IDSAI Seminar: Professor Tim Dodwell - Learning to Solve: Scalable Data-Driven Model Order Reduction for Digital Twins

I will talk about some of the very initial ideas coming from my Turing AI Fellowship, around new methodologies required to deliver massive calibrated mathematical simulations in real-time, aka the "Digital Twin".

Proper Orthogonal Decomposition, known as POD amongst many other names across the sciences, is a classical tool for revealing low dimensional structures in data. It is widely used as a model order reduction technique to produce low-dimensional representation of models, using offline simulations as the training data.

For me POD has some major issues: (1) It does not scale to very large problems (2) applying POD online still requires the assembly of the full model and hence scales no-better than well designed full model solvers. (3) The major bottleneck of generating a training set for POD calibrated on data remains. (4) POD does not naturally come with metrics to determine the uncertainty in their predicative abilities relative to the full model.

In the context of stochastic elliptic PDEs (which arise in ground water flow, structural mechanics and temperature flow problems), using research in domain decomposition, multi-level MCMC methods and emulators, I will outline a family of approaches which seek to tackle these challenges.