Modeling continuous processes from data

Details Modeling continuous processes from data Modeling continuous processes from data

Apr 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002phrve..65d6704s&link_type=abstract

Physical Review E, vol. 65, Issue 4, id. 046704

Computer Science

Performance

4

Time Series Analysis, Time Variability, Numerical Approximation And Analysis, Time Series Analysis, Numerical Simulations Of Chaotic Systems

Scientific paper

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.

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