Experimental Report on Establishing Solution Space Fingerprints for Observed Numerical Solutions Without Equations

Abstract

In scenarios where only observed numerical solutions are available and there are no explicit governing equations, direct equation fitting is prone to overfitting and is a cumbersome process. Therefore, this study proposes avoiding equation fitting. Instead, numerical solutions are collected, and their features are analyzed using methods such as solution space range estimation, Fast Fourier Transform (FFT), Discrete Cosine Transform (DCT), wavelet transform, and Hilbert-Huang Transform (HHT) to construct "fingerprint features" of the solutions. In the future, the recognition of unknown solutions can be achieved by checking the consistency between new solutions and these fingerprint features.