Abstract: Data-driven models that respect physical laws are robust to noise, require few training samples, and are highly generalizable. Although the dynamic mode decomposition (DMD) is a principal tool of data-driven fluid dynamics, it is rare for learned DMD models to obey physical laws such as symmetries, invariances, causalities, spatial locality, and conservation laws. Thus, Peter Baddoo presents physics-informed dynamic mode decomposition (piDMD), a suite of tools that incorporate physical structures into linear system identification. Specifically, he develops efficient and accurate algorithms that produce DMD models that obey the matrix analogues of user-specified physical constraints. Through a range of examples from fluid dynamics, he demonstrates the improved diagnostic, predictive, and interpretative abilities of piDMD. He considers examples from stability analysis, data-driven resolvent analysis, reduced-order modelling, control, and the low-data and high-noise regimes. Conversely, if the physical structures are unknown then, through cross-validation, piDMD can be used to discover the physical structures present in the observed system.
Speaker bio: Peter Baddoo earned an M.Math from the University of Oxford and a Ph.D. in applied mathematics at the University of Cambridge. He spent one year at Imperial College London as an EPSRC Doctoral Prize Fellow before moving to MIT as an instructor in applied mathematics. His Ph.D. thesis won the “Best Thesis Award” from the UK Fluids Network and was published in Springer Nature’s outstanding theses series.