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.

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.

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.

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.

UAV-based transient electromagnetic 3D forward modeling and inversion and analysis of exploration capability

Unmanned aerial vehicle transient electromagnetic(UAV-TEM)is a novel airborne exploration method that offers advantages such as low cost,simple operation,high exploration efficiency and suitability for near-surface exploration in complex terrain areas.To improve the accuracy of data interpretation in this method,the authors conducted a systematic three-dimensional(3D)forward modeling and inversion of the UAV-TEM.This study utilized the finite element method based on unstructured tetrahedral elements and employed the second-order backward Euler method for time discretization.This allowed for accurate 3D modeling and accounted for the effects of complex terrain.Based on these,the influence characteristics of flight altitudes and the sizes,burial depths,and resistivities of anomalies are compared and analyzed to explore the UAV-TEM systems’exploration capability.Lastly,four typical geoelectrical models of landslides are designed,and the inversion method based on the Gauss-Newton optimization method is used to image the landslide models and analyze the imaging effect of the UAV-TEM method on landslide geohazards.Numerical results showed that UAV-TEM could have better exploration resolution and fine imaging of nearsurface structures,providing important technical support for monitoring,early warning,and preventing landslides and other geological hazards.

Machine Learning-based Inverse Model for Few-Mode Fiber Designs

The medium for next-generation communication is considered as fiber for fast,secure communication and switching capability.Mode division and space division multiplexing provide an excellent switching capability with high data transmission rate.In this work,the authors have approached an inverse modeling technique using regression-based machine learning to design a weakly coupled few-mode fiber for facilitating mode division multiplexing.The technique is adapted to predict the accurate profile parameters for the proposed few-mode fiber to obtain the maximum number of modes.It is for a three-ring-core few-mode fiber for guiding five,ten,fifteen,and twenty modes.Three types of regression models namely ordinary least-square linear multi-output regression,k-nearest neighbors of multi-output regression,and ID3 algorithm-based decision trees for multi-output regression are used for predicting the multiple profile parameters.It is observed that the ID3-based decision tree for multioutput regression is the robust,highly-accurate machine learning model for fast modeling of FMFs.The proposed fiber claims to be an efficient candidate for the next-generation 5G and 6G backhaul networks using mode division multiplexing.

Similarity measure of sedimentary successions and its application in inverse stratigraphic modeling

This paper presents a unique and formal method of quantifying the similarity or distance between sedimentary facies successions from measured sections in outcrop or drilled wells and demonstrates its first application in inverse stratigraphic modeling. A sedimentary facies succession is represented with a string of symbols, or facies codes in its natural vertical order, in which each symbol brings with it one attribute such as thickness for the facies. These strings are called attributed strings. A similarity measure is defined between the attributed strings based on a syntactic pattern-recognition technique. A dynamic programming algorithm is used to calculate the similarity. Inverse stratigraphic modeling aims to generate quantitative 3D facies models based on forward stratigraphic modeling that honors observed datasets. One of the key techniques in inverse stratigraphic modeling is how to quantify the similarity or distance between simulated and observed sedimentary facies successions at data locations in order for the forward model to condition the simulation results to the observed dataset such as measured sections or drilled wells. This quantification technique comparing sedimentary successions is demonstrated in the form of a cost function based on the defined distance in our inverse stratigraphic modeling implemented with forward modeling optimization.

Identification of the unknown shielding parameters with gammaray spectrum using a derivative-free inverse radiation transport model

Identifying the unknown geometric and material information of a multi-shield object by analyzing the radiation signature measurements is always an important problem in national and global security. In order to identify the unknown shielding layer thicknesses of a source/shield system with gamma-ray spectra, we have developed a derivative-free inverse radiation transport model based on a differential evolution algorithm with global and local neighbourhoods(IRT-DEGL). In the present paper, the IRT-DEGL model is further extended for estimating the unknown thicknesses with random initial guesses and material mass densities of multi-shielding layers as well as their combinations. Using the detected gamma-ray spectra,the illustration of inverse studies is implemented and the main influence factors for inverse results are also analyzed.

Optimized constitutive equation of material property based on inverse modeling for aluminum alloy hydroforming simulation

By using aluminum alloys,the properties of the material in sheet hydroforming were obtained based on the identification of parameters for constitutive models by inverse modeling in which the friction coefficients were also considered in 2D and 3D simulations.With consideration of identified simulation parameters by inverse modeling,some key process parameters including tool dimensions and pre-bulging on the forming processes in sheet hydroforming were investigated and optimized.Based on the optimized parameters,the sheet hydroforming process can be analyzed more accurately to improve the robust design.It proves that the results from simulation based on the identified parameters are in good agreement with those from experiments.

An Online Model Correction Method Based on an Inverse Problem:Part I—Model Error Estimation by Iteration

Errors inevitably exist in numerical weather prediction （NWP） due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model （model error, denoted as ME）. In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System （GRAPES-GFS） for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature （SST） were both based on NCEP （National Centers for Environmental Prediction） FNL （final） data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.

An approach to estimating and extrapolating model error based on inverse problem methods:towards accurate numerical weather prediction

Model error is one of the key factors restricting the accuracy of numerical weather prediction （NWP）. Considering the continuous evolution of the atmosphere, the observed data （ignoring the measurement error） can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers＇ equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.

Inverse computation for cardiac sources using single current dipole and current multipole models

Two cardiac functional models are constructed in this paper. One is a single current model and the other is a current multipole model. Parameters denoting the properties of these two models are calculated by a least-square fit to the measurements using a simulated annealing algorithm. The measured signals are detected at 36 observation nodes by a superconducting quantum interference device （SQUID）. By studying the trends of position, orientation and magnitude of the single current dipole model and the current multipole model in the QRS complex during one time span and comparing the reconstructed magnetocardiography （MCG） of these two cardiac models, we find that the current multipole model is a more appropriate model to represent cardiac electrophysiological activity.

Retrieval of leaf biochemical properties by inversed PROSPECT model and hyperspectral indices:an application to Populus euphratica polymorphic leaves

Leaf biochemical properties have been widely assessed using hyperspectral reflectance information by inversion of PROSPECT model or by using hyperspectral indices, but few studies have focused on arid ecosystems. As a dominant species of riparian ecosystems in arid lands, Populus euphratica Oliv. is an unusual tree species with polymorphic leaves along the vertical profile of canopy corresponding to different growth stages. In this study, we evaluated both the inversed PROSPECT model and hyperspectral indices for estimating biochemical properties of P. euphratica leaves. Both the shapes and biochemical properties of P. euphratica leaves were found to change with the heights from ground surface. The results indicated that the model inversion calibrated for each leaf shape performed much better than the model calibrated for all leaf shapes, and also better than hyperspectral indices. Similar results were obtained for estimations of equivalent water thickness （EWT） and leaf mass per area （LMA）. Hyperspectral indices identified in this study for estimating these leaf properties had root mean square error （RMSE） and R2 values between those obtained with the two calibration strategies using the inversed PROSPECT model. Hence, the inversed PROSPECT model can be applied to estimate leaf biochemical properties in arid ecosystems, but the calibration to the model requires special attention.

Inverse modelling of aquifer parameters in basaltic rock with the help of pumping test method using MODFLOW software

The origin and movement of groundwater are the fundamental questions that address both the temporal and spatial aspects of ground water run and water supply related issues in hydrological systems.As groundwater flows through an aquifer,its composition and temperature may variation dependent on the aquifer condition through which it flows.Thus,hydrologic investigations can also provide useful information about the subsurface geology of a region.But because such studies investigate processes that follow under the Earth's shallow,obtaining the information necessary to answer these questions is not continuously easy.Springs,which discharge groundwater table directly,afford to study subsurface hydrogeological processes.The present study of estimation of aquifer factors such as transmissivity(T)and storativity(S)are vital for the evaluation of groundwater resources.There are several methods to estimate the accurate aquifer parameters(i.e.hydrograph analysis,pumping test,etc.).In initial days,these parameters are projected either by means of in-situ test or execution test on aquifer well samples carried in the laboratory.The simultaneous information on the hydraulic behavior of the well(borehole)that provides on this method,the reservoir and the reservoir boundaries,are important for efficient aquifer and well data management and analysis.The most common in-situ test is pumping test performed on wells,which involves the measurement of the fall and increase of groundwater level with respect to time.The alteration in groundwater level(drawdown/recovery)is caused due to pumping of water from the well.Theis(1935)was first to propose method to evaluate aquifer parameters from the pumping test on a bore well in a confined aquifer.It is essential to know the transmissivity(T=Kb,where b is the aquifer thickness;pumping flow rate,Q=TW(dh/dl)flow through an aquifer)and storativity(confined aquifer:S=bS_s,unconfined:S=S_y),for the characterization of the aquifer parameters in an unknown area so as to predict the rate of drawdown of the groundwater table/potentiometric surface throughout the pumping test of an aquifer.The determination of aquifer's parameters is an important basis for groundwater resources evaluation,numerical simulation,development and protection as well as scientific management.For determining aquifer's parameters,pumping test is a main method.A case study shows that these techniques have been fast speed and high correctness.The results of parameter's determination are optimized so that it has important applied value for scientific research and geology engineering preparation.

Model-constrained and data-driven double-supervision acoustic impedance inversion

Seismic impedance inversion is an important technique for structure identification and reservoir prediction.Model-based and data-driven impedance inversion are the commonly used inversion methods.In practice,the geophysical inversion problem is essentially an ill-posedness problem,which means that there are many solutions corresponding to the same seismic data.Therefore,regularization schemes,which can provide stable and unique inversion results to some extent,have been introduced into the objective function as constrain terms.Among them,given a low-frequency initial impedance model is the most commonly used regularization method,which can provide a smooth and stable solution.However,this model-based inversion method relies heavily on the initial model and the inversion result is band limited to the effective frequency bandwidth of seismic data,which cannot effectively improve the seismic vertical resolution and is difficult to be applied to complex structural regions.Therefore,we propose a data-driven approach for high-resolution impedance inversion based on the bidirectional long short-term memory recurrent neural network,which regards seismic data as time-series rather than image-like patches.Compared with the model-based inversion method,the data-driven approach provides higher resolution inversion results,which demonstrates the effectiveness of the data-driven method for recovering the high-frequency components.However,judging from the inversion results for characterization the spatial distribution of thin-layer sands,the accuracy of high-frequency components is difficult to guarantee.Therefore,we add the model constraint to the objective function to overcome the shortages of relying only on the data-driven schemes.First,constructing the supervisor1 based on the bidirectional long short-term memory recurrent neural network,which provides the predicted impedance with higher resolution.Then,convolution constraint as supervisor2 is introduced into the objective function to guarantee the reliability and accuracy of the inversion results,which makes the synthetic seismic data obtained from the inversion result consistent with the input data.Finally,we test the proposed scheme based on the synthetic and field seismic data.Compared to model-based and purely data-driven impedance inversion methods,the proposed approach provides more accurate and reliable inversion results while with higher vertical resolution and better spatial continuity.The inversion results accurately characterize the spatial distribution relationship of thin sands.The model tests demonstrate that the model-constrained and data-driven impedance inversion scheme can effectively improve the thin-layer structure characterization based on the seismic data.Moreover,tests on the oil field data indicate the practicality and adaptability of the proposed method.

Nonlinear inverse modeling of sensor based on back-propagation fuzzy logical system

Objective To correct the nonlinear error of sensor output,a new approach to sensor inverse modeling based on Back-Propagation Fuzzy Logical System(BP FS) is presented.Methods The BP FS is a computationally efficient nonlinear universal approximator,which is capable of implementing complex nonlinear mapping from its input pattern space to the output with fast convergence speed.Results The neuro-fuzzy hybrid system,i.e.BP FS,is then applied to construct nonlinear inverse model of pressure sensor.The experimental results show that the proposed inverse modeling method automatically compensates the associated nonlinear error in pressure estimation,and thus the performance of pressure sensor is significantly improved.Conclusion The proposed method can be widely used in nonlinearity correction of various kinds of sensors to compensate the effects of nonlinearity and temperature on sensor output.

Modeling of Diffusion Transport through Oral Biofilms with the Inverse Problem Method

Aim The purpose of this study was to develop a mathe-matical model to quantitatively describe the passive trans-port of macromolecules within dental biofilms. Methodology Fluorescently labeled dextrans with different molecular mass （3 kD,10 kD,40 kD,70 kD,2 000 kD） were used as a series of diffusion probes. Streptococcus mutans,Streptococcus sanguinis,Actinomyces naeslundii and Fusobacterium nucleatum were used as inocula for biofilm formation. The diffusion processes of different probes through the in vitro biofilm were recorded with a confocal laser microscope. Results Mathematical function of biofilm penetration was constructed on the basis of the inverse problem method. Based on this function,not only the relationship between average concentration of steady-state and molecule weights can be analyzed,but also that between penetrative time and molecule weights. Conclusion This can be used to predict the effective concentration and the penetrative time of anti-biofilm medicines that can diffuse through oral biofilm. Further-more,an improved model for large molecule is proposed by considering the exchange time at the upper boundary of the dental biofilm.

Inverse Calculation of Wave-Absorbing Structure Dimensions Based on Extended ANFIS Model

A new wave energy dissipation structure is proposed, aiming to optimize the dimensions of the structure and make the reflection of the structure maintain a low level within the scope of the known frequency band. An optimal extended ANFIS model combined with the wave reflection coefficient analysis for the estimation of the structure dimensions is established. In the premise of lower wave reflection coefficient, the specific sizes of the structure are obtained inversely, and the contribution of each related parameter on the structural reflection performance is analyzed. The main influencing factors are determined. It is found that the optimal dimensions of the proposed structure exist, which make the wave absorbing performance of the structure reach a perfect status under a wide wave frequency band.

The forward and inverse problem of cardiac magnetic fields based on concentric ellipsoid torso-heart model

This paper constructs a concentric ellipsoid torso-heart model by boundary element method and investigates the impacts of model structures on the cardiac magnetic fields generated by both equivalent primary source--a current dipole and volume currents. Then by using the simulated magnetic fields based on torso-heart model as input, the cardiac current sources--an array of current dipoles by optimal constrained linear inverse method are constructed. Next, the current dipole array reconstruction considering boundaries is compared with that in an unbounded homogeneous medium. Furthermore, the influence of random noise on reconstruction is also considered and the reconstructing effect is judged by several reconstructing parameters.

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.