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The discovery of equations with knowledge of the process origin is a temptingprospect. However, most equation discovery tools rely on gradient methods,which offer limited control over parameters. An alternative approach is theevolutionary equation discovery, which allows modification of almost everyoptimization stage. In this paper, we examine the modifications that can beintroduced into the evolutionary operators of the equation discovery algorithm,taking inspiration from directed evolution techniques employed in fields suchas chemistry and biology. The resulting approach, dubbed directed equationdiscovery, demonstrates a greater ability to converge towards accuratesolutions than the conventional method. To support our findings, we presentexperiments based on Burgers', wave, and Korteweg--de Vries equations.

Directed differential equation discovery using modified mutation and cross-over operators