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.

An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications.

Design of Protograph LDPC-Coded MIMO-VLC Systems with Generalized Spatial Modulation

This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID scheme, the information bits conveyed by the signal-domain(SiD) symbols and the spatial-domain(SpD) light emitting diode(LED)-index patterns are coded by a protograph low-density parity-check(P-LDPC) code. Specifically, we propose a signal-domain symbol expanding and re-allocating(SSER) method for constructing a type of novel generalized spatial modulation(GSM) constellations, referred to as SSERGSM constellations, so as to boost the performance of the BICGSM-ID MIMO-VLC systems.Moreover, by applying a modified PEXIT(MPEXIT) algorithm, we further design a family of rate-compatible P-LDPC codes, referred to as enhanced accumulate-repeat-accumulate(EARA) codes,which possess both excellent decoding thresholds and linear-minimum-distance-growth property. Both analysis and simulation results illustrate that the proposed SSERGSM constellations and P-LDPC codes can remarkably improve the convergence and decoding performance of MIMO-VLC systems. Therefore, the proposed P-LDPC-coded SSERGSM-mapped BICGSMID configuration is envisioned as a promising transmission solution to satisfy the high-throughput requirement of MIMO-VLC applications.

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.

An Effective Meshless Approach for Inverse Cauchy Problems in 2D and 3D Electroelastic Piezoelectric Structures

In the past decade,notable progress has been achieved in the development of the generalized finite difference method(GFDM).The underlying principle of GFDM involves dividing the domain into multiple sub-domains.Within each sub-domain,explicit formulas for the necessary partial derivatives of the partial differential equations(PDEs)can be obtained through the application of Taylor series expansion and moving-least square approximation methods.Consequently,the method generates a sparse coefficient matrix,exhibiting a banded structure,making it highly advantageous for large-scale engineering computations.In this study,we present the application of the GFDM to numerically solve inverse Cauchy problems in two-and three-dimensional piezoelectric structures.Through our preliminary numerical experiments,we demonstrate that the proposed GFDMapproach shows great promise for accurately simulating coupled electroelastic equations in inverse problems,even with 3%errors added to the input data.

Fuzzy-Inverse-Model-Based Networked Tracking Control Frameworks of Time-Varying Signals

Dear Editor,Tracking control in networked environment is a very challenging problem due to the contradiction of rapid response to the time-varying signal and the inevitable delay introduced by networks. This letter has proposed several fuzzy-inverse-model-based network tracking control frameworks which are helpful in handling the system with nonlinear dynamics and uncertainties.

Triple reverse order law for the Drazin inverse

In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented.

IGED:Towards Intelligent DDoS Detection Model Using Improved Generalized Entropy and DNN

As the scale of the networks continually expands,the detection of distributed denial of service(DDoS)attacks has become increasingly vital.We propose an intelligent detection model named IGED by using improved generalized entropy and deep neural network(DNN).The initial detection is based on improved generalized entropy to filter out as much normal traffic as possible,thereby reducing data volume.Then the fine detection is based on DNN to perform precise DDoS detection on the filtered suspicious traffic,enhancing the neural network’s generalization capabilities.Experimental results show that the proposed method can efficiently distinguish normal traffic from DDoS traffic.Compared with the benchmark methods,our method reaches 99.9%on low-rate DDoS(LDDoS),flooded DDoS and CICDDoS2019 datasets in terms of both accuracy and efficiency in identifying attack flows while reducing the time by 17%,31%and 8%.

Necessary and Sufficient Conditions for Oscillations of the Generalized Liénard Systems

In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.

Uncertainty quantification of inverse analysis for geomaterials using probabilistic programming

Uncertainty is an essentially challenging for safe construction and long-term stability of geotechnical engineering.The inverse analysis is commonly utilized to determine the physico-mechanical parameters.However,conventional inverse analysis cannot deal with uncertainty in geotechnical and geological systems.In this study,a framework was developed to evaluate and quantify uncertainty in inverse analysis based on the reduced-order model(ROM)and probabilistic programming.The ROM was utilized to capture the mechanical and deformation properties of surrounding rock mass in geomechanical problems.Probabilistic programming was employed to evaluate uncertainty during construction in geotechnical engineering.A circular tunnel was then used to illustrate the proposed framework using analytical and numerical solution.The results show that the geomechanical parameters and associated uncertainty can be properly obtained and the proposed framework can capture the mechanical behaviors under uncertainty.Then,a slope case was employed to demonstrate the performance of the developed framework.The results prove that the proposed framework provides a scientific,feasible,and effective tool to characterize the properties and physical mechanism of geomaterials under uncertainty in geotechnical engineering problems.

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.

Sequential Inverse Optimal Control of Discrete-Time Systems

This paper presents a novel sequential inverse optimal control(SIOC)method for discrete-time systems,which calculates the unknown weight vectors of the cost function in real time using the input and output of an optimally controlled discrete-time system.The proposed method overcomes the limitations of previous approaches by eliminating the need for the invertible Jacobian assumption.It calculates the possible-solution spaces and their intersections sequentially until the dimension of the intersection space decreases to one.The remaining one-dimensional vector of the possible-solution space’s intersection represents the SIOC solution.The paper presents clear conditions for convergence and addresses the issue of noisy data by clarifying the conditions for the singular values of the matrices that relate to the possible-solution space.The effectiveness of the proposed method is demonstrated through simulation results.

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.

Generalized load graphical forecasting method based on modal decomposition

In a“low-carbon”context,the power load is affected by the coupling of multiple factors,which gradually evolves from the traditional“pure load”to the generalized load with the dual characteristics of“load+power supply.”Traditional time-series forecasting methods are no longer suitable owing to the complexity and uncertainty associated with generalized loads.From the perspective of image processing,this study proposes a graphical short-term prediction method for generalized loads based on modal decomposition.First,the datasets are normalized and feature-filtered by comparing the results of Xtreme gradient boosting,gradient boosted decision tree,and random forest algorithms.Subsequently,the generalized load data are decomposed into three sets of modalities by modal decomposition,and red,green,and blue(RGB)images are generated using them as the pixel values of the R,G,and B channels.The generated images are diversified,and an optimized DenseNet neural network was used for training and prediction.Finally,the base load,wind power,and photovoltaic power generation data are selected,and the characteristic curves of the generalized load scenarios under different permeabilities of wind power and photovoltaic power generation are obtained using the density-based spatial clustering of applications with noise algorithm.Based on the proposed graphical forecasting method,the feasibility of the generalized load graphical forecasting method is verified by comparing it with the traditional time-series forecasting method.

Efficient Inverse Analysis for Solving a Coupled Conduction,Convection and Radiation Problem Involving Non⁃gray Participating Media

The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving the coupled conduction,convection,and radiation problem,leading to suboptimal efficiency that fails to meet real-time control demands.To overcome this difficulty,comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem.However,the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency.It is necessary to present an efficient method for the equivalence.The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer,and the gray-equivalent radiative characteristics are successfully recovered.It is our intention that the issue of low inverse efficiency,which has been observed when the least-squares method is employed,will be resolved.To enhance the performance of the Levenberg-Marquardt algorithm,a modification is implemented for determining the damping factor.Detailed investigations are also conducted to evaluate its accuracy,stability of convergence,efficiency,and robustness of the algorithm.Subsequently,a comparison is made between the results achieved using each method.

Analysis of Progressively Type-Ⅱ Inverted Generalized Gamma Censored Data and Its Engineering Application

A novel inverted generalized gamma(IGG)distribution,proposed for data modelling with an upside-down bathtub hazard rate,is considered.In many real-world practical situations,when a researcher wants to conduct a comparative study of the life testing of items based on cost and duration of testing,censoring strategies are frequently used.From this point of view,in the presence of censored data compiled from the most well-known progressively Type-Ⅱ censoring technique,this study examines different parameters of the IGG distribution.From a classical point of view,the likelihood and product of spacing estimation methods are considered.Observed Fisher information and the deltamethod are used to obtain the approximate confidence intervals for any unknown parametric function of the suggestedmodel.In the Bayesian paradigm,the same traditional inferential approaches are used to estimate all unknown subjects.Markov-Chain with Monte-Carlo steps are considered to approximate all Bayes’findings.Extensive numerical comparisons are presented to examine the performance of the proposed methodologies using various criteria of accuracy.Further,using several optimality criteria,the optimumprogressive censoring design is suggested.To highlight how the proposed estimators can be used in practice and to verify the flexibility of the proposed model,we analyze the failure times of twenty mechanical components of a diesel engine.

A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS

In this article,we consider the diffusion equation with multi-term time-fractional derivatives.We first derive,by a subordination principle for the solution,that the solution is positive when the initial value is non-negative.As an application,we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain.Finally,several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Inverse reliability analysis and design for tunnel face stability considering soil spatial variability

The traditional deterministic analysis for tunnel face stability neglects the uncertainties of geotechnical parameters,while the simplified reliability analysis which models the potential uncertainties by means of random variables usually fails to account for soil spatial variability.To overcome these limitations,this study proposes an efficient framework for conducting reliability analysis and reliability-based design(RBD)of tunnel face stability in spatially variable soil strata.The three-dimensional(3D)rotational failure mechanism of the tunnel face is extended to account for the soil spatial variability,and a probabilistic framework is established by coupling the extended mechanism with the improved Hasofer-Lind-Rackwits-Fiessler recursive algorithm(iHLRF)as well as its inverse analysis formulation.The proposed framework allows for rapid and precise reliability analysis and RBD of tunnel face stability.To demonstrate the feasibility and efficacy of the proposed framework,an illustrative case of tunnelling in frictional soils is presented,where the soil's cohesion and friction angle are modelled as two anisotropic cross-correlated lognormal random fields.The results show that the proposed method can accurately estimate the failure probability(or reliability index)regarding the tunnel face stability and can efficiently determine the required supporting pressure for a target reliability index with soil spatial variability being taken into account.Furthermore,this study reveals the impact of various factors on the support pressure,including coefficient of variation,cross-correlation between cohesion and friction angle,as well as autocorrelation distance of spatially variable soil strata.The results also demonstrate the feasibility of using the forward and/or inverse first-order reliability method(FORM)in high-dimensional stochastic problems.It is hoped that this study may provide a practical and reliable framework for determining the stability of tunnels in complex soil strata.

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).