Uncertainty Quantification Strategies for Multi-Physics Systems and Digital Twins

One of the main sources of renewable energy is wind, which generates tremendous power
while also reducing the need for greenhouse gas-emitting traditional power sources such as
hydrocarbons and coal. However, many wind turbines
installed in the early 2000's are nearing the end of their lifespan, and the problem remains
of how to maintain, reduce, or decommission these aging turbines in a cost efficient way. In this talk we describe a digital
twin for damage detection and maintenance scheduling of wind turbines which can track the condition of a wind turbine under different operating conditions. A key concern for wind energy that contributes to power production losses and high maintenance
costs is deterioration of the turbine blades over time from environmental stressors such as
lighting strikes, icing and accumulation of airborne particles which can result in leading edge erosion of the blades. We will
discuss surrogate modeling of the turbines and classification of levels of leading edge erosion via machine learning.

We first demonstrate the embedding of a Gaussian Process emulator of high resolution convection processes within a coarse climate numerical model. It leads to a reduction of some of the well know biases in climate modelling.  We then present a new type of emulator of any feed forward multi-physics system, by linking GP emulators of individual simulators, with large gains over the composite emulator of the whole system. The Deep Gaussian Process (DGP) is then presented as a surrogate that shares the structure of the linked emulator but enables the emulation of highly non-linear simulators without the knowledge of individual sub-processes. We then examine sharp changes in the outputs a computer simulator. These often indicate bifurcations or critical transitions within the investigated system, e.g. laminar v. turbulent behavior in fluid dynamics. An efficient approach that localizes these changes using DGPs with a minimal number of evaluations is introduced. We demonstrate the efficacy and efficiency of the proposed framework on the Rayleigh–Bénard convection.

The digital twin concept has its origins in industry. One industrial equipment manufacturer advertised its digital twin capabilities to its customers as ”No unplanned downtime” for its products. There is a compelling aspirational analog in healthcare: ``No unplanned doctor visits." Of course, the challenges of building digital twins for human patients are incomparably greater than for machinery. Nonetheless, there are now several instances of what might be called digital twins in medicine, and many more ongoing development projects. Aside from our incomplete understanding of human biology, relative sparseness of data characterizing human patients, and logistical difficulties in implementing computational models in healthcare, there are many mathematical and computational problems that need to be solved. Examples include calibration and validation of multiscale, hybrid, stochastic computational models, forecasting algorithms, and optimal control methods. This talk will describe some of these problems and outline a mathematical research program for the field.