Abstract

John von Neumann is often quoted as saying “with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” The implication seems to be that physical models should contain only a handful of parameters. A century later, however, we are happy to use physics-agnostic neural networks containing millions of parameters. What would von Neumann say? How should physical modellers respond?

In this talk, I will show that von Neumann’s quote is more nuanced than it sounds. I will then frame a response within a Bayesian framework, in which physical principles such as conservation of mass, momentum, and energy are treated as high quality prior information, with quantified uncertainty, expressed as PDEs or low order models. The information content of data can then be quantified and the likelihood of different candidate models can be compared after the data arrives. I will show how Bayesian inference becomes computationally tractable when combined with adjoint methods. I will demonstrate this through (i) assimilation of 3D Flow-MRI data in complex geometry into Finite Element CFD , (ii) assimilation of flame and acoustics data into low order models of a thermoacoustic system, which are then ranked by their likelihood given the data. The main message of the talk is “keep the physics in the model if you can.”