Inverse design of mechanical metamaterial achieving a prescribedconstitutive curve

Besides exhibiting excellent capabilities such as energy absorption,phase-transforming metamaterials offer a vast design space for achieving nonlinear constitutive relations.This is facilitated by switching between different patterns under deformation.However,the related inverse design problem is quite challenging,due to the lack of appropriate mathematical formulation and the convergence issue in the post-buckling analysis of intermediate designs.In this work,periodic unit cells are explicitly described by the moving morphable voids method and effectively analyzed by eliminating the degrees of freedom in void regions.Furthermore,by exploring the Pareto frontiers between error and cost,an inverse design formulation is proposed for unit cells.This formulation aims to achieve a prescribed constitutive curve and is validated through numerical examples and experimental results.The design approach presented here can be extended to the inverse design of other types of mechanical metamaterials with prescribed nonlinear effective properties.

OptoGPT: A foundation model for inverse design in optical multilayer thin film structures

Optical multilayer thin film structures have been widely used in numerous photonic applications.However,existing inverse design methods have many drawbacks because they either fail to quickly adapt to different design targets,or are difficult to suit for different types of structures,e.g.,designing for different materials at each layer.These methods also cannot accommodate versatile design situations under different angles and polarizations.In addition,how to benefit practical fabrications and manufacturing has not been extensively considered yet.In this work,we introduce OptoGPT(Opto Generative Pretrained Transformer),a decoder-only transformer,to solve all these drawbacks and issues simultaneously.

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

Recent years have witnessed significant advances in utilizing machine learning-based techniques for thermal metamaterial-based structures and devices to attain favorable thermal transport behaviors.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 nonlinear phononic crystal configurations based on multi-label classification learning neural networks

Phononic crystals,as artificial composite materials,have sparked significant interest due to their novel characteristics that emerge upon the introduction of nonlinearity.Among these properties,second-harmonic features exhibit potential applications in acoustic frequency conversion,non-reciprocal wave propagation,and non-destructive testing.Precisely manipulating the harmonic band structure presents a major challenge in the design of nonlinear phononic crystals.Traditional design approaches based on parameter adjustments to meet specific application requirements are inefficient and often yield suboptimal performance.Therefore,this paper develops a design methodology using Softmax logistic regression and multi-label classification learning to inversely design the material distribution of nonlinear phononic crystals by exploiting information from harmonic transmission spectra.The results demonstrate that the neural network-based inverse design method can effectively tailor nonlinear phononic crystals with desired functionalities.This work establishes a mapping relationship between the band structure and the material distribution within phononic crystals,providing valuable insights into the inverse design of metamaterials.

A Non-parametric Gradient-Based Shape Optimization Approach for Solving Inverse Problems in Directed Self-Assemblyof Block Copolymers

We consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts.Specifically,we model polymer selfassembly using the self-consistent field theory and derive,in a non-parametric setting,the sensitivity of the dissimilarity between the desired and the actual morphologies to arbitrary perturbations in the guiding pattern shape.The sensitivity is then used for the optimization of the confining pattern shapes such that the dissimilarity between the desired and the actual morphologies is minimized.The efficiency and robustness of the proposed gradient-based algorithm are demonstrated in a number of examples related to templating vertical interconnect accesses(VIA).

Inverse design for material anisotropy and its application for a compact X-cut TFLN on-chip wavelength demultiplexer

Inverse design focuses on identifying photonic structures to optimize the performance of photonic devices.Conventional scalar-based inverse design approaches are insufficient to design photonic devices of anisotropic materials such as lithium niobate(LN).To the best of our knowledge,this work proposes for the first time the inverse design method for anisotropic materials to optimize the structure of anisotropic-material based photonics devices.Specifically,the orientation dependent properties of anisotropic materials are included in the adjoint method,which provides a more precise prediction of light propagation within such materials.The proposed method is used to design ultra-compact wavelength division demultiplexers in the X-cut thin-film lithium niobate(TFLN)platform.By benchmarking the device performances of our method with those of classical scalar-based inverse design,we demonstrate that this method properly addresses the critical issue of material anisotropy in the X-cut TFLN platform.This proposed method fills the gap of inverse design of anisotropic materials based photonic devices,which finds prominent applications in TFLN platforms and other anisotropicmaterial based photonic integration platforms.

Inverse design and realization of an optical cavity-based displacement transducer with arbitrary responses

Optical cavity has long been critical for a variety of applications ranging from precise measurement to spectral analysis.A number of theories and methods have been successful in describing the optical response of a stratified optical cavity,while the inverse problem,especially the inverse design of a displacement sensitive cavity,remains a significant challenge due to the cost of computation and comprehensive performance requirements.This paper reports a novel inverse design methodology combining the characteristic matrix method,mixed-discrete variables optimization algorithm,and Monte Carlo method-based tolerance analysis.The material characteristics are indexed to enable the mixed-discrete variables optimization,which yields considerable speed and efficiency improvements.This method allows arbitrary response adjustment with technical feasibility and gives a glimpse into the analytical characterization of the optical response.Two entirely different light-displacement responses,including an asymmetric sawtooth-like response and a highly symmetric response,are dug out and experimentally achieved,which fully confirms the validity of the method.The compact Fabry-Perot cavities have a good balance between performance and feasibility,making them promising candidates for displacement transducers.More importantly,the proposed inverse design paves the way for a universal design of optical cavities,or even nanophotonic devices.

Inverse Kinematics Analysis of a 7-DOF Space Manipulator for Trajectory Design

To solve the inverse kinematics problem for redundant degrees of freedom（DOFs）manipulators has been and still continues to be quite challenging in the field of robotics.Aiming at trajectory planning for a 7-DOF space manipulator system,joint rotation trajectories are obtained from predetermined motion trajectories and poses of the end effector in Cartesian space based on the proposed generalized inverse kinematics method.A minimum norm method is employed to choose the best trajectory among available trajectories.Numerical simulations with the7-DOF manipulator show that the proposed method can achieve the planned trajectory and pose under the circumstances of minimum angular velocities.Moreover,trajectory results from the proposed kinematics model and inverse kinematics method has the advantages of simple modelling,low computation cost,easy to solve and plan trajectory conveniently.The smooth and continuous joint rotation functions obtained from the proposed method are suitable for practical engineering applications.

An efficient probabilistic design approach for tunnel face stability by inverse reliability analysis

In order to maintain the safety of underground constructions that significantly involve geo-material uncertainties,this paper delivers a new computation framework for conducting reliability-based design(RBD)of shallow tunnel face stability,utilizing a simplified inverse first-order reliability method(FORM).The limit state functions defining tunnel face stability are established for both collapse and blow-out modes of the tunnel face failure,respectively,and the deterministic results of the tunnel face support pressure are obtained through three-dimensional finite element limit analysis(FELA).Because the inverse reliability method can directly capture the design support pressure according to prescribed target reliability index,the computational cost for probabilistic design of tunnel face stability is greatly reduced.By comparison with Monte Carlo simulation results,the accuracy and feasibility of the proposed method are verified.Further,this study presents a series of reliability-based design charts for vividly understanding the limit support pressure on tunnel face in both cohesionless(sandy)soil and cohesive soil stratums,and their optimal support pressure ranges are highlighted.The results show that in the case of sandy soil stratum,the blowout failure of tunnel face is extremely unlikely,whereas the collapse is the only possible failure mode.The parametric study of various geotechnical uncertainties also reveals that ignoring the potential correlation between soil shear strength parameters will lead to over-designed support pressure,and the coefficient of variation of internal friction angle has a greater influence on the tunnel face failure probability than that of the cohesion.

High performance integrated photonic circuit based on inverse design method

The basic indexes of all-optical integrated photonic circuits include high-density integration,ultrafast response and ultralow energy consumption.Traditional methods mainly adopt conventional micro/nano-structures.The overall size of the circuit is large,usually reaches hundreds of microns.Besides,it is difficult to balance the ultrafast response and ultra-low energy consumption problem,and the crosstalk between two traditional devices is difficult to overcome.Here,we propose and experimentally demonstrate an approach based on inverse design method to realize a high-density,ultrafast and ultra-low energy consumption integrated photonic circuit with two all-optical switches controlling the input states of an all-optical XOR logic gate.The feature size of the whole circuit is only 2.5μm×7μm,and that of a single device is 2μm×2μm.The distance between two adjacent devices is as small as 1.5μm,within wavelength magnitude scale.Theoretical response time of the circuit is 150 fs,and the threshold energy is within 10 fJ/bit.We have also considered the crosstalk problem.The circuit also realizes a function of identifying two-digit logic signal results.Our work provides a new idea for the design of ultrafast,ultra-low energy consumption all-optical devices and the implementation of high-density photonic integrated circuits.

Artificial neural network based inverse design method for circular sliding slopes

Current design method for circular sliding slopes is not so reasonable that it often results in slope (sliding.) As a result, artificial neural network (ANN) is used to establish an artificial neural network based inverse design method for circular sliding slopes. A sample set containing 21 successful circular sliding slopes excavated in the past is used to train the network. A test sample of 3 successful circular sliding slopes excavated in the past is used to test the trained network. The test results show that the ANN based inverse design method is valid and can be applied to the design of circular sliding slopes.

Review on Applications of 3D Inverse Design Method for Pump

The 3D inverse design method, which methodology is far superior to the conventional design method that based on geometrical description, is gradually applied in pump blade design. However, no complete description about the method is outlined. Also, there are no general rules available to set the two important input parameters, blade loading distribution and stacking condition. In this sense, the basic theory and the mechanism why the design method can suppress the formation of secondary flow are summarized. And also, several typical pump design cases with different specific speeds ranging from centrifugal pump to axial pump are surveyed. The results indicates that, for centrifugal pump and mixed pump or turbine, the ratio of blade loading on the hub to that on the shroud is more than unit in the fore part of the blade, whereas in the aft part, the ratio is decreased to satisfy the same wrap angle for hub and shroud. And the choice of blade loading type depends on the balancing of efficiency and cavitation. If the cavitation is more weighted, the better choice is aft-loaded, otherwise, the fore-loaded or mid-loaded is preferable to improve the efficiency. The stacking condition, which is an auxiliary to suppress the secondary flow, can have great effect on the jet-wake outflow and the operation range for pump. Ultimately, how to link the design method to modem optimization techniques is illustrated. With the know-how design methodology and the know-how systematic optimization approach, the application of optimization design is promising for engineering. This paper summarizes the 3D inverse design method systematically.

AN INVERSE DESIGN OF ELECTROSTATIC FOCUSING FIELD FOR ELECTROSTATIC AND MAGNETIC IMAGING

An inverse design of electrostatic focusing field for electrostatic and magneticimaging is investigated.Using the potential superimposition theorem of electrostatic field inmulti-electrode system,a mathematical model has been developed and an optimization methodhas been introduced into computation for designing the electrostatic focusing field of the imagingsystem.

Benchmarking deep learning-based models on nanophotonic inverse design problems

Photonic inverse design concerns the problem of finding photonic structures with target optical properties.However,traditional methods based on optimization algorithms are time-consuming and computationally expensive.Recently,deep learning-based approaches have been developed to tackle the problem of inverse design efficiently.Although most of these neural network models have demonstrated high accuracy in different inverse design problems,no previous study has examined the potential effects under given constraints in nanomanufacturing.Additionally,the relative strength of different deep learning-based inverse design approaches has not been fully investigated.Here,we benchmark three commonly used deep learning models in inverse design:Tandem networks,Variational Auto-Encoders,and Generative Adversarial Networks.We provide detailed comparisons in terms of their accuracy,diversity,and robustness.We find that tandem networks and Variational Auto-Encoders give the best accuracy,while Generative Adversarial Networks lead to the most diverse predictions.Our findings could serve as a guideline for researchers to select the model that can best suit their design criteria and fabrication considerations.In addition,our code and data are publicly available,which could be used for future inverse design model development and benchmarking.

Inverse Molecule Design with Invertible Neural Networks as Generative Models

Using neural networks for supervised learning means learning a function that maps input x to output y. However, in many applications, the inverse learning is also wanted, i.e., inferring y from x, which requires invertibility of the learning. Since the dimension of input is usually much higher than that of the output, there is information loss in the forward learning from input to output. Thus, creating invertible neural networks is a difficult task. However, recent development of invertible learning techniques such as normalizing flows has made invertible neural networks a reality. In this work, we applied flow-based invertible neural networks as generative models to inverse molecule design. In this context, the forward learning is to predict chemical properties given a molecule, and the inverse learning is to infer the molecules given the chemical properties. Trained on 100 and 1000 molecules, respectively, from a benchmark dataset QM9, our model identified novel molecules that had chemical property values well exceeding the limits of the training molecules as well as the limits of the whole QM9 of 133,885 molecules, moreover our generative model could easily sample many molecules (x values) from any one chemical property value (y value). Compared with the previous method in the literature that could only optimize one molecule for one chemical property value at a time, our model could be trained once and then be sampled any multiple times and for any chemical property values without the need of retraining. This advantage comes from treating inverse molecule design as an inverse regression problem. In summary, our main contributions were two: 1) our model could generalize well from the training data and was very data efficient, 2) our model could learn bidirectional correspondence between molecules and their chemical properties, thereby offering the ability to sample any number of molecules from any y values. In conclusion, our findings revealed the efficiency and effectiveness of using invertible neural networks as generative models in inverse molecule design.

A Coordinate-Free Approach to the Design of Generalized Griffis-Duffy Platforms

Architectural singularity belongs to the Type II singularity,in which a parallel manipulator(PM)gains one or more degrees of freedom and becomes uncontrollable.PMs remaining permanently in a singularity are beneficial for linearto-rotary motion conversion.Griffis-Duffy(GD)platform is a mobile structure admitting a Bricard motion.In this paper,we present a coordinate-free approach to the design of generalized GD platforms,which consists in determining the shape and attachment of both the moving platform and the fixed base.The generalized GD platform is treated as a combination of six coaxial single-loop mechanisms under the same constraints.Owing to the inversion,hidden in the geometric structure of these single-loop mechanisms,the mapping from a line to a circle establishes the geometric transformation between the fixed base and the moving platform based on the center of inversion,and describes the shape and attachment of the generalized GD platform.Moreover,the center of inversion not only identifies the location of rotation axis,but also affects the shape of the platform mechanism.A graphical construction of generalized GD platforms using inversion,proposed in the paper,provides geometrically feasible solutions of the manipulator design for the requirement of the location of rotation axis.

Inverse design-based metamaterial transparent device and its multilayer realization

We propose an inverse method to determine the material parameters of a transparent device without any knowledge of the corresponding transformation function. The required parameters are independently obtained and expressed as functions of the introduced generator. Moreover, to remove the inhomogeneity and anisotropy of material parameters, a layered transparent device composed of only homogeneous and isotropic materials is presented based on the effective medium theory. The feasibility of using the layered device in antenna protection is also investigated. Full-wave simulation is carried out for verification. This work paves a new way toward designing metamaterial devices without specifying the underlying coordinate transformation, and has great guiding significance for the practical fabrication of transparent devices.

Basic Problems in Design and Inverse Engineering Solution for Outer Characteristic of Vehicle Suspension Shock Absorbers

Based on the theory and the practical experiences of linearity design of feasible design area and inverse solution of non linear outer characteristic of suspension shock absorber, in accordance with non linearity outer characteristic formed by open up damping coefficient, full open damping coefficient and smoothness to safety ratio of suspension shock absorber, a method and a research conclusion of the feasible design and inverse solution for the basic problems of designing and inverse solution of non linear outer characteristic of suspension damping components are provided.

Study on Approach for Computer-Aided Design and Machining of General Cylindrical Cam Using Relative Velocity and Inverse Kinematics

Cylindrical Cam Mechanism which is one of the best eq uipments to accomplish an accurate motion transmission is widely used in the fie lds of industries, such as machine tool exchangers, textile machinery and automa tic transfer equipments. This paper proposes a new approach for the shape design and manufacturing of the cylindrical cam. The design approach uses the relative velocity concept and the manufacturing approach uses the inverse kinematics concept. For the shape desig n, the contact points between the cam and the follower roller are calculated bas ed on relative velocity of which the direction is on the common tangential line, and then the whole shape of cam is determined from transformation of the coordi nate system. For the manufacturing procedures, the location and the orientation of cutter path can be allocated corresponding to the designed shape data. The in tegral NC code for multi-axis CNC machining center is created using the inverse kinematics concept from the data of the location and the orientation of cutter path. As the advantages of the proposed approach, the machine tool is designed t o having an alternative size in fabricating the general cam, while the tool must be fitted to diameter size of the follower in the conventional approach. Finally, CAD/CAM program, "Cylindrical DAM", is developed on C++ lan guage. This program can perform shape design, manufacturing and kinematics simul ation, which can make integral NC code for multi-axis CNC machining center. The proposed method can be applied easily on fields of industries.

Computer Aided Design and Performance Analysis of Inverse Fluidized Bed Biofilm Reactors with Special Reference to Bioplastic Synthesis

Poly Laevo Lactic Acid (PLLA), in spite of being an excellent bioplastic, has exorbitantly high market price due to the high cost of raw material (lactose, glucose, sucrose). Hence, its manufacture is being attempted starting from waste effluents such as cheese whey and molasses. Earlier studies on the same in fluidized bed and semifluidized bed biofilm reactors yielded encouraging results. The present study therefore involves design and analysis of inverse fluidized bed biofilm reactors for lactic acid synthesis. The performance features of the bioreactor have been studied both mathematically as well as experimentally. The inverse fluidized bed biofilm reactor has been found to provide more than 75% conversion of sucrose/lactose even at high capacities (high feed flow rates) exceeding 56,000 L/hr, within a reasonably low reactor volume. The fractional substrate conversion increases, though sluggishly, with increase in feed flow rate due to bed expansion and also with increase in cell mass concentration in biofilm due to enhancement in intrinsic rate of bioconversion. The inverse fluidized bed biofilm reactor of proposed design could be safely recommended for the commercial synthesis of polymer grade lactic acid from waste effluents such as cheese whey and molasses. The low operating cost of the bioreactor (due to downflow mode of operation) enhances the economy of the process. This would also help in significantly lowering the market price of the green plastic (PLLA) and shall promote its large scale manufacture and utilisation.