Peter J. Schmid

Dynamic Mode Decomposition and Its Variants

Annual Review of Fluid Mechanics · 2021-10-05 · 597 citations

Dynamic mode decomposition (DMD) is a factorization and dimensionality reduction technique for data sequences. In its most common form, it processes high-dimensional sequential measurements, extracts coherent structures, isolates dynamic behavior, and reduces complex evolution processes to their dominant features and essential components. The decomposition is intimately related to Koopman analysis and, since its introduction, has spawned various extensions, generalizations, and improvements. It…

Sparsifying the resolvent forcing mode via gradient-based optimisation

Journal of Fluid Mechanics · 2022-07-06 · 30 citations

We consider the use of sparsity-promoting norms in obtaining localised forcing structures from resolvent analysis. By formulating the optimal forcing problem as a Riemannian optimisation, we are able to maximise cost functionals whilst maintaining a unit-energy forcing. Taking the cost functional to be the energy norm of the driven response results in a traditional resolvent analysis and is solvable by a singular value decomposition (SVD). By modifying this cost functional with the $L_1$ -norm,…

SENSITIVITY ANALYSIS OF THERMOACOUSTIC INSTABILITIES

2024-11-07 · 1 citations

Nonlinear evolution of unstable solar inertial modes: The case of viscous modes on a differentially rotating sphere

arXiv (Cornell University) · 2026-03-09

On the Sun, the inertial mode with the largest observed amplitude (rms velocity exceeding $10$ m/s) is the high-latitude mode with longitudinal wavenumber $m=1$. In two dimensions, on the sphere, linear theory predicts that this mode is unstable due to a shear instability associated with latitudinal differential rotation (fast equator, slower polar regions). We investigate the evolution of this instability numerically and theoretically. The nonlinear vorticity equation is solved using direct num…

Learning dissipation and instability fields from chaotic dynamics

ArXiv.org · 2025-02-05

To make predictions or design control, information on local sensitivity of initial conditions and state-space contraction is both central, and often instrumental. However, it is not always simple to reliably determine instability fields or local dissipation rates, due to computational challenges or ignorance of the governing equations. Here, we construct an alternative route towards that goal, by estimating the Jacobian of a discrete-time dynamical system locally from the entries of the transiti…