Modeling continuous processes from data

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17 Citations (Web of Science)


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.
Original languageEnglish
Article number046704
Number of pages11
JournalPhysical Review E
Publication statusPublished - 2002


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