2026· IEEE Transactions on Geoscience and Remote Sensing· Vol 64, pp. 5914813-5914813· 0 citations· 52 references
Abstract
Electrical resistivity tomography (ERT) inversion is inherently nonlinear and ill-posed, and conventional algorithms often suffer from limited resolution due to their dependence on initial models and regularization. Recent deep learning (DL)-based approaches have shown potential for resolution enhancement but purely data-driven methods lack physical interpretability, while physics-constrained networks typically provide limited improvement and incur high computational cost. To address these challenges, we propose a physics-driven resolution refinement framework for ERT. The core idea is to learn a differentiable surrogate forward model from multiarray observations and use it as a physical guide to refine conventional inversion results. Specifically, a multiarray forward network is trained to jointly predict responses from Wenner- $\alpha $ , dipole–, and Schlumberger (SLM) arrays, capturing their complementary sensitivities through shared representation learning. Based on this learned forward mapping, the conventional inversion model is iteratively refined by enforcing cross-array response consistency, while an adaptively weighted supervision term is incorporated to stabilize the update. A Vision Mamba backbone is adopted to enhance feature representation and improve the recovery of fine-scale structures. Experiments on both synthetic and field data demonstrate that the proposed method improves anomaly delineation and structural detail recovery under the tested synthetic and field settings. Meanwhile, it enhances cross-array physical consistency and avoids the computational overhead associated with repeated numerical forward modeling. These results highlight the effectiveness of integrating learned forward physics with data-driven refinement for high-resolution ERT imaging.
Conventional acoustic impedance inversion methods have long faced technical bottlenecks such as inaccurate wavelet estimation and strong dependence on initial models. Although existing deep learning approaches can partially alleviate these problems, they often compromise model simplicity and training efficiency, while introducing new challenges such as limited generalizability and heavy reliance on labeled data. To overcome these limitations, this study proposes a lightweight inversion framework that tightly integrates physics-driven and data-driven paradigms. The physics-driven component adopts a neural network architecture largely consistent with traditional modeling processes, enabling direct optimization of physically meaningful parameters through backpropagation, thereby avoiding the construction of excessively complex inverse operators. Meanwhile, regularization methods are introduced to enforce geological prior knowledge (that is, the “layered geological model” assumption) on the network parameters, improving the spatial continuity of the reconstructed impedance models. The data-driven component employs an enhanced 2D U-Net integrated with Class Activation Mapping (U-Net-CAM) to generate accurate reference models from sparse well-log data. Tests on both synthetic and field datasets demonstrate the advantages of the proposed method: (1) physically interpretable network design; (2) strong robustness to noise and reduced dependence on training data; (3) higher accuracy and better spatial continuity compared to conventional and purely data-driven methods. This work provides a new perspective for addressing long-standing challenges in seismic impedance inversion.
Electromagnetic inverse scattering is a nonlinear and ill-posed computational imaging problem, where accurate reconstruction is challenging due to measurement limitations, noise, and high computational costs, especially for 3-D imaging. Although physics-driven neural networks (PDNNs) reduce the dependence on labeled training data, existing accelerated PDNN frameworks often rely on preliminary reconstruction-based region selection, which may introduce instability when the selected region is inaccurate. In this paper, a coordinate-residual physics-driven neural network (CRPDNN) is proposed for 3-D electromagnetic inverse scattering. CRPDNN represents the unknown complex contrast distribution using normalized spatial coordinates and a residual convolutional network, whose parameters are optimized by enforcing consistency between the measured and model-predicted scattered fields. Unlike existing subregion-accelerated PDNN approaches, CRPDNN does not require a preliminary reconstruction, thereby avoiding dependence on its accuracy. For the reported noise-free 3-D synthetic cases, CRPDNN achieves an average relative error of 2.10\%, compared with 7.97\% for CSI and 3.99\% for $L_{2/3}$-FBE-WCIE, while providing approximately 5.5- and 12.1-fold speedups over the two baselines, respectively. Additional 2-D comparisons further demonstrate its stability and computational efficiency relative to existing PDNN frameworks. CRPDNN also maintains reliable reconstruction performance under noisy measurements, and the 3-D Fresnel experiments further indicate its potential for practical imaging applications.
While full-waveform inversion (FWI) offers high-resolution ground penetrating radar (GPR) imaging, it is hampered by prohibitive computational costs and intrinsic sensitivity to initial models. Conversely, deep learning provides efficiency but often lacks physical constraints, leading to structural artifacts under noise. To reconcile high fidelity and robustness with computational efficiency, we propose a physics-consistent inversion framework driven by envelope data and a feature-enhanced forward module. A key innovation of our approach is shifting physical constraints from the noisy pixel domain to the robust latent feature manifold. Specifically, we construct a pretrained differentiable forward modeling engine and introduce a Latent Feature Injection mechanism. This strategy transfers multiscale structural semantics from the inversion network to the forward engine, enforcing strict physical compliance guided by the global geological context. This effectively compensates for the information bottleneck in traditional parameter prediction. Extensive experiments on synthetic and measured datasets demonstrate that our method significantly outperforms traditional baselines while maintaining the computational efficiency of deep learning. It exhibits superior inversion accuracy, robust noise immunity, and strong generalization capabilities.
Meijia Huang, Xiang Qiu, Yanqi Wu et al.· IEEE Transactions on Geoscie...· 0 citations
Radio telescope arrays are constrained by the number of antennas and baseline distribution, resulting in incomplete spatial-frequency sampling, limited image resolution, and blurring, distortion, and loss of small-scale structures caused by coupling between the primary and synthesized beams. Existing general-purpose model-driven methods remove observational effects sequentially and may accumulate errors, but cannot directly address limited imaging resolution, while data-driven methods lack explicit physical constraints. We propose PhySR, an end-to-end physics-informed neural network that combines a U-Net backbone, dynamic cascaded upsampling, a multiscale feature residual module, and a differentiable physical forward model incorporating the primary beam response, PSF convolution, and scale mapping. PhySR directly reconstructs high-resolution images from low-resolution dirty images without high-resolution labels while maintaining observation-domain consistency. Experiments on simulated SKA-Mid data show that, for 4x super-resolution, PhySR achieves a PSNR of 44.65 dB, an SSIM of 0.9940, and an RMSE of 0.0065. Compared with existing general-purpose methods, PSNR and SSIM improve by approximately 13.23 dB and 0.3760, respectively. Compared with mainstream deep learning models, PSNR and SSIM improve by 6.50 dB and 0.0682, while RMSE decreases by 0.0069. PhySR also remains stable for 2x and 8x super-resolution and achieves low observation-domain consistency errors, demonstrating advantages in coupling-effect removal, small-scale structure recovery, and physical consistency.
Hongkun Yang, Li Zhang, Ming Zhang et al.· 0 citations
Electrical resistivity tomography (ERT) is a subsurface imaging geophysical technique. Traditional ERT inversion methods, such as smoothness‐constrained least‐squares approaches, often suffer from discretization artifacts when reconstructing electrical resistivity from resistance measurements. To address the limitations of conventional ERT inversion, this study introduces a novel super‐resolution framework based on an Implicit Neural Representation (INR) to enhance 3D ERT inversion resolution beyond that achievable with standard Gauss‐Newton techniques. The proposed machine learning methodology effectively integrates high‐resolution two‐dimensional data with coarse three‐dimensional data to generate a higher‐resolution resistivity representation consistent with the measured apparent‐resistivity data. Validation using data from the Waste Isolation Pilot Plant (WIPP) site shows that the INR approach improves 3D inversion quality relative to Res3Dinv. For the WIPP data set, the INR model increases
R
2
from 0.107 to 0.361, reduces RMSE from 77.21 to 33.32 Ω·m, and reduces bias from 68.34 to 13.94 Ω·m (corresponding to relative improvements of 237.4%, 56.8%, and 79.6%, respectively). Tests on a synthetic domain with increased resistivity variation show even stronger performance enhancement:
R
2
increases from 0.149 to 0.740, RMSE decreases from 119.28 to 53.24 Ω·m, and bias decreases from 88.45 to 12.74 Ω·m (relative improvements of 396.6%, 55.4%, and 85.6%, respectively). Results demonstrate improved apparent‐resistivity prediction using INR, but the method is deterministic and does not provide formal uncertainty bounds. Generalization to other electrode arrays and systematic quantification of line‐density sensitivity remain future work.
Yusen Yuan, K. Carroll, Huichao Yin et al.· Journal of Geophysical Resea...· 0 citations
Deep learning (DL) techniques have been tentatively explored for geophysical inversion, but most inversion networks currently rely on a purely data-driven mode, where the training process is highly dependent on the data sets and lacks physical information constraints. In this article, we propose a physically constrained, data-driven magnetotelluric (MT) inversion algorithm that jointly optimizes the model and forward response by incorporating data misfit into the loss function. However, integrating traditional forward operators into modern DL frameworks presents challenges in computational efficiency and gradient propagation. To address this, we develop a high-precision DL-based forward operator to compute MT response misfit, enabling seamless integration and accelerated training. Test results show that over 95% of the relative errors in forward responses are within ±1%. An attention-based deep residual network (ADRN) is then employed to map MT responses to the 1-D geoelectric model, with the pretrained forward operator imposing physical constraints during inversion training to enhance generalization. Inversion results from both simulated data and marine MT data from the South Yellow Sea show that the physically constrained, data-driven inversion method improves robustness compared to the traditional purely data-driven mode. It effectively reduces the data mean square error (MSE) by approximately 70% on average while achieving nearly the same model misfit, thereby providing more reliable technical support for geophysical exploration.
Changqing Feng, Yuguo Li, Pan Li· IEEE Transactions on Geoscie...· 0 citations
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