Discovery of Differential Equations from Numerical Data

Authors:
Koichi Niijima;Hidemi Uchida;Eiju Hirowatari;Setsuo Arikawa
Affiliations:
-;-;-;-
Venue:
DS '98 Proceedings of the First International Conference on Discovery Science
Year:
1998

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Abstract

This paper proposes a method of discovering some kinds of differential equations with interval coefficients, which characterize or explain numerical data obtained by scientific observations and experiments. Such numerical data inevitably involve some ranges of errors, and hence they are represented by closed intervals in this paper. Usingth ese intervals, we design some interval inclusions which approximate integral equations equivalent to the differential equations. Interval coefficients in the differential equations are determined by solvingthe interval inclusions. Many combinations of interval coefficients can be obtained from numerical data. Based on these interval coefficients, the refutability of differential equations is discussed. As a result, we can identify a differential equation. The efficiency of our discoveringmeth od is verified by some simulations.