An evolutionary differential-equation discovery method (a knowledge-aware EPDE) that embeds background knowledge softly rather than as hard constraints. It represents knowledge as a probability distribution over candidate equation terms, extracted automatically from an initial guess by a simpler algorithm (or specified by an expert), and uses that distribution to bias the crossover and mutation operators toward favored terms while preserving the ability to reach any equation structure. This yields greater search stability and noise robustness than sparse-regression methods such as SINDy, shown on the Burgers, wave, and Korteweg-de Vries equations.
In data-driven discovery of differential equations, expert knowledge is usually injected as rigid constraints that fix the equation's form, reducing discovery to fitting coefficients. This paper pres…