Automatically Extracting Generalized Action of Non-conservative Systems

The principle of stationary generalized action for non-conservative systems is mathematically elegant and physically interpretable, however, only for very few systems the generalized actions can be constructed theoretically. This work addresses this issue and proposes a data-driven method to automatically extract the generalized action for non-conservative systems. Here, the optimization objective is set by the mathematical implication of generalized action; solving conditions are derived by the arbitrariness of variation; and the generalized action with sparse form is determined by the iterative optimization with dimension increasing stepwise. Numerical investigation for four representative systems illustrates the efficacy of this method, and in the meanwhile, reveals the non-uniqueness of generalized action. Implemented within an integral-variational framework, this method exhibits strong robustness to data noise.