Efficient Bayesian inference through self-supervised active learning
We have developed a physics-guided deep learning framework for geophysical inversion that incorporates Markov chain Monte Carlo (MCMC) sampling to assess the uncertainty associated with model parameters of interest. To enhance computational efficiency, a statistical sampling method is utilized to reduce the number of samples required while ensuring the training data remain both diverse and informative. As the inversion progresses iteratively, the training dataset is dynamically expanded using outputs from the stochastic sampler along with their corresponding forward responses. A supervised deep learning model is utilized, in which the Jensen-Shannon divergence is adopted as the loss function, and a Gaussian assumption is applied for analytical computation. We test the workflow on a seismic velocity model inversion, and successfully capture the geological features and velocity distributions, with results that closely match the reference model. Compared to the MCMC sampler applied to the whole data cube, the proposed workflow is more computationally efficient, as a small fraction of data is chosen using the active learning paradigm. This workflow is strongly generalizable and effective, making it suitable for a wide range of other inversion applications as well.