A Physics-guided Generative AI Toolkit for Geophysical Monitoring

Full-waveform inversion (FWI) plays a vital role in geoscience to explore the subsurface. It utilizes the seismic wave to image the subsurface velocity map. As the machine learning (ML) technique evolves, the data-driven approaches using ML for FWI tasks have emerged, offering enhanced accuracy and reduced computational cost compared to traditional physics-based methods. However, a common challenge in geoscience, the unprivileged data, severely limits ML effectiveness. The issue becomes even worse during model pruning, a step essential in geoscience due to environmental complexities. To tackle this, we introduce the EdGeo toolkit, which employs a diffusion-based model guided by physics principles to generate high-fidelity velocity maps. The toolkit uses the acoustic wave equation to generate corresponding seismic waveform data, facilitating the fine-tuning of pruned ML models. Our results demonstrate significant improvements in SSIM scores and reduction in both MAE and MSE across various pruning ratios. Notably, the ML model fine-tuned using data generated by EdGeo yields superior quality of velocity maps, especially in representing unprivileged features, outperforming other existing methods.

On the Hidden Waves of Image

In this paper, we introduce an intriguing phenomenon-the successful reconstruction of images using a set of one-way wave equations with hidden and learnable speeds. Each individual image corresponds to a solution with a unique initial condition, which can be computed from the original image using a visual encoder (e.g., a convolutional neural network). Furthermore, the solution for each image exhibits two noteworthy mathematical properties: (a) it can be decomposed into a collection of special solutions of the same one-way wave equations that are first-order autoregressive, with shared coefficient matrices for autoregression, and (b) the product of these coefficient matrices forms a diagonal matrix with the speeds of the wave equations as its diagonal elements. We term this phenomenon hidden waves, as it reveals that, although the speeds of the set of wave equations and autoregressive coefficient matrices are latent, they are both learnable and shared across images. This represents a mathematical invariance across images, providing a new mathematical perspective to understand images.

Edge-InversionNet: Enabling Efficient Inference of InversionNet on Edge Devices

Seismic full waveform inversion (FWI) is a widely used technique in geophysics for inferring subsurface structures from seismic data. And InversionNet is one of the most successful data-driven machine learning models that is applied to seismic FWI. However, the high computing costs to run InversionNet have made it challenging to be efficiently deployed on edge devices that are usually resource-constrained. Therefore, we propose to employ the structured pruning algorithm to get a lightweight version of InversionNet, which can make an efficient inference on edge devices. And we also made a prototype with Raspberry Pi to run the lightweight InversionNet. Experimental results show that the pruned InversionNet can achieve up to 98.2 % reduction in computing resources with moderate model performance degradation.

Learned Full Waveform Inversion Incorporating Task Information for Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) is an emerging imaging modality that holds great promise for breast imaging. Full-waveform inversion (FWI)-based image reconstruction methods incorporate accurate wave physics to produce high spatial resolution quantitative images of speed of sound or other acoustic properties of the breast tissues from USCT measurement data. However, the high computational cost of FWI reconstruction represents a significant burden for its widespread application in a clinical setting. The research reported here investigates the use of a convolutional neural network (CNN) to learn a mapping from USCT waveform data to speed of sound estimates. The CNN was trained using a supervised approach with a task-informed loss function aiming at preserving features of the image that are relevant to the detection of lesions. A large set of anatomically and physiologically realistic numerical breast phantoms (NBPs) and corresponding simulated USCT measurements was employed during training. Once trained, the CNN can perform real-time FWI image reconstruction from USCT waveform data. The performance of the proposed method was assessed and compared against FWI using a hold-out sample of 41 NBPs and corresponding USCT data. Accuracy was measured using relative mean square error (RMSE), structural self-similarity index measure (SSIM), and lesion detection performance (DICE score). This numerical experiment demonstrates that a supervised learning model can achieve accuracy comparable to FWI in terms of RMSE and SSIM, and better performance in terms of task performance, while significantly reducing computational time.

Does Full Waveform Inversion Benefit from Big Data?

This paper investigates the impact of big data on deep learning models for full waveform inversion (FWI). While it is well known that big data can boost the performance of deep learning models in many tasks, its effectiveness has not been validated for FWI. To address this gap, we present an empirical study that investigates how deep learning models in FWI behave when trained on OpenFWI, a collection of large-scale, multi-structural datasets published recently. Particularly, we train and evaluate the FWI models on a combination of 10 2D subsets in OpenFWI that contain 470K data pairs in total. Our experiments demonstrate that larger datasets lead to better performance and generalization of deep learning models for FWI. We further demonstrate that model capacity needs to scale in accordance with data size for optimal improvement.

$\mathbf{\mathbb{E}^{FWI}}$: Multi-parameter Benchmark Datasets for Elastic Full Waveform Inversion of Geophysical Properties

Elastic geophysical properties (such as P- and S-wave velocities) are of great importance to various subsurface applications like CO$_2$ sequestration and energy exploration (e.g., hydrogen and geothermal). Elastic full waveform inversion (FWI) is widely applied for characterizing reservoir properties. In this paper, we introduce $\mathbf{\mathbb{E}^{FWI}}$, a comprehensive benchmark dataset that is specifically designed for elastic FWI. $\mathbf{\mathbb{E}^{FWI}}$ encompasses 8 distinct datasets that cover diverse subsurface geologic structures (flat, curve, faults, etc). The benchmark results produced by three different deep learning methods are provided. In contrast to our previously presented dataset (pressure recordings) for acoustic FWI (referred to as OpenFWI), the seismic dataset in $\mathbf{\mathbb{E}^{FWI}}$ has both vertical and horizontal components. Moreover, the velocity maps in $\mathbf{\mathbb{E}^{FWI}}$ incorporate both P- and S-wave velocities. While the multicomponent data and the added S-wave velocity make the data more realistic, more challenges are introduced regarding the convergence and computational cost of the inversion. We conduct comprehensive numerical experiments to explore the relationship between P-wave and S-wave velocities in seismic data. The relation between P- and S-wave velocities provides crucial insights into the subsurface properties such as lithology, porosity, fluid content, etc. We anticipate that $\mathbf{\mathbb{E}^{FWI}}$ will facilitate future research on multiparameter inversions and stimulate endeavors in several critical research topics of carbon-zero and new energy exploration. All datasets, codes and relevant information can be accessed through our website at https://efwi-lanl.github.io/

HOSSnet: an Efficient Physics-Guided Neural Network for Simulating Crack Propagation

Hybrid Optimization Software Suite (HOSS), which is a combined finite-discrete element method (FDEM), is one of the advanced approaches to simulating high-fidelity fracture and fragmentation processes but the application of pure HOSS simulation is computationally expensive. At the same time, machine learning methods, shown tremendous success in several scientific problems, are increasingly being considered promising alternatives to physics-based models in the scientific domains. Thus, our goal in this work is to build a new data-driven methodology to reconstruct the crack fracture accurately in the spatial and temporal fields. We leverage physical constraints to regularize the fracture propagation in the long-term reconstruction. In addition, we introduce perceptual loss and several extra pure machine learning optimization approaches to improve the reconstruction performance of fracture data further. We demonstrate the effectiveness of our proposed method through both extrapolation and interpolation experiments. The results confirm that our proposed method can reconstruct high-fidelity fracture data over space and time in terms of pixel-wise reconstruction error and structural similarity. Visual comparisons also show promising results in long-term

Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness

Full waveform inversion (FWI) infers the subsurface structure information from seismic waveform data by solving a non-convex optimization problem. Data-driven FWI has been increasingly studied with various neural network architectures to improve accuracy and computational efficiency. Nevertheless, the applicability of pre-trained neural networks is severely restricted by potential discrepancies between the source function used in the field survey and the one utilized during training. Here, we develop a Fourier-enhanced deep operator network (Fourier-DeepONet) for FWI with the generalization of seismic sources, including the frequencies and locations of sources. Specifically, we employ the Fourier neural operator as the decoder of DeepONet, and we utilize source parameters as one input of Fourier-DeepONet, facilitating the resolution of FWI with variable sources. To test Fourier-DeepONet, we develop two new and realistic FWI benchmark datasets (FWI-F and FWI-L) with varying source frequencies and locations. Our experiments demonstrate that compared with existing data-driven FWI methods, Fourier-DeepONet obtains more accurate predictions of subsurface structures in a wide range of source parameters. Moreover, the proposed Fourier-DeepONet exhibits superior robustness when dealing with noisy inputs or inputs with missing traces, paving the way for more reliable and accurate subsurface imaging across diverse real conditions.

Image is First-order Norm+Linear Autoregressive

This paper reveals that every image can be understood as a first-order norm+linear autoregressive process, referred to as FINOLA, where norm+linear denotes the use of normalization before the linear model. We demonstrate that images of size 256$\times$256 can be reconstructed from a compressed vector using autoregression up to a 16$\times$16 feature map, followed by upsampling and convolution. This discovery sheds light on the underlying partial differential equations (PDEs) governing the latent feature space. Additionally, we investigate the application of FINOLA for self-supervised learning through a simple masked prediction technique. By encoding a single unmasked quadrant block, we can autoregressively predict the surrounding masked region. Remarkably, this pre-trained representation proves effective for image classification and object detection tasks, even in lightweight networks, without requiring fine-tuning. The code will be made publicly available.

Enhanced prediction accuracy with uncertainty quantification in monitoring CO2 sequestration using convolutional neural networks

Monitoring changes inside a reservoir in real time is crucial for the success of CO2 injection and long-term storage. Machine learning (ML) is well-suited for real-time CO2 monitoring because of its computational efficiency. However, most existing applications of ML yield only one prediction (i.e., the expectation) for a given input, which may not properly reflect the distribution of the testing data, if it has a shift with respect to that of the training data. The Simultaneous Quantile Regression (SQR) method can estimate the entire conditional distribution of the target variable of a neural network via pinball loss. Here, we incorporate this technique into seismic inversion for purposes of CO2 monitoring. The uncertainty map is then calculated pixel by pixel from a particular prediction interval around the median. We also propose a novel data-augmentation method by sampling the uncertainty to further improve prediction accuracy. The developed methodology is tested on synthetic Kimberlina data, which are created by the Department of Energy and based on a CO2 capture and sequestration (CCS) project in California. The results prove that the proposed network can estimate the subsurface velocity rapidly and with sufficient resolution. Furthermore, the computed uncertainty quantifies the prediction accuracy. The method remains robust even if the testing data are distorted due to problems in the field data acquisition. Another test demonstrates the effectiveness of the developed data-augmentation method in increasing the spatial resolution of the estimated velocity field and in reducing the prediction error.