Scheiter, Matthias1; Valentine, Andrew1; Sambridge, Malcolm1
1Research School of Earth Sciences, Australian National University, Canberra, Australia
In geophysics, most inverse methods fall into one of two categories: optimization, where a single solution is found through gradient descent; or ensemble inversion methods such as Markov chain Monte Carlo, where one or more best-fitting regions in model space are identified. Both of these classes have their drawbacks: optimization algorithms often find local rather than global optima, and ensemble methods are known for their high computational cost. In this presentation, we devise a new framework for geophysical inversion in which an ensemble of solutions is produced through optimization.
Our framework consists of three building blocks: a generator function that proposes models, either deterministically or probabilistically; a forward operator that simulates synthetic data for those models; and a discriminator function that somehow assesses the similarity of synthetic and observed data – either by comparing individual examples, or by looking at the overall properties of ensembles. The generator and discriminator can have adjustable parameters that are optimized with traditional gradient descent methods. After convergence, the generator can be used to sample an arbitrarily large number of models, forming regions in model space that explain the observed data and their uncertainty. The discriminator can be any pre-defined or evolving misfit measure.
In the simplest case, the generator could be identified as a function returning a single model, and the discriminator could be a L2 misfit measure. In this way, established optimization methods can be seen as a special case of this framework. As another example, the generator and discriminator can be neural networks and trained in an adversarial manner, as in generative adversarial networks. This provides a large degree of flexibility to find a meaningful model ensemble representing the solution of the inverse problem. The new framework combines the merits of finding an ensemble of solutions with the computational efficiency of optimization algorithms.
Matthias Scheiter started his PhD in seismology and mathematical geophysics at the Australian National University in 2019 and is supervised by Malcolm Sambridge and Andrew Valentine. The goal of his project is to develop new methods for geophysical inversion, mainly through the use of machine learning techniques.