An Intriguing Property of Geophysics Inversion

• URL: http://arxiv.org/abs/2204.13731v1
• Date: Thu, 28 Apr 2022 18:25:36 GMT
• Title: An Intriguing Property of Geophysics Inversion
• Authors: Yinan Feng, Yinpeng Chen, Shihang Feng, Peng Jin, Zicheng Liu, Youzuo Lin
• Abstract summary: Inversion techniques are widely used to reconstruct subsurface physical properties. The problems are governed by partial differential equations(PDEs) like the wave or Maxwell's equations. Recent studies leverage deep neural networks to learn the inversion mappings from geophysical measurements to the geophysical property directly.
• Score: 21.43509030627468
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity, and others) from surface-based geophysical measurements (e.g., seismic, electric/magnetic (EM) data). The problems are governed by partial differential equations~(PDEs) like the wave or Maxwell's equations. Solving geophysical inversion problems is challenging due to the ill-posedness and high computational cost. To alleviate those issues, recent studies leverage deep neural networks to learn the inversion mappings from geophysical measurements to the geophysical property directly. In this paper, we show that such a mapping can be well modeled by a \textit{very shallow}~(but not wide) network with only five layers. This is achieved based on our new finding of an intriguing property: \textit{a near-linear relationship between the input and output, after applying integral transform in high dimensional space.} In particular, when dealing with the inversion from seismic data to subsurface velocity governed by a wave equation, the integral results of velocity with Gaussian kernels are linearly correlated to the integral of seismic data with sine kernels. Furthermore, this property can be easily turned into a light-weight encoder-decoder network for inversion. The encoder contains the integration of seismic data and the linear transformation without need for fine-tuning. The decoder only consists of a single transformer block to reverse the integral of velocity. Experiments show that this interesting property holds for two geophysics inversion problems over four different datasets. Compared to much deeper InversionNet~\cite{wu2019inversionnet}, our method achieves comparable accuracy, but consumes significantly fewer parameters.

Related papers

• WiNet: Wavelet-based Incremental Learning for Efficient Medical Image Registration [68.25711405944239]
  Deep image registration has demonstrated exceptional accuracy and fast inference. Recent advances have adopted either multiple cascades or pyramid architectures to estimate dense deformation fields in a coarse-to-fine manner. We introduce a model-driven WiNet that incrementally estimates scale-wise wavelet coefficients for the displacement/velocity field across various scales.
  arXiv  Detail & Related papers  (2024-07-18T11:51:01Z)
• Transolver: A Fast Transformer Solver for PDEs on General Geometries [66.82060415622871]
  We present Transolver, which learns intrinsic physical states hidden behind discretized geometries. By calculating attention to physics-aware tokens encoded from slices, Transovler can effectively capture intricate physical correlations. Transolver achieves consistent state-of-the-art with 22% relative gain across six standard benchmarks and also excels in large-scale industrial simulations.
  arXiv  Detail & Related papers  (2024-02-04T06:37:38Z)
• A Physics-guided Generative AI Toolkit for Geophysical Monitoring [13.986582633154226]
  Full-waveform inversion (FWI) plays a vital role in geoscience to explore the subsurface. We introduce the EdGeo toolkit, which employs a diffusion-based model guided by physics principles to generate high-fidelity velocity maps.
  arXiv  Detail & Related papers  (2024-01-06T06:09:05Z)
• Geometry-Informed Neural Operator for Large-Scale 3D PDEs [76.06115572844882]
  We propose the geometry-informed neural operator (GINO) to learn the solution operator of large-scale partial differential equations. We successfully trained GINO to predict the pressure on car surfaces using only five hundred data points.
  arXiv  Detail & Related papers  (2023-09-01T16:59:21Z)
• Information Entropy Initialized Concrete Autoencoder for Optimal Sensor Placement and Reconstruction of Geophysical Fields [58.720142291102135]
  We propose a new approach to the optimal placement of sensors for reconstructing geophysical fields from sparse measurements. We demonstrate our method on the two examples: (a) temperature and (b) salinity fields around the Barents Sea and the Svalbard group of islands. We find out that the obtained optimal sensor locations have clear physical interpretation and correspond to the boundaries between sea currents.
  arXiv  Detail & Related papers  (2022-06-28T12:43:38Z)
• Physics-informed neural networks for solving parametric magnetostatic problems [0.45119235878273]
  This paper investigates the ability of physics-informed neural networks to learn the magnetic field response as a function of design parameters. We use a deep neural network (DNN) to represent the magnetic field as a function of space and a total of ten parameters.
  arXiv  Detail & Related papers  (2022-02-08T18:12:26Z)
• Exploring Multi-physics with Extremely Weak Supervision [23.421788453790302]
  We develop a new data-driven multi-physics inversion technique with extremely weak supervision. Our key finding is that the pseudo labels can be constructed by learning the local relationship among geophysical properties at very sparse locations. Our results show that we are able to invert for properties without explicit governing equations.
  arXiv  Detail & Related papers  (2022-02-03T18:55:09Z)
• Unsupervised Learning of Full-Waveform Inversion: Connecting CNN and Partial Differential Equation in a Loop [13.1144828613672]
  Full-Waveform Inversion (FWI) has been widely used in geophysics to estimate subsurface velocity maps from seismic data. We introduce a new large-scale dataset OpenFWI, to establish a more challenging benchmark for the community. Experiment results show that our model (using seismic data alone) yields comparable accuracy to the supervised counterpart.
  arXiv  Detail & Related papers  (2021-10-14T17:47:22Z)
• Physics informed neural networks for continuum micromechanics [68.8204255655161]
  Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong non-linear solutions by optimization. It is shown, that the domain decomposition approach is able to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world $mu$CT-scans.
  arXiv  Detail & Related papers  (2021-10-14T14:05:19Z)
• ResNet-LDDMM: Advancing the LDDMM Framework Using Deep Residual Networks [86.37110868126548]
  In this work, we make use of deep residual neural networks to solve the non-stationary ODE (flow equation) based on a Euler's discretization scheme. We illustrate these ideas on diverse registration problems of 3D shapes under complex topology-preserving transformations.
  arXiv  Detail & Related papers  (2021-02-16T04:07:13Z)
• Physics-Consistent Data-driven Waveform Inversion with Adaptive Data Augmentation [12.564534712461331]
  We develop a new hybrid computational approach to solve full-waveform inversion (FWI) We develop a data augmentation strategy that can improve the representativity of the training set. We apply our method to synthetic elastic seismic waveform data generated from a subsurface geologic model built on a carbon sequestration site at Kimberlina, California.
  arXiv  Detail & Related papers  (2020-09-03T17:12:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.