Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/4820
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Title: Modeling continuous processes from data
Authors: Small, M
Judd, K
Mees, A
Issue Date: 11-Apr-2002
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.
Keywords: Algorithms
Data reduction
Error analysis
Integration
Mathematical models
Polynomials
Vectors
Publisher: American Physical Society
Journal: Physical review. E, Statistical, nonlinear, and soft matter physics 
ISSN: 1539-3755
EISSN: 1550-2376
DOI: 10.1103/PhysRevE.65.046704
Rights: Physical Review E © 2002 The American Physical Society. The Journal's web site is located at http://pre.aps.org/
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