ON THE APPLICATION OF GENERALIZED INVERSE FOR COMPUTING EIGEN-SENSITIVITY

In this paper the mathematical definition of the minimum energy generalized inverse is given and its application for computing eigen-sensitivity is demonstrated.By comparing it with the others,this paper clarifies the merits of the present algorithm.Furthermore,an erroneous relation which is still widely used is rectified.

Efficient Generalized Inverse for Solving Simultaneous Linear Equations

Solving large scale system of Simultaneous Linear Equations (SLE) has been (and continue to be) a major challenging problem for many real-world engineering and science applications. Solving SLE with singular coefficient matrices arises from various engineering and sciences applications [1]-[6]. In this paper, efficient numerical procedures for finding the generalized (or pseudo) inverse of a general (square/rectangle, symmetrical/unsymmetrical, non-singular/singular) matrix and solving systems of Simultaneous Linear Equations (SLE) are formulated and explained. The developed procedures and its associated computer software (under MATLAB [7] computer environment) have been based on “special Cholesky factorization schemes” (for a singular matrix). Test matrices from different fields of applications have been chosen, tested and compared with other existing algorithms. The results of the numerical tests have indicated that the developed procedures are far more efficient than the existing algorithms.

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.

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.

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.

Quasi-plastic deformation mechanisms and inverse Hall-Petch relationship in nanocrystalline boron carbide under compression

Grain boundaries(GBs)play a significant role in the deformation behaviors of nanocrystalline ceramics.Here,we investigate the compression behaviors of nanocrystalline boron carbide(nB_(4)C)with varying grain sizes using molecular dynamics simulations with a machine-learning force field.The results reveal quasi-plastic deformation mechanisms in nB_(4)C:GB sliding,intergranular amorphization and intragranular amorphization.GB sliding arises from the presence of soft GBs,leading to intergranular amorphization.Intragranular amorphization arises from the interaction between grains with unfavorable orientations and the softened amorphous GBs,and finally causes structural failure.Furthermore,nB_(4)C models with varying grain sizes from 4.07 nm to 10.86 nm display an inverse Hall-Petch relationship due to the GB sliding mechanism.A higher strain rate in nB_(4)C often leads to a higher yield strength,following a 2/3 power relationship.These deformation mechanisms are critical for the design of ceramics with superior mechanical properties.

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.

Multifunctional inverse opal microcarriers-based cytokines delivery system with stem cell homing capability for osteoarthritis treatment

Osteoarthritis has been regarded as a complex and serious degenerative disease.Attempts in this area are focused on improving the curative effect of stem cell-based therapies.In this work,we present a novel inverse opal microcarriers-based cytokines delivery system to induce autologous stem cell homing for osteoarthritis treatment.Considering their important role in stem cell recruitment and chondro-genic differentiation respectively,platelet-derived growth factor BB(PDGF-BB)and transforming growth factorβ3(TGF-β3)are loaded into inverse opal microcarriers as model cytokines.Since cytokine release induces the corresponding variations in characteristic reflection spectra and structural colors,the inverse opal microcarriers possess the optical self-reporting capacity to monitor the release process.In vitro cell experiments reveal that inverse opal microcarriers could successfully recruit the gathering of mesenchymal stem cells through the release of loaded cytokines.Based on these features,we have demonstrated the enhanced therapeutic effect of PDGF-BB and TGF-β3 loaded inverse opal microcarriers in the treatment of rat osteoarthritis models.These results indicate that the multifunctional inverse opal microcarriers-based cytokines delivery system wouldfind broad prospects in osteoarthritis treatment and other biomedicalfields.

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.

Research on Anthropomorphic Obstacle Avoidance Trajectory Planning for Adaptive Driving Scenarios Based on Inverse Reinforcement Learning Theory

The forward design of trajectory planning strategies requires preset trajectory optimization functions,resulting in poor adaptability of the strategy and an inability to accurately generate obstacle avoidance trajectories that conform to real driver behavior habits.In addition,owing to the strong time-varying dynamic characteristics of obstacle avoidance scenarios,it is necessary to design numerous trajectory optimization functions and adjust the corresponding parameters.Therefore,an anthropomorphic obstacle-avoidance trajectory planning strategy for adaptive driving scenarios is proposed.First,numerous expert-demonstrated trajectories are extracted from the HighD natural driving dataset.Subsequently,a trajectory expectation feature-matching algorithm is proposed that uses maximum entropy inverse reinforcement learning theory to learn the extracted expert-demonstrated trajectories and achieve automatic acquisition of the optimization function of the expert-demonstrated trajectory.Furthermore,a mapping model is constructed by combining the key driving scenario information that affects vehicle obstacle avoidance with the weight of the optimization function,and an anthropomorphic obstacle avoidance trajectory planning strategy for adaptive driving scenarios is proposed.Finally,the proposed strategy is verified based on real driving scenarios.The results show that the strategy can adjust the weight distribution of the trajectory optimization function in real time according to the“emergency degree”of obstacle avoidance and the state of the vehicle.Moreover,this strategy can generate anthropomorphic trajectories that are similar to expert-demonstrated trajectories,effectively improving the adaptability and acceptability of trajectories in driving scenarios.

Incorporating Lasso Regression to Physics-Informed Neural Network for Inverse PDE Problem

Partial Differential Equation(PDE)is among the most fundamental tools employed to model dynamic systems.Existing PDE modeling methods are typically derived from established knowledge and known phenomena,which are time-consuming and labor-intensive.Recently,discovering governing PDEs from collected actual data via Physics Informed Neural Networks(PINNs)provides a more efficient way to analyze fresh dynamic systems and establish PEDmodels.This study proposes Sequentially Threshold Least Squares-Lasso(STLasso),a module constructed by incorporating Lasso regression into the Sequentially Threshold Least Squares(STLS)algorithm,which can complete sparse regression of PDE coefficients with the constraints of l0 norm.It further introduces PINN-STLasso,a physics informed neural network combined with Lasso sparse regression,able to find underlying PDEs from data with reduced data requirements and better interpretability.In addition,this research conducts experiments on canonical inverse PDE problems and compares the results to several recent methods.The results demonstrated that the proposed PINN-STLasso outperforms other methods,achieving lower error rates even with less data.

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).

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.

Stability Analysis of Inverse Lax-Wendroff Procedure for a High order Compact Finite Difference Schemes

This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.

Improved multi-scale inverse bottleneck residual network based on triplet parallel attention for apple leaf disease identification

Accurate diagnosis of apple leaf diseases is crucial for improving the quality of apple production and promoting the development of the apple industry. However, apple leaf diseases do not differ significantly from image texture and structural information. The difficulties in disease feature extraction in complex backgrounds slow the related research progress. To address the problems, this paper proposes an improved multi-scale inverse bottleneck residual network model based on a triplet parallel attention mechanism, which is built upon ResNet-50, while improving and combining the inception module and ResNext inverse bottleneck blocks, to recognize seven types of apple leaf(including six diseases of alternaria leaf spot, brown spot, grey spot, mosaic, rust, scab, and one healthy). First, the 3×3 convolutions in some of the residual modules are replaced by multi-scale residual convolutions, the convolution kernels of different sizes contained in each branch of the multi-scale convolution are applied to extract feature maps of different sizes, and the outputs of these branches are multi-scale fused by summing to enrich the output features of the images. Second, the global layer-wise dynamic coordinated inverse bottleneck structure is used to reduce the network feature loss. The inverse bottleneck structure makes the image information less lossy when transforming from different dimensional feature spaces. The fusion of multi-scale and layer-wise dynamic coordinated inverse bottlenecks makes the model effectively balances computational efficiency and feature representation capability, and more robust with a combination of horizontal and vertical features in the fine identification of apple leaf diseases. Finally, after each improved module, a triplet parallel attention module is integrated with cross-dimensional interactions among channels through rotations and residual transformations, which improves the parallel search efficiency of important features and the recognition rate of the network with relatively small computational costs while the dimensional dependencies are improved. To verify the validity of the model in this paper, we uniformly enhance apple leaf disease images screened from the public data sets of Plant Village, Baidu Flying Paddle, and the Internet. The final processed image count is 14,000. The ablation study, pre-processing comparison, and method comparison are conducted on the processed datasets. The experimental results demonstrate that the proposed method reaches 98.73% accuracy on the adopted datasets, which is 1.82% higher than the classical ResNet-50 model, and 0.29% better than the apple leaf disease datasets before preprocessing. It also achieves competitive results in apple leaf disease identification compared to some state-ofthe-art methods.

Novel thick-target inverse kinematics method for the astrophysical ^(12)C+^(12)C fusion reaction

The ^(12)C+^(12)C fusion is one of the most important reactions in modern nuclear astrophysics.The trend and magnitude of the reaction rate within the Gamow window strongly influence various astrophysical processes.However,direct measurement of this reaction is extremely difficult,which makes it necessary to develop indirect methods.In this study,the ^(23)Na+p reaction system was used to study the compound nucleus ^(24)Mg.We employed a thick-target inverse kinematics method combined with theγ-charged-particle coincidence technique to measure the proton andα exit channels of ^(24)Mg.Technical details of the ^(23)Na+p thick-target inverse kinematics experiment and analysis are presented herein.

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.

Adjuvant chemotherapy for isolated resectable colorectal lung metastasis: A retrospective study using inverse probability treatment weighting propensity analysis

BACKGROUND The benefit of adjuvant chemotherapy(ACT)for patients with no evidence of disease after pulmonary metastasis resection(PM)from colorectal cancer(CRC)remains controversial.AIM To assess the efficacy of ACT in patients after PM resection for CRC.METHODS This study included 96 patients who underwent pulmonary metastasectomy for CRC at a single institution between April 2008 and July 2023.The primary end-point was overall survival(OS);secondary endpoints included cancer-specific survival(CSS)and disease-free survival(DFS).An inverse probability of treat-ment-weighting(IPTW)analysis was conducted to address indication bias.Sur-vival outcomes compared using Kaplan-Meier curves,log-rank test,Cox regre-ssion and confirmed by propensity score-matching(PSM).RESULTS With a median follow-up of 27.5 months(range,18.3-50.4 months),the 5-year OS,CSS and DFS were 72.0%,74.4%and 51.3%,respectively.ACT had no significant effect on OS after PM resection from CRC[original cohort:P=0.08;IPTW:P=0.15].No differences were observed for CSS(P=0.12)and DFS(P=0.68)between the ACT and non-ACT groups.Multivariate analysis showed no association of ACT with better survival,while sublobar resection(HR=0.45;95%CI:0.20-1.00,P=0.049)and longer disease-free interval(HR=0.45;95%CI:0.20-0.98,P=0.044)were associated with improved survival.CONCLUSION ACT does not improve survival after PM resection for CRC.Further well-designed randomized controlled trials are needed to determine the optimal ACT regimen and duration.

A Two-step Inverse Method for Quantitative Damage Evaluation of Plate-like Structures Using Vibration Approach

This study presents a novel two-step approach to assess plate-like structural laminar damages,particularly for delamination damage detection of composite structures.Firstly,a 2-D continuous wavelet transform is employed to identify the damage location and sizes from vibration curvature data.An inverse method is subsequently then used to determine the bending stiffness reduction ratio along a specified direction,enabling the quantification of the delamination severity.The method employed in this study is an extension of the one-dimensional inverse method developed in a previous work of the authors.The applicability of the two-step inverse approach is demonstrated in a simulation analysis and by an experimental study on a cantilever composite plate containing a single delamination.The inverse method is shown to have the capacity to reveal the detailed damage information of delamination within a constrained searching space and can be used to determine the effective flexural stiffness of composite plate structures,even in cases of complex delamination damage.