Inversion Algorithm Research Articles

Magnetic surface geometry inversion of Kimberlites in Botswana

AbstractSurface geometry inversion of geophysical data has recently been introduced as an effective approach for generating surface‐based geological models. The models obtained through surface geometry inversion clearly delineate the contacts between distinct rock units, making them easily interpretable by geologists. Surface geometry inversion has shown promising preliminary results in other works, but the practical application of surface geometry inversion on real geophysical data has not been thoroughly investigated. To move towards a better understanding of the practicalities involved, we applied surface geometry inversion to a real magnetic dataset acquired over two kimberlite pipes located in north‐central Botswana. The objective was to assess the effectiveness and limitations of the surface geometry inversion approach in accurately characterizing the subsurface geometry and identifying the boundaries of the kimberlite pipes. We first perform an anomaly separation approach to isolate the magnetic anomalies associated with the kimberlite pipes. A surface geometry inversion algorithm was applied to the original and separated datasets using various initial models and other control parameters. Several tests were performed to investigate the effects that data processing, initial models, and other parameter choices have on the surface geometry inversion results. We successfully recover the geometry, extension and dip of the two kimberlite pipes. We discuss the results of our various tests and provide advice for practitioners interested in applying surface geometry inversion methods to their data. Our work indicates that surface geometry inversion can be used as a complementary approach to voxel inversion, and we propose an iterative surface geometry inversion algorithm as a possible alternative approach to voxel inversion for simple geological scenarios. This work provides valuable insights into the appropriate application of surface geometry inversion on real geophysical datasets.

Controllable Seismic Velocity Synthesis Using Generative Diffusion Models

AbstractAccurate seismic velocity estimations are vital to understanding Earth's subsurface structures, assessing natural resources, and evaluating seismic hazards. Machine learning‐based inversion algorithms have shown promising performance in regional (i.e., for exploration) and global velocity estimations, while their effectiveness hinges on access to large and diverse training data sets whose distributions generally cover the target solutions. Additionally, enhancing the precision and reliability of velocity estimation also requires incorporating prior information, for example, geological classes, well logs, and subsurface structures, but current statistical or neural network‐based methods are not flexible enough to handle such multimodal information. To address both challenges, we propose to use conditional generative diffusion models for seismic velocity synthesis in which we readily incorporate those priors. This approach enables the generation of seismic velocities that closely match the expected target distribution, offering data sets informed by both expert knowledge and measured data to support training for data‐driven geophysical methods. We demonstrate the flexibility and effectiveness of our method through training diffusion models on the OpenFWI data set under various conditions, including class labels, well logs, reflectivity images, and the combination of these priors. The performance of the approach under out‐of‐distribution conditions further underscores its generalization ability, showcasing its potential to provide tailored priors for velocity inverse problems and create specific training data sets for machine learning‐based geophysical applications.

Innovative imaging of iron deposits using cross‐gradient joint inversion of potential field data with petrophysical correlation

AbstractThis study demonstrates the application of the cross‐gradient joint inversion method to investigate iron mineralization zones within a volcano‐sedimentary environment. The presence of minerals with intense contrasts in density or magnetic susceptibility, such as hematite or magnetite, facilitates modelling the distribution of ore bodies with depth. Our approach involves establishing a unified interpretation of reconstructed density and susceptibility models through both independent and joint inversion with sparsity regularization in conjunction with a petrophysical model resulting from core data. This approach provides an ideal strategy to uncover the realistic geologic setting of iron ore deposits. We initially simulated a synthetic model closely resembling real‐case scenarios to assess the efficacy of the cross‐gradient joint inversion algorithm in comparison to independent inversion. Subsequently, the inversion algorithms were implemented on gravity and magnetic data, collected over an area of 500 × 600 m2 in Shavaz iron‐bearing deposits located in the central Iranian block. The primary iron oxide–apatite type mineralization in the study area is associated with the Nain–Dehshir–Baft fault as a NW–SE trending strike‐slip fault. Although both inversion methods yield satisfactory models, incorporating the cross‐gradient constraint in joint inversion resulted in a more constrained delineation of iron–oxide ore deposits in the fault system. This improvement facilitates the differentiation between hematite and a small percentage of magnetite, providing a more accurate estimation of ore depth. Inversion results suggest that the magnetite mineralization is coated with extensive hematite mineralization and both are positioned relatively within the same depth interval, covered by approximately a 15–25 m sequence of sediments.

Quantitative multistage fracturing efficiency evaluation using cross-well strain measurements

Cross-well strain measurements acquired through low-frequency distributed acoustic sensing (LF-DAS) is a maturing technique used to monitor and diagnose the efficiency of hydraulic fracturing treatments. Although LF-DAS has demonstrated potential in characterizing far-field fracture communication and geometry, the prevailing analysis in this field has historically relied on qualitative interpretations, focusing on the timing and location of frac hits. In response to the evolving landscape of quantitative studies in this area, we present an advanced quantitative technique using our novel Green-function based inversion algorithm to calculate time-dependent far-field fracture width. The adopted algorithm uses the 3D displacement discontinuity method to relate fracture aperture to strains measured by LF-DAS along a monitor well during stimulation treatments. This approach is demonstrated on a subset of four treatment stages where distributed acoustic sensing (DAS) and distributed temperature sensing (DTS) were acquired within the injection well, alongside LF-DAS from a nearby monitor well. LF-DAS inversion results indicate the loss of zonal isolation in three of the monitored stages, leading to significantly smaller fracture widths at the monitor well for targeted treatment stages, and reactivated fractures in the adjacent previous stages. These interpretations are cross validated through the integration of in-well DAS and DTS analysis, where severe interstage fluid communication is observed. The inverted fracture widths quantify the impact on far-field fracture geometry associated with poor stage isolation and decreased fracturing efficiency. This new approach demonstrates the potential of LF-DAS for quantitative analysis and interpretation, facilitating improved understanding and optimization of hydraulic stimulation, going beyond its conventional qualitative role in fracturing diagnostics.

Crustal-mantle layering deposits in the Von Kármán crater, South Pole-Aitken basin

Comprehending the properties of the Moon's crust and mantle materials is essential for decoding its interior. Whether the South Pole-Aitken (SPA) basin potentially excavated the upper mantle materials remains mysterious. The Chang'E Four Lunar Penetrating Radar (LPR) has provided an unprecedented opportunity to investigate the SPA basin in the Von Kármán (VK) crater. Utilizing a data-driven generative deep learning inversion algorithm, the subsurface physical properties along the Yutu-2 path were determined. 4 distinct deposit zones were discovered beneath the surface. All zones feature an upper low-permittivity (paleo-)regolith layer overlaying on a lower high-permittivity layer of rockier ejecta or basal basalt. Zone 1, an ejecta layer from the Finsen crater within the SPA Compositional Anomaly, has a bulk density (2.81±0.22g/cm3) denser than that of highland crust represented by materials originating from VKL and VKL' craters in the Mg-Pyroxene Annulus, which are present in Zones 2 and 3. This suggests the possible presence of mantle materials in Zone 1, providing the first diagnostic evidence that the SPA impact may have penetrated the upper lunar mantle.

Large-scale 3D inversion of semi-airborne electromagnetic data — Topography and induced polarization effects in a graphite exploration scenario

The transition toward renewable energies demands a secure supply of critical raw materials and requires efficient noninvasive methods for deep earth resource exploration. The novel, deep electromagnetic (EM) sounding for the mineral exploration semi-airborne EM (semi-AEM) exploration concept aims at the efficient exploration of resources down to a depth of 1 km. Here, we evaluate a large-scale semi-AEM exploration study in a graphite mining district in eastern Bavaria, Germany. The derived 3D semi-AEM model is based on approximately 70,000 complex-valued data points recorded using seven transmitters. Strong conductivity contrasts with dominant east–west-trending anomalies are visible. Shallow high-conductivity structures correlate well with the known occurrence of graphite and match existing helicopter-borne EM results. The main anomaly reaches down to several hundred meters depth. To investigate different interpretation scenarios for large-scale semi-AEM data, we determine the effect of topography and analyze the feasibility of fast 2D inversion applications. To validate the robustness of the 3D semi-AEM model, the data set is inverted with two different 3D inversion algorithms and the results are compared. The presence of graphite leads to significant induced polarization (IP) effects with considerably high chargeabilities superposing EM induction. We include these effects in a realistic 3D inversion using a synthetic data study to analyze if the IP effect alters the overall conductivity structure and demonstrate that the obtained 3D model is reliable.

Hybrid Inverse Weed Optimization Algorithm with Math-Flame Optimization Algorithm

In this work, two Meta-Heuristic Algorithms were hybridized, the first is the Invers Weed optimization algorithm (IWO), which is a passing multiple algorithm, and the second is the Moth-flame Optimization Algorithm (MFO). Which depend in their behavior on the intelligence of the swarm and the intelligence of society, and they have unique characteristics that exceed the characteristics of the intelligence of other swarms because they are efficient in achieving the right balance between exploration and exploitation. So the new algorithm improves the initial population that is randomly generated, A process of hybridization was made between the IWO and MFO Algorithm to call The new hybrid algorithm (IWOMFO). The new hybrid algorithm was used for 16 high-scaling optimization functions with different community sizes and 250 repetitions. The Algorithm showed access to optimal solutions by achieving the value Minority () for most of these functions and the results of this algorithm are compared with the basic algorithms IWO, MFO

Damage identification of reinforced concrete slabs using experimental modal testing and finite element model updating

Condition assessment and health monitoring of reinforced concrete structures is an essential part of their effective maintenance throughout their service life. Vibration-based damage detection and health monitoring is one of the most popular global approaches where experimentally measured modal parameters, such as frequencies, mode shapes, etc. are compared to their corresponding finite element counterparts to estimate possible stiffness loss. The present investigation implements a vibration-based parameter estimation algorithm for updating a finite-element (FE) model for damage assessment of reinforced concrete slabs using measured frequency response functions (FRF) data through a mixed numerical-experimental technique. An inverse eigen-sensitivity algorithm has been implemented to minimize the error function realized as the weighted differences in the mode shapes and frequencies of the FE model and the modal test data. Three reinforced concrete slabs were subjected to real physical damage conditions to verify the efficacy of the proposed methodology. The technique is found to be resilient in the presence of modal and coordinate sparsity. In general, damage can be assessed even if the portions of the structure are inaccessible to the users, thereby extending the possibility of its application to most of the practical configurations of reinforced concrete slabs.

2-D Slicewise Waveform Inversion of Sound Speed and Acoustic Attenuation for Ring Array Ultrasound Tomography Based on a Block LU Solver.

Ultrasound tomography is an emerging imaging modality that uses the transmission of ultrasound through tissue to reconstruct images of its mechanical properties. Initially, ray-based methods were used to reconstruct these images, but their inability to account for diffraction often resulted in poor resolution. Waveform inversion overcame this limitation, providing high-resolution images of the tissue. Most clinical implementations, often directed at breast cancer imaging, currently rely on a frequency-domain waveform inversion to reduce computation time. For ring arrays, ray tomography was long considered a necessary step prior to waveform inversion in order to avoid cycle skipping. However, in this paper, we demonstrate that frequency-domain waveform inversion can reliably reconstruct high-resolution images of sound speed and attenuation without relying on ray tomography to provide an initial model. We provide a detailed description of our frequency-domain waveform inversion algorithm with open-source code and data that we make publicly available.

Spectral induced polarization tomography inversion: Hybridizing homotopic continuation with Bayesian inversion

Induced polarization tomography offers the potential to better characterize the subsurface structures by considering spectral content from data acquisition over a broad frequency range. Spectral induced polarization (SIP) tomography is generally defined as a nonlinear inverse problem commonly solved through deterministic gradient-based methods. To this end, the spectral parameters, i.e., direct current resistivity, chargeability, relaxation time, and frequency exponent, are resolved by individually or simultaneously inverting all frequency data, followed by fitting a generalized Cole-Cole model to the inverted complex resistivities. Due to the high correlation between the Cole-Cole model parameters and a lack of knowledge about the initial approximation of the spectral parameters, using the classical least-squares methods may lead to inaccurate solutions and impede reliable uncertainty analysis. To cope with these limitations, we introduce a new approach based on a hybrid application of a globally convergent homotopic continuation method and a Bayesian inference to reconstruct the distribution of the subsurface spectral parameters. The homotopic optimization, owing to its fast and global convergence, is first implemented to invert multifrequency SIP data sets aimed at retrieving the complex-valued resistivity. Then, Bayesian inversion based on a Markov chain Monte Carlo (MCMC) sampling method, along with a priori information including the lower and upper bounds of the prior distributions, is used to invert the complex resistivity for the Cole-Cole model parameters. By applying the MCMC inversion algorithm, a full nonlinear uncertainty appraisal can be provided. We numerically evaluate the performance of our method using synthetic and real data examples in the presence of topographical effects. Numerical results prove that the homotopic continuation method outperforms the classic, smooth inversion algorithm in the sense of approximation accuracy and computational efficiency. In addition, we determine that our hybrid inversion strategy provides reliable representations of the main features and structure of the earth’s subsurface in terms of the spectral parameters.

Divertor heat load estimates on NSTX and DIII-D using new and open-source 2D inversion analysis code

A thermography inversion algorithm has been developed in the open-source Python-based computer code, HYPERION, to calculate the heat flux incident on plasma-facing components (PFCs) in axisymmetric tokamaks. The chosen mesh size at the surface significantly affects the calculated transient heat flux results. The calculated transient heat flux will exceed the real value when the mesh size tends to zero but will underestimate the real value when the mesh size is large. A criterion for determining the appropriate mesh size for the transient heat flux calculation will be discussed. The numerical scheme for HYPERION uses a 2D fully implicit finite-difference approach, allowing temperature-dependent thermal properties of PFC materials. The inversion algorithm is benchmarked against established heat flux calculation codes, TACO and THEODOR, based on thermography data from NSTX and DIII-D respectively. The primary benefits of HYPERION compared to TACO and THEODOR are that it is open-source and it allows for the optimization of mesh thickness along the substrate. The algorithm also accounts for the thermal properties of thin surface layers that characteristically form on PFCs due to plasma-material interactions. The agreement between HYPERION and THEODOR is excellent, as the percent difference between the codes is ∼5% on average in the case of the DIII-D data for moderate to high heat flux. Verification tests with TACO show slightly higher average percent differences of 8% and 12%. In using HYPERION to study filaments in heat flux, the initial results indicate that small ELMs filaments significantly broaden the divertor heat flux, and decrease divertor peak flux. Compared to the inter-ELM, the small ELM filaments decrease the divertor peak surface temperature. With intermittent divertor filaments, the divertor heat flux width is comparable with that found in L-mode.

Two‐dimensional controlled source electromagnetic inversion algorithm based on a space domain forward modeling approach

AbstractWe develop a two‐dimensional controlled‐source electromagnetic inversion algorithm employing a space domain forward modelling algorithm. The space domain forward modelling algorithm is devised by imposing boundary conditions on the plane perpendicular to the strike direction that passes through the source position. The boundary conditions for various source types are derived using the symmetric/antisymmetric character of the electric and magnetic fields. The benchmarking analysis reveals that roughly eight grids are sufficient for discretizing space in the strike directions for accurate forward response computations. For inverse modelling, the inexact Gauss–Newton optimization technique is utilized. Numerical inversion experiments of synthetic and real‐field data clearly demonstrate the versatility and robustness of the developed algorithm. The inversion experimentations also concur with the forward response benchmarking analysis and suggest that only a few grids (around eight) are adequate to discretize space in the strike direction. The developed algorithm is more than one order efficient compared to a wavenumber domain code.

Computationally Efficient Emulation of Spheroidal Elastic Deformation Sources Using Machine Learning Models: A Gaussian‐Process‐Based Approach

AbstractElastic continuum mechanical models are widely used to compute deformations due to pressure changes in buried cavities, such as magma reservoirs. In general, analytical models are fast but can be inaccurate as they do not correctly satisfy boundary conditions for many geometries, while numerical models are slow and may require specialized expertise and software. To overcome these limitations, we trained supervised machine learning emulators (model surrogates) based on parallel partial Gaussian processes which predict the output of a finite element numerical model with high fidelity but >1,000× greater computational efficiency. The emulators are based on generalized nondimensional forms of governing equations for finite non‐dipping spheroidal cavities in elastic halfspaces. Either cavity volume change or uniform pressure change boundary conditions can be specified, and the models predict both surface displacements and cavity (pore) compressibility. Because of their computational efficiency, using the emulators as numerical model surrogates can greatly accelerate data inversion algorithms such as those employing Bayesian Markov chain Monte Carlo sampling. The emulators also permit a comprehensive evaluation of how displacements and cavity compressibility vary with geometry and material properties, revealing the limitations of analytical models. Our open‐source emulator code can be utilized without finite element software, is suitable for a wide range of cavity geometries and depths, includes an estimate of uncertainties associated with emulation, and can be used to train new emulators for different source geometries.

Computational Homogenization for Inverse Design of Surface-based Inflatables

Surface-based inflatables are composed of two thin layers of nearly inextensible sheet material joined together along carefully selected fusing curves. During inflation, pressure forces separate the two sheets to maximize the enclosed volume. The fusing curves restrict this expansion, leading to a spatially varying in-plane contraction and hence metric frustration. The inflated structure settles into a 3D equilibrium that balances pressure forces with the internal elastic forces of the sheets. We present a computational framework for analyzing and designing surface-based inflatable structures with arbitrary fusing patterns. Our approach employs numerical homogenization to characterize the behavior of parametric families of periodic inflatable patch geometries, which can then be combined to tessellate the sheet with smoothly varying patterns. We propose a novel parametrization of the underlying deformation space that allows accurate, efficient, and systematical analysis of the stretching and bending behavior of inflated patches with potentially open boundaries. We apply our homogenization algorithm to create a database of geometrically diverse fusing patterns spanning a wide range of material properties and deformation characteristics. This database is employed in an inverse design algorithm that solves for fusing curves to best approximate a given input target surface. Local patches are selected and blended to form a global network of curves based on a geometric flattening algorithm. These fusing curves are then further optimized to minimize the distance of the deployed structure to target surface. We show that this approach offers greater flexibility to approximate given target geometries compared to previous work while significantly improving structural performance.

Bayesian inversion for in-situ thermal characterisation of walls in the presence of thermal anomalies

This paper develops a Bayesian inverse modelling framework for the in-situ characterisation of walls' thermal performance in the presence of thermal anomalies subject to uncertainty. For any given wall, the proposed framework uses in-situ contact measurements of temperature and heat flux in order to approximate the (posterior) distribution of a set of parameters which are inputs of a 3D heat transfer model of the wall that accounts for the presence of unknown anomalies. The set of inputs that we infer include (i) the geometry of the thermal anomaly as well was its material properties, (ii) the as-built thermophysical properties of the clear part (i.e. without anomaly) of the wall (iii) surface resistances and (iv) modelling errors that arise from unaccounted sources of uncertainty in the boundary conditions. The geometry of the unknown thermal anomaly is parameterised with a level-set function that is inferred within the proposed Bayesian approach. In order to incorporate prior statistical information of the thermal anomaly, a Gaussian process conditioned on measurements from thermal images is employed to build a prior on the level-set function. The posterior distribution of inferred inputs is approximated via the implementation of an Ensemble Kalman Inversion algorithm that provides stable and accurate approximations of the posterior. This paper also proposes a methodology that uses the inferred 3D model to derive a thermally equivalent 1D model of the wall that is suitable for its integration with existing building energy performance software. The proposed inverse modelling technique is experimentally validated by characterising the thermal performance of an insulation panel in the presence of a thermal anomaly. Our computations show that the proposed approach produces a 3D model that accurately describes thermal performance, and a derived equivalent 1D model that effectively reproduces the dynamic thermal performance of the insulation panel in the presence of the thermal anomaly.

Imaging a two-layered conductive medium by a modified factorization method

In this paper, we consider the inverse acoustic scattering problem of determining a two-layered inhomogeneous medium with a conductive transmission condition from far-field measurements. The well-posedness of the direct problem can be established by applying a variational method. For the inverse problem, we shall develop a modified factorization method for recovering the shape and location of the two-layered conductive medium. Finally, we provide some numerical experiments to demonstrate the practicability of the inversion algorithms.

Real-time Bayesian inversion in resin transfer moulding using neural surrogates

In Resin Transfer Moulding (RTM), local variations in reinforcement properties (porosity and permeability) and the formation of gaps along the reinforcement edges result in non-uniform resin flow patterns, which may cause defects in the produced composite component. The ensemble Kalman inversion (EKI) algorithm has previously been used to invert in-process data to estimate local reinforcement properties. However, implementation of this algorithm in some applications is limited by the requirement to run thousands of computationally expensive resin flow simulations. In this study, a machine learning approach is used to train a surrogate model which can emulate resin flow simulations near-instantaneously. A partition of the flow domain into a low-dimensional representation enables an artificial neural network (ANN) surrogate to make accurate predictions, with a simple architecture. When the ANN is integrated within the EKI algorithm, estimates for local reinforcement permeability and porosity can be achieved in real time, as was verified by virtual and lab experiments. Since EKI utilises the Bayesian framework, estimates are given within confidence intervals and statements can be made on-line regarding the probability of defects within sections of the reinforcement. The proposed framework has shown good predictive capabilities for the set of laboratory experiments and estimates for reinforcement properties were always computed within 1 s.

COBLAH: A chaotic OBL initialized hybrid algebraic-heuristic algorithm for optimal S-box construction

The Substitution box (S-box) is the main nonlinear component responsible for the cryptographic strength of any Substitution-Permutation Network (SPN) based block cipher. Generating the S-box with optimal cryptographic properties is one of cryptography's most challenging combinatorial problems because of its enormous search space, lack of guidance, and conflicting performance criteria. This paper introduces a novel Chaotic Opposition-based Learning Initialized Hybrid Algebraic-Heuristic (COBLAH) algorithm, combining the favorable traits of Algebraic and heuristics methods based on Galois field inversion, affine mapping, and Genetic Algorithm (GA). The Galois field inversion and affine mapping are used to construct the S-box, while the GA guides the algebraic construction to find the best bit-matrix and additive vector based on any irreducible polynomial for GF(28). GA initializes with a random population generated using a newly constructed cosine-cubic map incorporated with binarization and Opposition-based Learning (OBL). Further, Multi-Objective Optimization Ratio Analysis (MOORA) is utilized to identify the best S-box from the final optimized population. The performance of the proposed algorithm is evaluated by comparing the generated COBLAH S-box with more than twenty state-of-the-art S-boxes, including Advanced Encryption Standard (AES), Skipjack, Gray, and Affine Power Affine (APA). The COBLAH S-box has nonlinearity 112, Strict Avalanche Criterion (SAC) offset 0.0202, Distance to SAC (DSAC) 332, Differential Approximation Probability (DP) 0.0625, Linear Approximation Probability (LP) 0.0156, Bit Independence Criterion-Strict Avalanche Criterion (BIC-SAC) 0.50006, and Bit Independence Criterion-Nonlinearity (BIC-NL) 112, which stands as the optimal observed thus far. The absence of fixed and opposite fixed points and the fact that it adheres to a single cycle aligns the COBLAH S-box with an ideal S-box. In addition, an image encryption mechanism is utilized to encrypt and decrypt the different images sourced from the standard USC-SIPI image dataset using COBLAH S-box and compared against different state-of-the-art S-boxes based on various image characteristics.

Modular digital twin modelling method for 10 kV cable lines based on real‐time temperature field inversion

AbstractState perception of long‐span 10 kV cable lines is one of the critical issues in building intelligent distribution networks. Digital twin (DT), which can map the physical status of equipment in real‐time, has received extensive attention. However, traditional modelling methods cannot meet the requirement of long‐span complex DT's real‐time computation and scalability. In order to reduce the modelling cost and improve the calculation speed, a modular DT modelling method for cable lines based on real‐time temperature field inversion is proposed. The authors develop a modular reduced‐order modelling method that applies to long‐span 10 kV cable lines. Combined with the temperature field inversion, a DT inversion algorithm is proposed to evaluate the transient temperature field and contact resistance inside cable lines, which has been used to evaluate the emergency load capacity. Finally, temperature rise tests verified the DT inversion algorithm's correctness. The operating status of cable lines was evaluated through the modular DT, and the emergency time and emergency ampacity were calculated. The result shows that the new method meets the real‐time and high‐precision requirements of DT calculation in actual operation scenarios. It can be easily extended to cable lines of different voltage levels.

Tree internal defects detection method based on ResNet improved subspace optimization algorithm

The erosion behavior of trunk borers leads to the destruction of trunk structure and the formation of internal defects, which significantly impacts the ecological and economic value of trees. Traditional non-destructive testing (NDT) methods are costly and have low resolution, whereas electromagnetic NDT methods are more suitable for high-resolution detection and imaging. However, solving the highly nonlinear electromagnetic inverse scattering problems (ISPs) for small-sized defects with high contrast is challenging. Therefore, this paper proposes an improved subspace optimization algorithm based on a ResNet network called SOM-ResNet. SOM-ResNet incorporates physical principles into deep learning networks by simulating the iterative process of induced current and contrast, thereby enhancing its ability to accurately detect small objects with high contrast. Experimental results demonstrate that SOM-ResNet outperforms single inversion algorithms in detecting complex scatterers with small to medium-sized targets, validating its excellent performance.