# InversionNet: A Real-Time and Accurate Full Waveform Inversion with CNNs and continuous CRFs Source: [InversionNet: A Real-Time and Accurate Full Waveform Inversion with CNNs and continuous CRFs]() Collection index: [llms.txt]() Data updated: 2025-10-26T06:48:44.412Z Authors: Yue Wu, Youzuo Lin Published: 2018-10-26T02:06:05.000Z ## Abstract Full-waveform inversion problems are usually formulated as optimization problems, where the forward-wave propagation operator $f$ maps the subsurface velocity structures to seismic signals. The existing computational methods for solving full-waveform inversion are not only computationally expensive, but also yields low-resolution results because of the ill-posedness and cycle skipping issues of full-waveform inversion. To resolve those issues, we employ machine-learning techniques to solve the full-waveform inversion. Specifically, we focus on applying the convolutional neural network~(CNN) to directly derive the inversion operator $f^{-1}$ so that the velocity structure can be obtained without knowing the forward operator $f$. We build a convolutional neural network with an encoder-decoder structure to model the correspondence from seismic data to subsurface velocity structures. Furthermore, we employ the conditional random field~(CRF) on top of the CNN to generate structural predictions by modeling the interactions between different locations on the velocity model. Our numerical examples using synthetic seismic reflection data show that the propose CNN-CRF model significantly improve the accuracy of the velocity inversion while the computational time is reduced. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Forward mapping on 2D Heat Equation 16 x 16 finite element mesh (test)](): Forward mapping; 2D Heat Equation 16 x 16 finite element mesh (test); Average Relative Error: 1.09. - [Forward Problem (PtO) on 2D Navier-Stokes (test)](): Forward Problem (PtO); 2D Navier-Stokes (test); Average Relative Error: 2.99. - [Inverse Mapping on 2D Heat Equation 16 x 16 finite element mesh (test)](): Inverse mapping; 2D Heat Equation 16 x 16 finite element mesh (test); Average Relative Error: 50.18. - [Inverse Problem on 2D Navier-Stokes (test)](): Inverse Problem; 2D Navier-Stokes (test); Average Relative Error: 40.2. ## Original sources and implementation [Original paper]() [PDF]()