Discovery of Differential Equations from Numerical Data
نویسندگان
چکیده
This paper proposes a method of discovering some kinds of di erential equations with interval coe cients, which characterize or explain numerical data obtained by scienti c observations and experiments. Such numerical data inevitably involve some ranges of errors, and hence they are represented by closed intervals in this paper. Based on these intervals, we design some interval inclusions which approximate integral equations equivalent to the di erential equations. Interval coe cients of the di erential equations are determined by solving the interval inclusions. Many combinations of interval coe cients can be obtained from numerical data. We nd out a di erential equation whose coe cients consist of intersections of the computed interval coe cients. The refutability of the di erential equation is also discussed. Our discovering method is veri ed by some simulations.
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