@inproceedings{li2022neuralsi,
  title={NeuralSI: Structural Parameter Identification in Nonlinear Dynamical Systems},
  author={Li, Xuyang and Bolandi, Hamed and Salem, Talal and Lajnef, Nizar and Boddeti, Vishnu Naresh},
  booktitle={European Conference on Computer Vision},
  pages={332--348},
  year={2022},
  organization={Springer}
}

In this work, we propose NeuralSI for nonlinear dynamic system identification that allows us to discover the unknown parameters of partial differential equations from measured sensing data.

Upon estimating the unknown system parameters, we apply them to the differential model and efficiently prognosticate the time evolution of the structural response. It is observed that the modulus coefficient $P$ matches well with the sinusoidal ground truth since the modulus dominates the magnitude of the response.

The ground truth and predicted dynamic displacement response, along with the error are visualized at beam midspan. The maximum peak-peak value in the displacement error is only 0.3% of the ground truth. The peak error in temporal extrapolation does not increase much compared to the peak error in temporal interpolation.

We tested the effect of the number of dense layers, training sample ratio, and minibatch size on the parameter identification and prediction of dynamic responses.

At last, we investigate the performance of NeuralSI compared to PINN and DNN, under a limited training data regime across different input beam loading conditions. This replicates the expected challenges in monitoring real structures with limited sensors and sampling capabilities.

Due to a limited amount of data for training, the DNN fails to predict the response. Furthermore, both PINN and DNN fail to extrapolate the structural behavior temporally.

The trade-off among the three methods is evaluated.