Forecasting of nonlinear dynamics based on symbolic invariance

Forecasting unknown dynamics is of great interest across many physics-related disciplines. However, data-driven machine learning methods are bothered by the poor generalization issue. To this end, a forecasting model based on symbolic invariance (i.e., expressions/equations that represent intrinsic system mechanisms) proposed. By training and pruning neural network wrapped in numerical integrator, we develop an invariant structure represents evolution function thus can generalize well to unseen data. counter noise effect, algorithmic framework for probabilistic has also been developed leveraging non-parametric Bayesian inference method. Additionally, account univariate partially observed from with multiple state variables, further leverage delay coordinate embedding find more self-contained embedding. The performance proposed demonstrated both synthetic real-world nonlinear shown better over popular deep models short/medium horizons. Moreover, comparison dictionary-based regression suggests better-behaved efficient optimization when search space enormous.