A simulator predicts what should happen; sensors, surveys and assays report what did happen, sparsely and with noise. We treat data fusion as a Bayesian problem: a model is combined with the measurements that bear on it to produce a probability distribution over the state of the system, and that uncertainty is carried through to the decision.
In 2024 we began work on adapting pre-trained models to sparse, real-time observations, using differentiable models inside a Bayesian inference problem. These methods are now implemented and tested in our numerical library, which the agents framework and the biology library behind Curasynth use.
Current work
- State estimation. Kalman, extended, unscented, ensemble and particle filters, with smoothers, invariant filters on manifolds for navigation, and factor graphs for the batch problem. Every nonlinear filter must reduce to the exact Kalman result on a linear-Gaussian model; that one property is asserted in tests and catches more errors than any accuracy comparison.
- Multi-target tracking. Gating that reports its own size, interacting-multiple-model and probability-hypothesis-density filters, and set metrics (OSPA, GOSPA) for when the number of targets is itself unknown.
- Inverse problems. Maximum a posteriori estimation, posterior Cramér–Rao bounds on what any estimator could achieve, and forward and adjoint sensitivities through differential equations, so gradient-based fitting uses derivatives computed from the model instead of finite-difference approximations.
- Likelihood-free calibration. Simulation-based inference (approximate Bayesian computation with sequential Monte Carlo, regression adjustment, synthetic likelihood and indirect inference) for simulators that can be run but not written down as a density.
- Uncertainty quantification and decision analysis. Sobol and Shapley sensitivity with error bars, reliability by FORM and SORM, multilevel and multifidelity Monte Carlo, and value of information (EVPI, EVPPI, EVSI) with the estimation bias reported separately. Sequential choices are posed as Markov decision processes, observed or partially observed.
- libraries in one layered numerical stack, from linear algebra to decision analysis
- 12libraries in one layered numerical stack, from linear algebra to decision analysis
- reference results captured from established toolchains and checked in tests
- 52reference results captured from established toolchains and checked in tests
Use in our products
- Curasynth reports support for a hypothesis as a range (belief and plausibility) and lists evidence that has not been collected.
- Fitila Agents uses an evidential core, not the language model, to combine observations, and ranks the next measurement by its expected value per unit of cost.
- TerraNavitas Subsurface is the physics such a posterior is computed over. Uncertainty studies on it are delivered with our team today, and come to the workbench next.
Open problems
- Surrogates inside filters. Ensemble and particle filters are limited by the speed of the model they propagate. We are testing verified surrogates in the forecast step while keeping the posterior accurate.
- Value of information at field scale. Choosing which well to log, which survey to fly or which assay to run. The methods exist; the work is making them fast enough to use routinely.
- Combining different kinds of evidence. Probabilities from a model, intervals from an assay and graded claims from a paper cannot be combined with a single rule. We are working on representations that combine them while preserving what each one means.