{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T06:12:16Z","timestamp":1787983936656,"version":"build-2784847793"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,3]]},"abstract":"<jats:p>Many of the tools of dynamical systems and control theory have gone largely unused for fluids, because the governing equations are so dynamically complex, both high-dimensional and nonlinear. Model reduction involves finding low-dimensional models that approximate the full high-dimensional dynamics. This paper compares three different methods of model reduction: proper orthogonal decomposition (POD), balanced truncation, and a method called balanced POD. Balanced truncation produces better reduced-order models than POD, but is not computationally tractable for very large systems. Balanced POD is a tractable method for computing approximate balanced truncations, that has computational cost similar to that of POD. The method presented here is a variation of existing methods using empirical Gramians, and the main contributions of the present paper are a version of the method of snapshots that allows one to compute balancing transformations directly, without separate reduction of the Gramians; and an output projection method, which allows tractable computation even when the number of outputs is large. The output projection method requires minimal additional computation, and has a priori error bounds that can guide the choice of rank of the projection. Connections between POD and balanced truncation are also illuminated: in particular, balanced truncation may be viewed as POD of a particular dataset, using the observability Gramian as an inner product. The three methods are illustrated on a numerical example, the linearized flow in a plane channel.<\/jats:p>","DOI":"10.1142\/s0218127405012429","type":"journal-article","created":{"date-parts":[[2005,5,31]],"date-time":"2005-05-31T08:20:40Z","timestamp":1117527640000},"page":"997-1013","source":"Crossref","is-referenced-by-count":773,"title":["MODEL REDUCTION FOR FLUIDS, USING BALANCED PROPER ORTHOGONAL DECOMPOSITION"],"prefix":"10.1142","volume":"15","author":[{"given":"C. W.","family":"ROWLEY","sequence":"first","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/280\/04630"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1398044"},{"key":"rf4","first-page":"1906","volume":"58","author":"Cortelezzi L.","journal-title":"Phys. Rev."},{"key":"rf5","volume-title":"Hydrodynamic Stability","author":"Drazin P. G.","year":"1981"},{"key":"rf6","series-title":"Texts in Applied Mathematics","volume-title":"A Course in Robust Control Theory: A Convex Approach","volume":"36","author":"Dullerud G. E.","year":"1999"},{"key":"rf7","doi-asserted-by":"crossref","first-page":"2600","DOI":"10.1063\/1.858894","volume":"5","author":"Farrell B. F.","journal-title":"Phys. Fluids"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511622700"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.657"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1987.1104549"},{"key":"rf12","volume-title":"Stochastic Tools in Turbulence","author":"Lumley J. L.","year":"1970"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1981.1102568"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901389049"},{"key":"rf15","first-page":"115","volume":"189","author":"Rowley C. W.","journal-title":"Physica"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(93)90117-O"},{"key":"rf17","first-page":"561","author":"Sirovich L.","journal-title":"Q. Appl. Math."},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.2514\/2.1570"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405012429","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:06:57Z","timestamp":1565122017000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405012429"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3]]},"references-count":16,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,3]]}},"alternative-id":["10.1142\/S0218127405012429"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405012429","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,3]]}}}