Learning differential equations from mixed nonlinear dynamics models

For decades, researchers have attempted to use computational algorithms for finding analytical laws from the recorded data. However, previous studies mainly focused on proposing more efficient regression algorithms for learning equations from the given data. An equally important problem, namely how can we algorithmically ensure that the set of candidate variables in the search space are complete and spared from the unnecessary terms has not been given much attention. In this study, we propose a framework to realize the identification of inappropriate potential variables in the equation learning. Specifically, by introducing the causal inference method into the procedure of equation learning, we can effectively recognize terms that confound in the variable space. The pipeline of our method is given, while examples of ecological and physical systems are used to show that we can improve the accuracy of the learnt equations by eliminating the identified confusing terms in the library of potential variables.