Session: 07-19-01 Machine Learning and Artificial Intelligence in Dynamics and Vibrations I

Paper Number: 77246

Start Time: Tuesday, 07:40 PM

77246 - A Physics-Informed Recurrent Neural Network Approach for Long-Term Predictive Modeling of Nonlinear Dynamical Systems 

Long-term prediction of future states has been challenging in data-driven modeling of nonlinear dynamical systems as the prediction error can accumulate over the prediction horizon. One of the potential reasons is the lack of robustness for the data-driven model. In this study we present a recurrent neural network (RNN) framework with an adaptive training strategy to model nonlinear dynamical systems from data for long-time prediction of futurestates. Specifically, we exploit the recurrence of networks to improve the model robustnessby by explicitly incorporating the multi-step prediction error accumulation into the training of the data-driven model. Furthermore, we introduce an adaptive training strategy, where the prediction horizon gradually increases to facilitate the RNN model training. The resulting model is expected to be robust as it is enforced to adapt to the error accumulation over a prediction horizon in the closed-loop training phase.

Specifically, we first introduce a surrogate neural network module to model the temporal evolution of nonlinear dynamics informed by the general representation with ODE. Furthermore, we propose a RNN framework to improve the model robustness for the long-time prediction. Finally we propose an adaptive strategy to facilitate the RNN training, where the prediction horizon gradually increases from a small value with the training progress. We demonstrate the proposed approach on a family of Duffing oscillators, including autonomous and non-autonomous systems with various attractors, and discuss its advantages and limitations. We compare the proposed framework with the Multistep-NN approach.

We observe that the adaptive-T strategy has a better performance with lower normalized mean squared error (NMSE) and higher squared correlation coefficient (SCC) for long-term prediction of future states on the testing dataset. while the constant-T strategy has shown an unstable and irregular performance with different choice of T. The advantage of proposed adaptive strategy is its ability to facilitate the RNN training with a gradually-increased demand on model robustness. On the other side, we also compare the proposed adaptive-RNN method with a similar work Multistep Neural Network. The adaptive-RNN framework shows high accuracy on the long-term prediction of future states for the considered duffing system.

In this study we also identify and discuss two challenges which are worth further research for data-driven modeling of nonlinear dynamics. (1) Small-amplitude oscillations around equilibriums are difficult to accurately predict. The potential reason is that small-amplitude trajectories in training set are easy to be ignored due to the small MSE loss which is generally positively correlated with the amplitude. (2) A small prediction error at critical transition points (e.g. saddle point) in nonlinear dynamics is likely to lead predicted evolution to a wrong region. One possible reason is the lack of training data for such unique points.

Presenting Author: Shanwu Li Michigan Technological University

Authors:

Yongchao Yang Michigan Technological University
Shanwu Li Michigan Technological University