On Applying Generative AI to Inverse Problems

Geoscience is full of inverse problems where treating model parameters as known and forward modeling observable data from them is comparatively easy while going the other direction, i.e. inferring model inputs based on observed data, is significantly harder. Generative AI can be applied to many such problems, since training data can be generated by forward modeling combined with unconditional sampling, avoiding the need to invert. Here, we begin by describing the difficulties involved in generating conditional realizations of sedimentary facies for use in reservoir modeling using conventional geostatistical methods. We then frame this difference in difficulty of unconditional and conditional sampling as one example of a general pattern that applies to inverse problems more broadly. This leads into a brief discussion of how generative AI techniques can be brought to bear on this type of problem, expressed in terms of Bayesian inference. We also mention the necessity of being able to trust that the generated output does in fact approximate a sample from the intended posterior probability distribution, and we sketch one calibration approach which can be used to build up this trust. Finally, as an example, we present results from an experiment in applying an autoregressive transformer to the problem of seismic inversion to lithology-fluid classes.