Dynamic mode decomposition with core sketch

Journal Article · Fri Jun 10 00:00:00 EDT 2022 · Physics of Fluids

DOI:https://doi.org/10.1063/5.0095163· OSTI ID:1979099

Ahmed, Shady Emad ^[1]; Dabaghian, Pedram H. ^[2]; San, Omer ^[2]; Bistrian, Diana Alina ^[3]; Navon, Ionel M. ^[4]

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1. Oklahoma State Univ., Stillwater, OK (United States); Oklahoma State Univ., Stillwater, OK (United States)
2. Oklahoma State Univ., Stillwater, OK (United States)
3. Politehnica University of Timisoara, Hunedoara, Transylvania (Romania)
4. Florida State Univ., Tallahassee, FL (United States)

With the increase in collected data volumes, either from experimental measurements or high fidelity simulations, there is an ever-growing need to develop computationally efficient tools to process, analyze, and interpret these datasets. Modal analysis techniques have gained great interest due to their ability to identify patterns in the data and extract valuable information about the system being considered. Dynamic mode decomposition (DMD) relies on elements of the Koopman approximation theory to compute a set of modes, each associated with a fixed oscillation frequency and a decay/growth rate. Extracting these details from large datasets can be computationally expensive due to the need to implement singular value decomposition of the input data matrix. Sketching algorithms have become popular in numerical linear algebra where statistical theoretic approaches are utilized to reduce the cost of major operations. A sketch of a matrix is another matrix, which is significantly smaller, but still sufficiently approximates the original system. We put forth an efficient DMD framework, SketchyDMD, based on a core sketching algorithm that captures information about the range and corange (their mutual relationship) of input data. The proposed sketching-based framework can accelerate various portions of the DMD routines, compared to classical methods that operate directly on the raw input data. We conduct numerical experiments using the spherical shallow water equations as a prototypical model in the context of geophysical flows. In conclusion, we show that the proposed SketchyDMD is superior to existing randomized DMD methods that are based on capturing only the range of the input data.

• Research Organization: Oklahoma State Univ., Stillwater, OK (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: SC0019290
• OSTI ID: 1979099
• Alternate ID(s): OSTI ID: 1871848
• Journal Information: Physics of Fluids, Journal Name: Physics of Fluids Journal Issue: 6 Vol. 34; ISSN 1070-6631
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
mechanics
physics