Speaker
Description
Inferring a three-dimensional shape from sparse, indirect measurements is a severely ill-posed inverse problem, which arises throughout the physical and biological sciences. Doing so successfully with principled Bayesian uncertainties requires a tractable parametrisation of geometry, and a strong prior encoding domain knowledge of plausible shapes.
In this talk we show how a pretrained geometry foundation model, in our case one built for engineering optimisation, can be adapted to supply both, and embedded in an end-to-end differentiable simulator. We do so using only O(100) example geometries and without retraining or fine-tuning the foundation model. We instead fit a shape prior in the model's latent space using a covariance-aware variant of probabilistic PCA that maximises the likelihood of generating the decoded geometries rather than their latent codes, while remaining fully differentiable. The resulting low-dimensional, well-conditioned parameter space opens the inverse problem to a range of inference strategies.
As an example application, we consider asteroid lightcurve inversion: using gradient-based MAP estimation we infer shapes for 3,236 asteroids from Gaia DR3 photometry without the convexity assumption standard to that the field, while truncated sequential neural posterior estimation yields the first Bayesian uncertainties on non-convex asteroid geometries. Requiring only a foundation model with a vector latent space and a handful of domain example geometries, the outlined recipe should transfer cheaply to other geometric inverse problems, and to Bayesian inference with latent-variable generative models more broadly.