A prior regularized full waveform inversion using generative diffusion models

Full waveform inversion (FWI) has the potential to provide high-resolution subsurface model estimations. However, due to limitations in observation, e.g., regional noise, limited shots or receivers, and band-limited data, it is hard to obtain the desired high-resolution model with FWI. To address this challenge, we propose a new paradigm for FWI regularized by generative diffusion models. Specifically, we pre-train a diffusion model in a fully unsupervised manner on a prior velocity model distribution that represents our expectations of the subsurface and then adapt it to the seismic observations by incorporating the FWI into the sampling process of the generative diffusion models. What makes diffusion models uniquely appropriate for such an implementation is that the generative process retains the form and dimensions of the velocity model. Numerical examples demonstrate that our method can outperform the conventional FWI with only negligible additional computational cost. Even in cases of very sparse observations or observations with strong noise, the proposed method could still reconstruct a high-quality subsurface model. Thus, we can incorporate our prior expectations of the solutions in an efficient manner. We further test this approach on field data, which demonstrates the effectiveness of the proposed method

Three-dimensional generalization and verification of structured bounding surface model for natural clay

As the proposed structured bounding surface model can only be used to solve planar strain problems of natural soft clay, a three-dimensional adaptive failure criterion is adopted to improve the model to capture the three-dimensional behaviors of natural soft clay. The three-dimensional adaptive failure criterion incorporated in this model can cover the Lade-Duncan criterion and the Matsuoka-Nakai criterion as its special ones. The structured bounding surface model is generalized into three-dimensional stress space by using the three-dimensional adaptive failure criterion. After improved with the three-dimensional adaptive failure criterion, the model can be seen as a modified bounding surface model which considers the destructuration and three-dimensional behaviors and neglects the anisotropy of natural soft clay. The simulations of undrained compression and extension tests of K0 consolidation state Bothkennar clay shows the unimportance of neglecting anisotropy in this model. It was validated on Pisa clay that the improved model can simulate well the three dimensional behaviors of natural soft clay under true triaxial conditions

Formulation of structured bounding surface model with a destructuration law for natural soft clay

A destructuration law considering both isotropic destructuration and frictional destructuration was suggested to simulate the loss of structure of natural soft clay during plastic straining. The term isotropic destructuration was used to address the reduction of the bounding surface, and frictional destructuration addresses the decrease of the critical state stress ratio as a reflection of reduction of internal friction angle. A structured bounding surface model was formulated by incorporating the proposed destructuration law into the framework of bounding surface constitutive model theory. The proposed model was validated on Osaka clay through undrained triaxial compression test and one-dimensional compression test. The influences of model parameters and bounding surface on the performance of the proposed model were also investigated. It is proved by the good agreement between predictions and experiments that the proposed model can well capture the structured behaviors of natural soft clay

NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition

Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the use of costly data and improve the generalization ability. However, these physics constraints, based on certain finite dimensional approximations over the function space, must resolve the smallest scaled physics to ensure the accuracy and stability of the simulation, resulting in high computational costs from large input, output, and neural networks. This paper proposes a general acceleration methodology called NeuralStagger by spatially and temporally decomposing the original learning tasks into several coarser-resolution subtasks. We define a coarse-resolution neural solver for each subtask, which requires fewer computational resources, and jointly train them with the vanilla physics-constrained loss by simply arranging their outputs to reconstruct the original solution. Due to the perfect parallelism between them, the solution is achieved as fast as a coarse-resolution neural solver. In addition, the trained solvers bring the flexibility of simulating with multiple levels of resolution. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations, which leads to an additional $10\sim100\times$ speed-up. Moreover, the experiment also shows that the learned model could be well used for optimal control.Comment: ICML 2023 accepte