Characterizations of m-weak group inverses

To characterize m-weak group inverses,several algebraic methods are used,such as the use of idempotents,one-side principal ideals,and units.Consider an element a within a unitary ring that possesses Drazin invertibility and an involution.This paper begins by outlining the conditions necessary for the existence of the m-weak group inverse of a.Moreover,it explores the criteria under which a can be considered pseudo core invertible and weak group invertible.In the context of a weak proper*-ring,it is proved that a is weak group invertible if,and only if,a D can serve as the weak group inverse of au,where u represents a specially invertible element closely associated with a D.The paper also introduces a counterexample to illustrate that a D cannot universally serve as the pseudo core inverse of another element.This distinction underscores the nuanced differences between pseudo core inverses and weak group inverses.Ultimately,the discussion expands to include the commuting properties of weak group inverses,extending these considerations to m-weak group inverses.Several new conditions on commuting properties of generalized inverses are given.These results show that pseudo core inverses,weak group inverses,and m-weak group inverses are not only closely linked but also have significant differences that set them apart.

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.

Geostatistical seismic inversion and 3D modelling of metric flow units,porosity and permeability in Brazilian presalt reservoir

Flow units(FU)rock typing is a common technique for characterizing reservoir flow behavior,producing reliable porosity and permeability estimation even in complex geological settings.However,the lateral extrapolation of FU away from the well into the whole reservoir grid is commonly a difficult task and using the seismic data as constraints is rarely a subject of study.This paper proposes a workflow to generate numerous possible 3D volumes of flow units,porosity and permeability below the seismic resolution limit,respecting the available seismic data at larger scales.The methodology is used in the Mero Field,a Brazilian presalt carbonate reservoir located in the Santos Basin,who presents a complex and heterogenic geological setting with different sedimentological processes and diagenetic history.We generated metric flow units using the conventional core analysis and transposed to the well log data.Then,given a Markov chain Monte Carlo algorithm,the seismic data and the well log statistics,we simulated acoustic impedance,decametric flow units(DFU),metric flow units(MFU),porosity and permeability volumes in the metric scale.The aim is to estimate a minimum amount of MFU able to calculate realistic scenarios porosity and permeability scenarios,without losing the seismic lateral control.In other words,every porosity and permeability volume simulated produces a synthetic seismic that match the real seismic of the area,even in the metric scale.The achieved 3D results represent a high-resolution fluid flow reservoir modelling considering the lateral control of the seismic during the process and can be directly incorporated in the dynamic characterization workflow.

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.

Assessing the effects of model parameter assumptions on surface-wave inversion results

Surface-wave inversion is a powerful tool for revealing the Earth's internal structure.However,aside from shear-wave velocity(v_(S)),other parameters can influence the inversion outcomes,yet these have not been systematically discussed.This study investigates the influence of various parameter assumptions on the results of surface-wave inversion,including the compressional and shear velocity ratio(v_(P)/v_(S)),shear-wave attenuation(Q_(S)),density(ρ),Moho interface,and sedimentary layer.We constructed synthetic models to generate dispersion data and compared the obtained results with different parameter assumptions with those of the true model.The results indicate that the v_(P)/v_(S) ratio,Q_(S),and density(ρ) have minimal effects on absolute velocity values and perturbation patterns in the inversion.Conversely,assumptions about the Moho interface and sedimentary layer significantly influenced absolute velocity values and perturbation patterns.Introducing an erroneous Mohointerface depth in the initial model of the inversion significantly affected the v_(S) model near that depth,while using a smooth initial model results in relatively minor deviations.The assumption on the sedimentary layer not only affects shallow structure results but also impacts the result at greater depths.Non-linear inversion methods outperform linear inversion methods,particularly for the assumptions of the Moho interface and sedimentary layer.Joint inversion with other data types,such as receiver functions or Rayleigh wave ellipticity,and using data from a broader period range or higher-mode surface waves,can mitigate these deviations.Furthermore,incorporating more accurate prior information can improve inversion results.

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.

Layer-Valley Hall Effect under Inversion and Time-Reversal Symmetries

Hall effects have been the central paradigms in modern physics,materials science and practical applications,and have led to many exciting breakthroughs,including the discovery of topological Chern invariants and the revolution of metrological resistance standard.To date,the Hall effects have mainly focused on a single degree of freedom(Do F),and most of them require the breaking of spatial-inversion and/or time-reversal symmetries.Here we demonstrate a new type of Hall effect,i.e.,layer-valley Hall effect,based on a combined layer-valley Do F characterized by the product of layer and valley indices.The layer-valley Hall effect has a quantum origin arising from the layer-valley contrasting Berry curvature,and can occur in nonmagnetic centrosymmetric crystals with both spatial-inversion and time-reversal symmetries,transcending the symmetry constraints of single Do F Hall effect based on the constituent layer or valley index.Moreover,the layer-valley Hall effect is highly tunable and shows a W-shaped pattern in response to the out-of-plane electric fields.Additionally,we discuss the potential detection approaches and material-specific design principles of layer-valley Hall effect.Our results demonstrate novel Hall physics and open up exotic paradigms for new research direction of layer-valleytronics that exploits the quantum nature of the coupled layer-valley DoF.

An illustrated guide to:Parsimonious multi-scale full-waveform inversion

Having been a seemingly unreachable ideal for decades,3-D full-waveform inversion applied to massive seismic datasets has become reality in recent years.Often achieving unprecedented resolution,it has provided new insight into the structure of the Earth,from the upper few metres of soil to the entire globe.Motivated by these successes,the technology is now being translated to medical ultrasound and non-destructive testing.Despite remarkable progress,the computational cost of fullwaveform inversion continues to be a major concern.It limits the amount of data that can be exploited,and it largely inhibits quantitative and comprehensive uncertainty analyses.These notes complement a presentation on recent developments in full-waveform inversion that are intended to reduce computational cost and assimilate more data,thereby improving tomographic resolution.The suite of strategies includes flexible and user-friendly spectral-element simulations,the design of wavefieldadapted meshes that harness prior information on wavefield geometry,dynamic mini-batch optimisation that naturally takes advantage of data redundancies,and collaborative multi-scale updating to jointly constrain crustal and mantle structure.

Linearized waveform inversion for vertical transversely isotropic elastic media:Methodology and multi-parameter crosstalk analysis

Seismic migration and inversion are closely related techniques to portray subsurface images and identify hydrocarbon reservoirs.Seismic migration aims at obtaining structural images of subsurface geologic discontinuities.More specifically,seismic migration estimates the reflectivity function(stacked average reflectivity or pre-stack angle-dependent reflectivity)from seismic reflection data.On the other hand,seismic inversion quantitatively estimates the intrinsic rock properties of subsurface formulations.Such seismic inversion methods are applicable to detect hydrocarbon reservoirs that may exhibit lateral variations in the inverted parameters.Although there exist many differences,pre-stack seismic migration is similar with the first iteration of the general linearized seismic inversion.Usually,seismic migration and inversion techniques assume an acoustic or isotropic elastic medium.Unconventional reservoirs such as shale and tight sand formation have notable anisotropic property.We present a linearized waveform inversion(LWI)scheme for weakly anisotropic elastic media with vertical transversely isotropic(VTI)symmetry.It is based on two-way anisotropic elastic wave equation and simultaneously inverts for the localized perturbations(ΔVp_(0)/Vp_(0)/Vs_(0)/Vs_(0)/,Δ∈,Δδ)from the long-wavelength reference model.Our proposed VTI-elastic LWI is an iterative method that requires a forward and an adjoint operator acting on vectors in each iteration.We derive the forward Born approximation operator by perturbation theory and adjoint operator via adjoint-state method.The inversion has improved the quality of the images and reduces the multi-parameter crosstalk comparing with the adjoint-based images.We have observed that the multi-parameter crosstalk problem is more prominent in the inversion images for Thomsen anisotropy parameters.Especially,the Thomsen parameter is the most difficult to resolve.We also analyze the multi-parameter crosstalk using scattering radiation patterns.The linearized waveform inversion for VTI-elastic media presented in this article provides quantitative information of the rock properties that has the potential to help identify hydrocarbon reservoirs.

Self-potential inversion based on Attention U-Net deep learning network

Landfill leaks pose a serious threat to environmental health,risking the contamination of both groundwater and soil resources.Accurate investigation of these sites is essential for implementing effective prevention and control measures.The self-potential(SP)stands out for its sensitivity to contamination plumes,offering a solution for monitoring and detecting the movement and seepage of subsurface pollutants.However,traditional SP inversion techniques heavily rely on precise subsurface resistivity information.In this study,we propose the Attention U-Net deep learning network for rapid SP inversion.By incorporating an attention mechanism,this algorithm effectively learns the relationship between array-style SP data and the location and extent of subsurface contaminated sources.We designed a synthetic landfill model with a heterogeneous resistivity structure to assess the performance of Attention U-Net deep learning network.Additionally,we conducted further validation using a laboratory model to assess its practical applicability.The results demonstrate that the algorithm is not solely dependent on resistivity information,enabling effective locating of the source distribution,even in models with intricate subsurface structures.Our work provides a promising tool for SP data processing,enhancing the applicability of this method in the field of near-subsurface environmental monitoring.

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.

Characterization of a 4.1 Mb inversion harboring the stripe rust resistance gene YR86 on wheat chromosome 2AL

Wheat cultivar Zhongmai 895 was earlier found to carry YR86 in an 11.6 Mb recombination-suppressed region on chromosome 2AL when crossed with Yangmai 16.To fine-map the YR86 locus,we developed two large F2 populations from crosses Emai 580/Zhongmai 895 and Avocet S/Zhongmai 895.Remarkably,both populations exhibited suppressed recombination in the same 2AL region.Collinearity analysis across Chinese Spring,Aikang 58,and 10+wheat genomes revealed a 4.1 Mb chromosomal inversion spanning 708.5-712.6 Mb in the Chinese Spring reference genome.Molecular markers were developed in the breakpoint and were used to assess a wheat cultivar panel,revealing that Chinese Spring,Zhongmai 895,and Jimai 22 shared a common sequence named InvCS,whereas Aikang 58,Yangmai 16,Emai 580,and Avocet S shared the sequence named InvAK58.The inverted configuration explained the suppressed recombination observed in all three bi-parental populations.Normal recombination was observed in a Jimai 22/Zhongmai 895 F2 population,facilitating mapping of YR86 to a genetic interval of 0.15 cM corresponding to 710.27-712.56 Mb falling within the inverted region.Thirty-three high-confidence genes were annotated in the interval using the Chinese Spring reference genome,with six identified as potential candidates for YR86 based on genome and transcriptome analyses.These results will accelerate map-based cloning of YR86 and its deployment in wheat breeding.

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.

Probabilistic seismic inversion based on physics-guided deep mixture density network

Deterministic inversion based on deep learning has been widely utilized in model parameters estimation.Constrained by logging data,seismic data,wavelet and modeling operator,deterministic inversion based on deep learning can establish nonlinear relationships between seismic data and model parameters.However,seismic data lacks low-frequency and contains noise,which increases the non-uniqueness of the solutions.The conventional inversion method based on deep learning can only establish the deterministic relationship between seismic data and parameters,and cannot quantify the uncertainty of inversion.In order to quickly quantify the uncertainty,a physics-guided deep mixture density network(PG-DMDN)is established by combining the mixture density network(MDN)with the deep neural network(DNN).Compared with Bayesian neural network(BNN)and network dropout,PG-DMDN has lower computing cost and shorter training time.A low-frequency model is introduced in the training process of the network to help the network learn the nonlinear relationship between narrowband seismic data and low-frequency impedance.In addition,the block constraints are added to the PG-DMDN framework to improve the horizontal continuity of the inversion results.To illustrate the benefits of proposed method,the PG-DMDN is compared with existing semi-supervised inversion method.Four synthetic data examples of Marmousi II model are utilized to quantify the influence of forward modeling part,low-frequency model,noise and the pseudo-wells number on inversion results,and prove the feasibility and stability of the proposed method.In addition,the robustness and generality of the proposed method are verified by the field seismic data.

Stochastic seismic inversion and Bayesian facies classification applied to porosity modeling and igneous rock identification

We apply stochastic seismic inversion and Bayesian facies classification for porosity modeling and igneous rock identification in the presalt interval of the Santos Basin. This integration of seismic and well-derived information enhances reservoir characterization. Stochastic inversion and Bayesian classification are powerful tools because they permit addressing the uncertainties in the model. We used the ES-MDA algorithm to achieve the realizations equivalent to the percentiles P10, P50, and P90 of acoustic impedance, a novel method for acoustic inversion in presalt. The facies were divided into five: reservoir 1,reservoir 2, tight carbonates, clayey rocks, and igneous rocks. To deal with the overlaps in acoustic impedance values of facies, we included geological information using a priori probability, indicating that structural highs are reservoir-dominated. To illustrate our approach, we conducted porosity modeling using facies-related rock-physics models for rock-physics inversion in an area with a well drilled in a coquina bank and evaluated the thickness and extension of an igneous intrusion near the carbonate-salt interface. The modeled porosity and the classified seismic facies are in good agreement with the ones observed in the wells. Notably, the coquinas bank presents an improvement in the porosity towards the top. The a priori probability model was crucial for limiting the clayey rocks to the structural lows. In Well B, the hit rate of the igneous rock in the three scenarios is higher than 60%, showing an excellent thickness-prediction capability.

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.

Inversion method of deflection of the vertical based on SWOT wide-swath altimeter data

The deflection of the vertical(DOV)is the key information in the study of ocean gravity field.However,in most areas,the precision of the prime component of DoV is significantly lower than that of the meridian component.To obtain higher accuracy and resolution of ocean gravity information,researchers have proposed a novel altimeter called the wide-swath altimeter.This altimeter allows for the simultaneous acquisition of high-precision and high-resolution two-dimensional measurements of sea surface height(SSH).In this paper,the Surface Water and Ocean Topography(SWOT)mission with a wide-swath altimeter on board is selected for research.One cycle of swoT sea surface height data is simulated to inverse the DOV in the Arabian Sea(45°E—80°E,0°-30°N),and the inversion results are compared with those of conventional altimeter data.The results demonstrate that the difference between the meridian and prime components derived from the inversion of swoT wide-swath data is minimal,significantly outperforming the inversion results of conventional nadir altimeter data.The advantage of swoT wide-swath altimeter lies in its ability to use the multi-directional geoid slope at any sea surface measurement point to invert the components in the meridian and prime directions.To investigate the impact of this advantage on inversion precision,this paper employs a method to calculate the gradient of the geoid in multiple directions to invert DoV components.The improvement effect of calculating the gradient of the geoid in multiple directions on the precision of DoV component is analyzed.It is found that the accuracy of DoV inversion has significantly improved with the increase of geodetic gradient calculation direction.In addition,the effects of various errors and grid spacing in SwoT wide sea surface height data on the precision of Dov inversion are also analyzed.

Full waveform inversion based on hybrid gradient

The low-wavenumber components in the gradient of full waveform inversion(FWI)play a vital role in the stability of the inversion.However,when FWI is implemented in some high frequencies and current models are not far away from the real velocity model,an excessive number of low-wavenumber components in the gradient will also reduce the convergence rate and inversion accuracy.To solve this problem,this paper firstly derives a formula of scattering angle weighted gradient in FWI,then proposes a hybrid gradient.The hybrid gradient combines the conventional gradient of FWI with the scattering angle weighted gradient in each inversion frequency band based on an empirical formula derived herein.Using weighted hybrid mode,we can retain some low-wavenumber components in the initial lowfrequency inversion to ensure the stability of the inversion,and use more high-wavenumber components in the high-frequency inversion to improve the convergence rate.The results of synthetic data experiment demonstrate that compared to the conventional FWI,the FWI based on the proposed hybrid gradient can effectively reduce the low-wavenumber components in the gradient under the premise of ensuring inversion stability.It also greatly enhances the convergence rate and inversion accuracy,especially in the deep part of the model.And the field marine seismic data experiment also illustrates that the FWI based on hybrid gradient(HGFWI)has good stability and adaptability.