You will develop the probabilistic foundations of subsurface inference. That includes making sure every model returns calibrated uncertainty, and that every new measurement is optimally chosen.
The central problem is to infer high-dimensional fields from data that constrain them only indirectly, through physical models that are expensive to evaluate. Our unknowns are 3D distributions of physical and geological properties, often with millions of parameters, and the forward models that link them to observations are only approximately correct. The data is compositional, censored and non-Gaussian, and each new measurement is expensive. Deciding what to measure next is therefore pivotal.
Our team has strength in adjoint-based geophysical inversion. This role adds rigorous probability, spatial statistics and decision theory. You will work alongside inversion researchers, ML engineers and geoscientists.
What your first year looks like
- Build dimension-robust Bayesian inversion methods in function space for posteriors with expensive forward models. These include pCN, HMC, sequential Monte Carlo and variational methods.
- Develop spatial priors for geology and grade that respect what geologists know about structure. These will use Gaussian and non-Gaussian random fields and SPDE representations.
- Model compositional and censored geochemical data directly, rather than transforming the problem away.
- Formulate measurement selection as Bayesian experimental design, using value of information and POMDPs, and make it robust to model misspecification.
- Pose thermodynamic equilibrium as constrained convex optimisation, and derive error bounds for the learned surrogates that replace it.
- Work with the ML engineers to keep surrogate-based and amortised inference calibrated against exact methods.
You have:
- A PhD in applied mathematics, statistics or probability.
- Depth in at least two of the following: Bayesian computation and Monte Carlo methods, spatial statistics and random fields, optimal experimental design and stochastic control, and convex and constrained optimisation.
- Fair programming know-how (Python or Julia; working knowledge of JAX or PyTorch is sufficient).
Nice to have:
- Research publications in Bayesian inverse problems, uncertainty quantification, spatial statistics or experimental design (strongly preferred).
- 3+ years of postdoctoral or industry research.
- Multi-fidelity or surrogate-assisted uncertainty quantification.
- Robust Bayesian methods under misspecification.
- Experience with PDE-constrained inverse problems in any field, such as geophysics, medical imaging or climate.
Interested? Write to us at gondwana@altcarbon.com with the role in the subject line.