When Real Data Is Impossible
Some problems don't have enough real data. Not because the data wasn't collected — because the events themselves don't happen often enough. A 1-in-500-year flood. A black-swan sensor failure mode. A novel pathogen transmission pattern.
For these problems, the standard ML playbook fails at the data collection step.
Physics-Informed Generation
For our climate sensing deployment (see our applied note on PCON), we needed training data for rare ocean temperature anomalies — events with a recurrence interval of 8–15 years. The historical record has 40 years of data, which means 3–5 examples. That's not a training set; it's an anecdote.
Our approach: use a physics-based ocean circulation model (based on NEMO, an established ocean code) as a stochastic simulator. We parameterized the simulator over 23 physically meaningful variables (thermocline depth, Coriolis forcing, salinity gradient, etc.) and used a diffusion model to learn a prior over these parameters from historical data.
At generation time, we sample parameter configurations that would produce rare events, run the simulator forward, and use the outputs as synthetic training data.
Validation
We validated the approach on the 3 held-out observed rare events. The synthetic training data produced a model that detected all 3 events with:
A model trained on real data only had 2/3 detection rate and 2.1 false positives per year.