Physics-Informed, Data-Driven and Hybrid Approaches to Space-Time Systems

In this talk I will discuss two different approaches to characterize space-time systems. This first one is model-driven and loosely inspired by physics, assumes that the system is locally diffusive through a stochastic partial differential equation, and can be efficiently approximated with a Gaussian Markov random field. This approximation will be used to produce a stochastic generator of simulated multi-decadal global temperature, thereby offering a fast alternative to the generation of large climate model ensembles.

The second approach is instead data-driven, and relies on (deep) neural networks in time. Instead of traditional machine learning methods aimed at inferring an extremely large parameter space, we instead rely on an alternative fast, sparse and computationally efficient echo state network dynamics on an appropriately dimensionally reduced spatial field. The additional computational time is then used to produce an ensemble and probabilistically calibrate the forecast. The approach will be used to produce air pollution forecasts from a citizen science network in San Francisco and forecasting wind energy in Saudi Arabia.

Towards the end of the presentation, I will discuss how these two broad frameworks could be used in synergy to allow for improved predictability and understanding of space-time systems whose physical understanding is currently limited and/or largely influenced by parametrizations.