainly caused by Fabry-Perot resonance, surface plasmon resonance, local surface plasmon resonance, and the hybrid coupling among them. Our proposed design with high-broadband absorption has significant potential for thermoelectric and thermal emitters, solar thermal energy harvesting, and invisible device applications.

Optimization of a Francis Turbine Runner by Means of Inverse Design and CFD Calculation

A Francis turbine runner was optimized by a combination of means of the 3D Inverse Design Method and Computational Fluid Dynamics (CFD). An experiment of the directly optimized conventional turbine confirms the validation of CFD calculation. A new meridional shape was designed by Design of Experiments with CFD and the database of meridional shape factors. Angular momentum at the runner inlet was corrected to cover the effects of the boundary layer from runner upstream domains such as stay vanes and guide vanes. Using the meridional shape and the corrected angular momentum and considering the secondary flow mechanism, blade loading distribution and stacking condition were optimized. It led to the decrease of secondary flow energy near the runner inlet and of the runner loss. The full-domain CFD calculation confirms that the total loss of the new turbine at the design point is 4[%] lower than that of the conventional one. This result shows the 3D Inverse Design Method is practical to control the secondary flow in the Francis turbine runners and optimize the shape.

Effects of different vortex designs on optimization results of mixed-flow pump

Turbomachinery optimization based on the inverse design method (IDM) has been investigated in several previous studies, however, due to head constraints, most of these studies have adopted the constant impeller outlet angular momentum (IOAM) distribution, namely the free vortex design, which in turn reduces the optimization effect. To overcome these drawbacks, forced and compound vortex designs are proposed here by parameterizing the IOAM using a parabola, and the effects of different vortex designs on the optimization results of a mixed-flow pump impeller are investigated. First, a baseline mixed-flow pump is simulated and experimentally verified. Second, based on the IDM, the impeller is parameterized for the three vortex designs. Finally, it is optimized by artificial neural network and genetic algorithm to maximize the weighted efficiency at 0.8Q des, 1.0Q des and 1.2Q des, and the results are analyzed. The results show that the weighted efficiency of the forced and compound vortex design is improved by 1.33% and 1.69% respectively compared to free vortex design. The internal flow analysis reveals that the improved efficiency of the compound vortex design can be attributed to the improved impeller-outlet flow regime. Finally, the energy characteristics of the preferred and baseline models are compared using the entropy production method.

Optimization loop based on adjoint sensitivity analysis for flows through porous media with adsorption

AbstractIn the past few years, the development of inverse design and optimization methods has opened up new possibilities. The adjoint method is of great significance in that context, since it permits high fidelity to flow‐physics at comparatively low computational costs. The present work focuses on adsorbed gas storage systems. Its contribution is the development of an alternative approach to the adjoint contour problem, which ensures that the latter is as well‐posed as the physical problem, itself. This approach proves to be fully consistent with Cacuci's methodology for computing sensitivity derivatives, which enables us to extend their scope. It allows for the evaluation of sensitivities with respect to parameters other than those pertaining to geometry, that is, to those that control the system operation such as average mass flux, convective heat transfer, inlet and external temperature. The main goal of this work is to obtain and validate a basic structure of an optimization loop algorithm (OLA) based on adjoint method, applied to adsorption natural gas storage systems, with pressure and density of adsorption as objective functions.

Inverse design strategies for buckling-guided assembly of 3D surfaces based on topology optimization

Complex three-dimensional (3D) mesostructures in advanced functional materials are attracting increasing interest, due to their widespread applications. Mechanically-guided 3D assembly through compressive buckling provides deterministic routes to a rich diversity of 3D mesostructures and microelectronic devices, with feature sizes ranging from sub-microscale to millimeter-scale. Existing studies established inverse design methods that map the target 3D geometry onto an unknown 2D precursor, but mainly focusing on filamentary ribbon-type geometries. Although strategies relying on spatial thickness variation of 2D precursors have been reported to achieve inverse design of 3D surfaces, this could lead to a lack of compatibility with well-developed planar fabrication technologies. In the framework of buckling-guided 3D assembly, this paper presents a computational method based on topology optimization to solve the inverse design problem of 3D surfaces from 2D precursors with uniform thickness distributions. Specifically, curvy ribbon components were exploited to discretize nondevelopable target surfaces, and then optimized to ensure that the assembled 3D surface has the best match with the target geometry. Combined computational and experimental studies over a dozen of elaborate examples, encompassing both the caged and even general target surfaces, demonstrate the effectiveness and applicability of the proposed method.

Design of architectured composite materials with an efficient, adaptive artificial neural network-based generative design method

In recent years, machine learning methods have been applied increasingly in material design and discovery. While these approaches have demonstrated promising performance and produced novel materials that are unachievable previously, most existing machine learning methods are supervised methods and need millions of labeled training data. The construction of the training data requires massive computational resource and is extremely time-consuming, forming a major bottleneck of machine learning approaches. In this work, an efficient artificial neural network-based inverse design method is developed for the design of architectured composite materials with novel properties. By adopting an adaptive learning and optimization strategy, the design space can be effectively explored, thereby greatly reducing the number of required labeled training data. In addition, a generative adversarial network is used to generate design candidates which drastically reduces the number of design variables and speeds up the optimization process. The excellent performance of the method is demonstrated on the design of several novel composite materials such as materials with high toughness, high stiffness near theoretical upper bound. Compared with some existing machine learning based methods, a two-order-magnitude reduction in the number of labeled training data has been achieved while maintaining the same level of design performance.

Graded Kirigami Composites for Programmed Strain Distributions

AbstractStretchable devices and components have emerged as a vital platform for wearable electronics, biomedical sensors, and soft robotics. However, the soft‐rigid interfaces that arise when integrating rigid components with soft and deformable substrates can cause stress concentrations, leading to premature failure of devices at these multi‐material interfaces. Here, a stiffness‐graded kirigami composite is introduced to control strain transitions at soft‐rigid interfaces. The graded composite consists of soft elastomers bonded to rigid kirigami films with defined beam architectures to tune the stiffness gradient along the loading direction. Kirigami geometry is designed by coupling finite element analysis with experimental digital image correlation to achieve diverse strain profiles for flexible interfaces. Furthermore, an inverse design method is utilized to determine kirigami patterns to obtain predefined strain fields. These stiffness‐graded kirigami composites create opportunities for more robust soft‐rigid interfaces and defect‐tolerant stretchable devices and robots.

Optimal design of microwave absorber using novel variational autoencoder from a latent space search strategy

This paper introduces a new objective-driven design method based on deep learning for meta-structure absorber for X-band (8–12 GHz) application. The method consists of three steps; at Step 1, developing a simulator to predict a spectrum of microwave from a conductive layer of absorber as an image input, at Step 2, designing an autoencoder network to take the patterns as input and outputs the same pattern, at Step 3, making an inverse design method for a new pattern under a given goal (spectrum). The proposed method was verified by comparing with the reflectance spectrum calculated by FDTD on the designed absorber with an optimal conductive pattern layer. For the effective training of a general random-like pixel patterns, the variational autoencoder (VAE) that uses a new adaptive annealing loss and a symmetricity layer block in VAE decoder is suggested to improve the training performance. The covariance Matrix Adaptation Evolution Strategy (CMA-ES) which searches the optimal pattern in the VAE latent space is used for suggesting the candidates of the optimal pattern. The proposed method can find an optimal absorber with minimum −16 dB reflectance in X-band that exceed the best absorption among all the training samples obtained by FDTD.

Ultra-Compact Power Splitters with Low Loss in Arbitrary Direction Based on Inverse Design Method

The power splitter is a device that splits the energy from an input signal into multiple outputs with equal or uneven energy. Recently, the use of algorithms to intelligently design silicon-based photonic devices has attracted widespread attention. Thus, many optimization algorithms, which are called inverse design algorithms, have been proposed. In this paper, we use the Direct Binary Search (DBS) algorithm designed with three 1 × 3 power splitters with arbitrary directions theoretically. They have any direction and can be connected to other devices in any direction, which greatly reduces the space occupied by the optical integrated circuit. Through the simulation that comes about, we are able to get the insertion loss (IL) of the device we designed to be less than 5.55 dB, 5.49 dB, and 5.32 dB, separately. Then, the wavelength is 1530–1560 nm, so it can be used in the optical communication system. To discuss the impact of the footprint on device performance, we also designed another device with the same function as the second one from the above three devices. Its IL is less than 5.40 dB. Although it occupies a larger area, it has an advantage in IL. Through the design results, three 1 × 3 power splitters can be freely combined to realize any direction, multi-channel, ultra-compact power splitters, and can be better connected with different devices to achieve different functions. At the same time, we also show an example of a combination. The IL of each port of the combined 1 × 6 power splitter is less than 8.82 dB.

Review of machine learning‐driven design of polymer‐based dielectrics

Polymer-based dielectrics are extensively applied in various electrical and electronic devices such as capacitors, power transmission cables and microchips, in which a variety of distinct performances such as the dielectric and thermal properties are desired. To fulfil these properties, the emerging machine learning (ML) technique has been used to establish a surrogate model for the structure–property linkage analysis, which provides an effective tool for the rational design of the chemical and morphological structure of polymers/nanocomposites. In this article, the authors reviewed the recent progress in the ML algorithms and their applications in the rational design of polymer-based dielectrics. The main routes for collecting training data including online libraries, experiments and high-throughput computations are first summarized. The fingerprints charactering the microstructures of polymers/nanocomposites are presented, followed by the illustration of ML models to establish a mapping between the fingerprinted input and the target properties. Further, inverse design methods such as evolution searching strategies and generative models are described, which are exploited to accelerate the discovery of new polymer-based dielectrics. Moreover, structure–property linkage analysis techniques such as Pearson correlation calculation, decision-tree-based methods and interpretable neural networks are summarized to identify the key features affecting the target properties. The future development prospects of the ML-driven design method for polymer-based dielectrics are also presented in this review.

A Review: Elastic Metamaterials and Inverse Design Methods for Shock and Vibration Mitigation

The development of engineering technology puts forward more demanding requirements for the performance of materials, many of which cannot be met by the existing natural materials. In addition to exploring and refining new natural materials, it is possible to arrange designed microstructures according to periodicity or other rules to produce man-made materials that do not exist in nature itself, mostly due to the development of additive manufacturing (AM) technology. These artificial materials are known as metamaterials. In the past few years, the design and application of metamaterials have made great progress. This paper reviews the research of elastic metamaterials in recent years, which includes both traditional metamaterials with fixed structural properties and active metamaterials with tunable properties. Among many application scenarios, this paper mainly focuses on elastic metamaterials’ applications in vibration control, impact mitigation and wave attenuation. In addition, this paper also discusses the development of metamaterial inverse design or optimization design, with special attention to the application of topology optimization (TO) technology in this area.

All-optical binary computation based on inverse design method

Abstract The development of information technology urgently requires ultrafast, ultra-low energy consumption and ultra-high-capacity data computing abilities. Traditional computing method of electronic chips is limited by the bottleneck of Moore’s Law. All-optical computing of photonic chips provides a promising way to realize such high-performance data computing abilities. Until now, it is still a huge challenge to realize all-optical four arithmetic operations at the same time on a photonic chip. Here, we propose a new encoding scheme for all-optical binary computation, including n-bit addition, subtraction, multiplication and division. We theoretically present n-bit calculation and experimentally demonstrate 1 bit calculation. The computation part includes a half binary adder and a shifter, whose feature sizes are only 2 μm × 19.5 μm and 4 μm × 9 μm, respectively. The half binary adder and shifter consist of three low-loss basic devices through inverse design method. The distance between two adjacent basic devices is smaller than 1.5 μm, within wavelength magnitude scale. The response time is the propagation time of the signal light in a single device, within 100 fs. The threshold energy consumption is within 10 fJ/bit. Our results provide a new method to realize ultrafast, ultra-low energy consumption and ultra-high-capacity data processing abilities all-optical n-bit binary computing.

Mode-division multiplexing phase-sensitive amplification for mode selective and mode equalized phase regenerative amplifications

In this work, mode-division multiplexing (MDM) phase-sensitive amplification (PSA) for all-optical mode selective and mode equalized phase regeneration is presented and investigated. MDM PSA relies on reasonable phase-matching conditions, which makes intramode four-wave mixing in the fiber much stronger than that of cross-mode. It enables multimode signals to interact mainly with the same spatial mode pumps and idlers. Thus, MDM signals can obtain synchronous phase regeneration and avoid cross talk with different mode signals. To achieve this, we designed an appropriate few-mode fiber by an inverse design method based on a neural network for obtaining the desired phase mismatch and low modal dispersion. The results show that effective phase regeneration can be achieved for the degraded 40 Gbit/s binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) signals. For BPSK signals, error vector magnitudes (EVMs) of the regenerated signal on two modes are reduced from − 8.013 d B and − 8.068 d B to − 24.867 d B , and − 26.090 d B , respectively. For QPSK signals, the EVMs are reduced from − 16.767 d B and − 16.583 d B to − 24.867 d B and − 24.822 d B , respectively.

Controllable inverse design of auxetic metamaterials using deep learning

As typical mechanical metamaterials with negative Poisson’s ratios, auxetic metamaterials exhibit counterintuitive auxetic behaviors that are highly dependent on their geometric arrangements. The realization of the geometric arrangement required to achieve a negative Poisson’s ratio relies considerably on the experience of designers and trial-and-error approaches. This report proposes an inverse design method for auxetic metamaterials using deep learning, in which a batch of auxetic metamaterials with a user-defined Poisson’s ratio and Young’s modulus can be generated by a conditional generative adversarial network without prior knowledge. The network was trained based on supervised learning using a large number of geometrical patterns generated by Voronoi tessellation. The performance of the network was demonstrated by verifying the mechanical properties of the generated patterns using finite element method simulations and uniaxial compression tests. The successful realization of user-desired properties can potentially accelerate the inverse design and development of mechanical metamaterials.

Spin separation based on-chip optical polarimeter via inverse design

Abstract Polarimetry has been demonstrated essential in various disciplines, such as optical communications, imaging, and astronomy. On-chip nanostructures for polarization measurements are most expected to replace the conventional bulk elements, and hence minimize the polarimeter for integrated applications. Some on-chip nanophotonic polarimeter via polarization detection has been implemented, in which the separation of two spin polarized states is needed. However, due to the relatively low coupling efficiency or complicated photonic silicon circuits, on-chip polarimetry using a single device still remains challenging. Here, we introduce and investigate an on-chip polarimeter with nanostructures using the inverse design method. The developed device shows the ability to detect the four polarization components of light, two of which are the spin polarizations, and the other two are the linear polarizations. The retrieved Stokes parameters with experimentally tested data are in close agreement with the numerical results. We also show the proof of concept demonstration for high-speed Stokes vector optical signals detection. In the high-speed communication experiment with data rate up to 16 GBd, the detected optical signals via polarization measurements at multiple wavelengths in the C-band were recovered with the bit error rate below the 20% forward error correction threshold. The proposed on-chip polarimeter shows promising performance both in Stokes polarimetry and high-speed optical communication applications.

An inverse design method of the acoustic lens

The traditional forward and inverse diffraction iterative lens design method that replaces the amplitude according to the desired sound field distribution can achieve most sound field distributions under unitary conditions. However, when the sound field distribution we desired contains a sharp plane with abrupt changes, the traditional method will ignore the severe energy loss of the truncated plane. The designed lens will produce a ringing effect, which reduces the quality of the lens. Inspired by the Yang Gu algorithm that can be applied to non-unitary conditions, this paper proposes an acoustic lens design method based on a simulated annealing particle swarm algorithm to overcome the shortcomings of traditional forward and inverse iterative algorithms. The feasibility of this method is verified by designing a lens with a flat-top sound pressure. This paper provides a more widely applicable method in an acoustic lens design.

Efficient Design for Integrated Photonic Waveguides with Agile Dispersion.

Chromatic dispersion engineering of photonic waveguide is of great importance for Photonic Integrated Circuit in broad applications, including on-chip CD compensation, supercontinuum generation, Kerr-comb generation, micro resonator and mode-locked laser. Linear propagation behavior and nonlinear effects of the light wave can be manipulated by engineering CD, in order to manipulate the temporal shape and frequency spectrum. Therefore, agile shapes of dispersion profiles, including typically wideband flat dispersion, are highly desired among various applications. In this study, we demonstrate a novel method for agile dispersion engineering of integrated photonic waveguide. Based on a horizontal double-slot structure, we obtained agile dispersion shapes, including broadband low dispersion, constant dispersion and slope-maintained linear dispersion. The proposed inverse design method is objectively-motivated and automation-supported. Dispersion in the range of 0–1.5 ps/(nm·km) for 861-nm bandwidth has been achieved, which shows superior performance for broadband low dispersion. Numerical simulation of the Kerr frequency comb was carried out utilizing the obtained dispersion shapes and a comb spectrum for 1068-nm bandwidth with a 20-dB power variation was generated. Significant potential for integrated photonic design automation can be expected.

Inverse Design Framework With Invertible Neural Networks for Passive Vibration Suppression in Phononic Structures

Abstract Automated inverse design methods are critical to the development of metamaterial systems that exhibit special user-demanded properties. While machine learning approaches represent an emerging paradigm in the design of metamaterial structures, the ability to retrieve inverse designs on-demand remains lacking. Such an ability can be useful in accelerating optimization-based inverse design processes. This paper develops an inverse design framework that provides this capability through the novel usage of invertible neural networks (INNs). We exploit an INN architecture that can be trained to perform forward prediction over a set of high-fidelity samples and automatically learns the reverse mapping with guaranteed invertibility. We apply this INN for modeling the frequency response of periodic and aperiodic phononic structures, with the performance demonstrated on vibration suppression of drill pipes. Training and testing samples are generated by employing a transfer matrix method. The INN models provide competitive forward and inverse prediction performance compared to typical deep neural networks (DNNs). These INN models are used to retrieve approximate inverse designs for a queried non-resonant frequency range; the inverse designs are then used to initialize a constrained gradient-based optimization process to find a more accurate inverse design that also minimizes mass. The INN-initialized optimizations are found to be generally superior in terms of the queried property and mass compared to randomly initialized and inverse DNN-initialized optimizations. Particle swarm optimization with INN-derived initial points is then found to provide even better solutions, especially for the higher-dimensional aperiodic structures.

Deep learning based multistage method for inverse design of supercritical airfoil

In the preliminary aerodynamic design phase of transonic wing, inverse design of supercritical airfoils plays an important role in acquiring practical results. However, traditional inverse design approach in transonic regime highly dependents on the manual design experience and physical model simulation, which is time consuming and poses a challenge for its applications in engineering problems. In order to relieve these drawbacks, a novel method is proposed for inverse design of supercritical airfoils based on Wasserstein generative adversarial network (WGAN), genetic algorithm (GA) and deep convolutional neural network (DCNN). This method consists of three stages. First, design characteristics of transonic pressure coefficient (CP) distribution in physics are well captured and imitated by WGAN. Then, GA is used to select task-oriented CP via adjusting controllable latent variables in generator of WGAN. Next, physical-existing CP selected by GA is recovered to corresponding airfoil by DCNN with high efficiency and accuracy. Cases using the dataset sampled based on RAE2822 airfoil are carried out to show effectiveness of submodules involved. Finally, design performance of proposed multistage method is further verified by specific design goals. Test cases indicate that selected CP by GA according to the aerodynamic design criteria can be accurately reflected on inverse designed airfoils, which are confirmed by well agreements between high-fidelity simulation result and selected CP. The proposed method is a promising design approach that can quickly achieve optimal airfoils without significant loss of accuracy.

Ultra-compact multichannel optical waveguide crossings designed by a particle swarm optimized method

Ultra-compact multichannel optical waveguide crossings are designed by a particle swarm optimized inverse-design method. The 2 × 2 TE (TM) device has an ultra-small footprint of 2 ×2μm2 and exhibits a high transmission efficiency of 69.1% (89.7%) and low crosstalk of −34.4 dB (−84.8 dB) at 1550 nm. The devices can work within a large range of pixel size and waveguide width, suggesting high process tolerance of the design method. To further extend the functionality, a 3 × 3 device with the same size is designed, which exhibits a remarkable transmission efficiency of 47.6%, 61.8%, 67.2%, and low crosstalk of −33.3 dB, −39.2 dB, and −49.9 dB, respectively, for the three transmission paths. In addition, by adjusting the structure, other types of 3 × 3 devices with different transmission paths are demonstrated. The ultra-compact broad-bandwidth high-process-tolerance optical waveguide crossings have great potential in high-integration photonic-integrated circuits.