Chiplet employs advanced packaging techniques to heterogeneously integrate chips with different processes and functions, featuring multidie integration and high density. However, the increased power density and thermal coupling within these systems introduce significant electrothermal issues, leading to heat accumulation and power management complexities. Meanwhile, due to the complex multilayer heterogeneous integration and multiscale geometric features of chiplet systems, the number of degrees of freedom increases sharply, resulting in significant computational challenges and high demands for computational resources. Traditional numerical methods, such as finite element analysis (FEA), although capable of providing high-accuracy results, are computationally expensive. This work proposes a parametric dynamic mode decomposition (DMD)-based reduced-order modeling method for the electrothermal analysis, extending DMD to handle variations in parameters such as convection coefficients and thermal conductivity, thereby enabling robust analysis for diverse design requirements. As a matrix decomposition technique based on singular value decomposition (SVD), DMD extracts low-rank structures that capture both temporal dynamics and spatial correlations. The numerical results show that the proposed method provides an efficient and reliable solution for electrothermal analysis of chiplets, achieving a 4–9 times speedup over commercial software like COMSOL Multiphysics, making it an alternative for optimization design and reliability analysis of advanced systems.

Determination of petrophysical parameters is regarded as a critical task for the exploration and production of oil and gas reservoirs. Traditionally, the joint inversion of electromagnetic (EM) and seismic data under petrophysics constraints can be exploited to reconstruct the distribution of reservoir petrophysical parameters. However, methods involved with such schemes face challenges when solving high-contrast nonlinear inverse scattering problems due to the complexity of the relationship between resistivity/velocity and petrophysical properties and the nonuniqueness of these inverse problems. Here, to resolve these challenges, we have developed a field data transformation-joint inversion method (FDT-JIS) to directly reconstruct the distribution of porosity and water saturation. Specifically, the chain rule to transform geophysical parameters into petrophysical parameters is leveraged, and the field data transformation module is subsequently utilized to transform the scattered field data generated under the test configuration into those under the training configuration. Finally, a joint network is adopted to establish the mapping relationship between EM and acoustics data and petrophysical parameters to attain the inversion of petrophysical parameters. With numerical examples, we demonstrate that FDT-JIS not only allows different transceiver configurations to be used in training and testing, but also accurately reconstructs petrophysical parameters of complex models with high contrast in noisy environments.

In this work, a hybrid forward-inverse neural network (HFINN) with a transceiver transformation module (TTM) is proposed to increase the generalizability of machine learning-based electromagnetic (EM) inversion methods. The HFINN consists of two parts: a forward module and an inverse module. The inverse module combines the Res-Net with a fully convolutional network (FCN), which is called “Res-FCN,” to show the performance in wideband inversion; however, the data misfit from Res-FCN often remains high because it only minimizes the model misfit; thus, a forward module based on a classical neural network, U-Net, is trained first to alleviate the problem of large data misfit. To train HFINN better, a new loss function is proposed so that the frequency information is used as a prior physical constraint to optimize HFINN. Meanwhile, to further improve the generalizability of HFINN, TTM is incorporated into the HFINN as physical assistance so that it does not need to be retrained for different transceiver configurations. A total of 4000 random test samples are employed to verify the performance of the proposed HFINN, and the average model misfit is 27.15%. Six numerical examples are also provided to verify the inversion performance of HFINN over the whole frequency band. After adding the forward module, the average data misfit of the result is reduced by 7.5%. The numerical results show that HFINN performs well across the whole frequency band, even when the testing transceiver configuration is different from the training transceiver configuration.

In elastic wave inverse scattering problems, the material-property reconstruction, e.g. distributions of mass density, compressional wave speed, and shear wave speed from a limited set of measurement data, has attracted considerable research interest. However, simultaneous inversion of multiple parameters endures high computation costs, and reconstructed compressional and shear speeds may become unrealistic if no physical constraint is imposed. Meanwhile, because large objects with high contrasts over the background medium tend to induce high nonlinearity during the inversion process, it is difficult to obtain high-quality high-contrast material properties. To overcome such difficulties, we have developed a multi-module deep learning scheme with physical constraint for multi-parameter elastic wave inversion of high-contrast objects in inhomogeneous media. This scheme consists of (1) a preliminary imaging module (PIM), in which a deep residual network (ResNet) is employed to convert the scattered field data into the preliminary inversion images, (2) an image-enhancement module (IEM), in which a U-Net is employed to further enhance the image quality, and (3) a convolutional neural network (CNN) that is employed as the physical constraint module (PCM) to allow elastic wave parameters to satisfy actual physical constraint. Numerical examples have demonstrated that the proposed scheme not only accurately achieves multi-parameter elastic wave inversion, but also has good generalizability. Finally, the scheme can be applied to complex objects with high contrasts in both noise-free and noisy environments.

This article first presents machine-learning (ML) inversion of resistivity profiles from multifrequency electromagnetic measurements on undulating terrain surfaces based on synthetic data training by the mixed spectral element method (MSEM). The inversion method combines several advanced technologies with various merits. A semiregular mesh generation method is designed and developed for adaption to complex undulating terrain and multifrequency measured data, and the proposed meshing technology is also suitable for modeling different training models under the same undulating terrain. By simulating the application scenarios of measurements, the apparent resistivity data at eight frequencies from 1 to 2048 Hz are simulated with the 2.5-D MSEM to ensure the accuracy and efficiency of the simulation of undulating terrains. Fast simulation of stochastic models for training datasets is achieved by twisting and extruding the initial model obtained by Bostick inversion. Since the unknown weight matrices are solved only once in the training process, the extreme learning machine (ELM) is used for ML inversion to reduce the training cost and obtain high-precision inversion results. Then it is applied to reconstruct a metallogenic model to verify the method’s validity and accuracy and to reconstruct the resistivity profile of underground ore bodies with actual measurements. The results show that the proposed method can be effectively used to detect metal ores at a depth of less than 3000 m underground.

An efficient two-dimensional (2-D) electromagnetic (EM) full-wave inversion (FWI) method based on the hybrid spectral-element spectral-integral (SESI) forward solver is proposed. In the forward scattering computation, the scalar Helmholtz equation is discretized and solved by the spectral element method (SEM). Its computational domain is truncated by a circle on which a 2-D surface integral equation is performed and the spectral-integral method (SIM) is used to accelerate its solution. Transmitters and receivers are placed outside the circular boundary and they are connected to the equivalent current on the circle by Green’s functions. In each iteration of FWI, the sensitivity matrix is updated by the electric field values solved by SESI only in the internal nodes inside the computation domain. Then the conjugate gradient (CG) method is used to solve for the relative permittivity and conductivity values in the corresponding interior elements. Meanwhile, the structural consistency constraint (SCC) algorithm is adopted to gradually compress the inversion domain and guarantee the inversion accuracy. Several numerical experiments are carried out not only to show the computation efficiency of the SESI forward solver but also to verify the correctness of the iterative inversion procedure as well as the effectiveness of SCC.