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Title: Modeling continuous processes from data
Authors: Small, Michael
Judd, Kevin
Mees, Alistair
Subjects: Algorithms
Data reduction
Error analysis
Mathematical models
Issue Date: 11-Apr-2002
Publisher: American Physical Society
Source: Physical review E, statistical, nonlinear, and soft matter physics, Apr. 2002, v. 65, no. 4, 046704, p. 1-11.
Abstract: Experimental and simulated time series are necessarily discretized in time. However, many real and artificial systems are more naturally modeled as continuous-time systems. This paper reviews the major techniques employed to estimate a continuous vector field from a finite discrete time series. We compare the performance of various methods on experimental and artificial time series and explore the connection between continuous (differential) and discrete (difference equation) systems. As part of this process we propose improvements to existing techniques. Our results demonstrate that the continuous-time dynamics of many noisy data sets can be simulated more accurately by modeling the one-step prediction map than by modeling the vector field. We also show that radial basis models provide superior results to global polynomial models.
Rights: Physical Review E © 2002 The American Physical Society. The Journal's web site is located at
Type: Journal/Magazine Article
DOI: 10.1103/PhysRevE.65.046704
ISSN: 1539-3755 (print)
1550-2376 (online)
Appears in Collections:EIE Journal/Magazine Articles

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