Abstract
There is a strong need for explanation model development and selection (especially, partial differ-ential equation : PDE) using big data from interesting phenomena. In the inductive PDE derivation from big data, at present, the PDE computation results have been regarded as big data in order to establish a methodolo-gy. Assuming that a PDE is a linear regression model composed of partial differential terms, the coefficients are estimated by regression analysis, and the difference (error) between the true and the estimated coefficients is minimized. In the conventional method, since the partial differential term is calculated by differential ap-proximation, it is difficult to analyze the cause of the error.
To solve the problem, we take PDEs with exact solutions and compute the partial differential term by differen-tiating the solution analytically. Considering that PDE does not depend on initial conditions, we hypothesized that the error is caused by insufficient comprehensiveness of the initial conditions. For the exact solution of the advection-diffusion equation with system noise superimposed, we calculated the error relative to the true value of the coefficient. The exact solution was calculated by changing the initial conditions at random, and we con-firmed that a negative correlation between the number of initial conditions and the error.
