6 papers
Coarse-grained and emergent distributed parameter systems from data
Hassan Arbabi, Felix P. Kemeth, Tom Bertalan +1
We explore the derivation of distributed parameter system evolution laws (and in particular, partial differential operators and associated partial differential equations, PDEs) fro…
Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
Hassan Arbabi, Judith E. Bunder, Giovanni Samaey +2
The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural…
Search strategy in a complex and dynamic environment: the MH370 case
Stefan Ivić, Bojan Crnković, Hassan Arbabi +3
Search and detection of objects on the ocean surface is a challenging task due to the complexity of the drift dynamics and lack of known optimal solutions for the path of the searc…
Spectral analysis of mixing in 2D high-Reynolds flows
Hassan Arbabi, Igor Mezic
We use spectral analysis of Eulerian and Lagrangian dynamics to study the advective mixing in an incompressible 2D bounded cavity flow. A significant property of such a rotational…
Prandtl-Batchelor theorem for flows with quasi-periodic time dependence
Hassan Arbabi, Igor Mezić
The classical Prandtl-Batchelor theorem (Prandtl 1904; Batchelor 1956) states that in the regions of steady 2D flow where viscous forces are small and streamlines are closed, the v…
A data-driven Koopman model predictive control framework for nonlinear flows
Hassan Arbabi, Milan Korda, Igor Mezic
The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data.…