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Register a new userInversionNet3D: Efficient and Scalable Learning for 3D Full Waveform Inversion
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Seismic full-waveform inversion (FWI) techniques aim to find a high-resolution subsurface geophysical model provided with waveform data. Some recent effort in data-driven FWI has shown some encouraging results in obtaining 2D velocity maps. However, due to high computational complexity and large memory consumption, the reconstruction of 3D high-resolution velocity maps via deep networks is still a great challenge. In this paper, we present InversionNet3D, an efficient and scalable encoder-decoder network for 3D FWI. The proposed method employs group convolution in the encoder to establish an effective hierarchy for learning information from multiple sources while cutting down unnecessary parameters and operations at the same time. The introduction of invertible layers further reduces the memory consumption of intermediate features during training and thus enables the development of deeper networks with more layers and higher capacity as required by different application scenarios. Experiments on the 3D Kimberlina dataset demonstrate that InversionNet3D achieves state-of-the-art reconstruction performance with lower computational cost and lower memory footprint compared to the baseline.
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In this article, continuous Galerkin finite elements are applied to perform full waveform inversion (FWI) for seismic velocity model building. A time-domain FWI approach is detailed that uses meshes composed of variably sized triangular elements to discretize the domain. To resolve both the forward and adjoint-state equations, and to calculate a mesh-independent gradient associated with the FWI process, a fully-explicit, variable higher-order (up to degree $k=5$ in $2$D and $k=3$ in 3D) mass lumping method is used. By adapting the triangular elements to the expected peak source frequency and properties of the wavefield (e.g., local P-wavespeed) and by leveraging higher-order basis functions, the number of degrees-of-freedom necessary to discretize the domain can be reduced. Results from wave simulations and FWIs in both $2$D and 3D highlight our developments and demonstrate the benefits and challenges with using triangular meshes adapted to the material proprieties. Software developments are implemented an open source code built on top of Firedrake, a high-level Python package for the automated solution of partial differential equations using the finite element method.
Full waveform inversion (FWI) delivers high-resolution images of the subsurface by minimizing iteratively the misfit between the recorded and calculated seismic data. It has been attacked successfully with the Gauss-Newton method and sparsity promoting regularization based on fixed multiscale transforms that permit significant subsampling of the seismic data when the model perturbation at each FWI data-fitting iteration can be represented with sparse coefficients. Rather than using analytical transforms with predefined dictionaries to achieve sparse representation, we introduce an adaptive transform called the Sparse Orthonormal Transform (SOT) whose dictionary is learned from many small training patches taken from the model perturbations in previous iterations. The patch-based dictionary is constrained to be orthonormal and trained with an online approach to provide the best sparse representation of the complex features and variations of the entire model perturbation. The complexity of the training method is proportional to the cube of the number of samples in one small patch. By incorporating both compressive subsampling and the adaptive SOT-based representation into the Gauss-Newton least-squares problem for each FWI iteration, the model perturbation can be recovered after an l1-norm sparsity constraint is applied on the SOT coefficients. Numerical experiments on synthetic models demonstrate that the SOT-based sparsity promoting regularization can provide robust FWI results with reduced computation.
Seizure detection algorithms must discriminate abnormal neuronal activity associated with a seizure from normal neural activity in a variety of conditions. Our approach is to seek spatiotemporal waveforms with distinct morphology in electrocorticographic (ECoG) recordings of epileptic patients that are indicative of a subsequent seizure (preictal) versus non-seizure segments (interictal). To find these waveforms we apply a shift-invariant k-means algorithm to segments of spatially filtered signals to learn codebooks of prototypical waveforms. The frequency of the cluster labels from the codebooks is then used to train a binary classifier that predicts the class (preictal or interictal) of a test ECoG segment. We use the Matthews correlation coefficient to evaluate the performance of the classifier and the quality of the codebooks. We found that our method finds recurrent non-sinusoidal waveforms that could be used to build interpretable features for seizure prediction and that are also physiologically meaningful.
The Hessian matrix plays an important role in correct interpretation of the multiple scattered wave fields inside the FWI frame work. Due to the high computational costs, the computation of the Hessian matrix is not feasible. Consequently, FWI produces overburden related artifacts inside the target zone model, due to the lack of the exact Hessian matrix. We have shown here that Marchenko-based target-oriented Full Waveform Inversion can compensate the need of Hessian matrix inversion by reducing the non-linearity due to overburden effects. This is achieved by exploiting Marchenko-based target replacement to remove the overburden response and its interactions with the target zone from residuals and inserting the response of the updated target zone into the response of the entire medium. We have also shown that this method is more robust with respect to prior information than the standard gradient FWI. Similarly to standard Marchenko imaging, the proposed method only requires knowledge of the direct arrival time from a focusing point to the surface and the reflection response of the medium.
Multiview representation learning is very popular for latent factor analysis. It naturally arises in many data analysis, machine learning, and information retrieval applications to model dependent structures among multiple data sources. For computational convenience, existing approaches usually formulate the multiview representation learning as convex optimization problems, where global optima can be obtained by certain algorithms in polynomial time. However, many pieces of evidence have corroborated that heuristic nonconvex approaches also have good empirical computational performance and convergence to the global optima, although there is a lack of theoretical justification. Such a gap between theory and practice motivates us to study a nonconvex formulation for multiview representation learning, which can be efficiently solved by a simple stochastic gradient descent (SGD) algorithm. We first illustrate the geometry of the nonconvex formulation; Then, we establish asymptotic global rates of convergence to the global optima by diffusion approximations. Numerical experiments are provided to support our theory.
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