## Abstract

In this chapter, we propose a composite neural network framework for modeling impulsive nonlinear dynamics, which is typically in the form of high-order time differentiation. The proposed composite neural network utilizes multiple orders of time-differentiated dynamics to model large time-varying nonlinearities. It consists of three sequentially connected feed-forward subnetworks learning from simpler, lower order time-differentiated dynamics to more complicated, higher order time-differentiated dynamics in sequence. Setting the final output to the second-order time-differentiated responses which are highly nonlinear quantities commonly observed in forms of force or acceleration, the first, the second, and the third subnetworks predict the zeroth-, the first-, and the second-order responses, respectively, by taking outputs of the previous subnetworks as their inputs. The structured connection among multiple subnetworks allows precise data-driven modeling of elaborated dynamics by expanding the network observations from single-order to multi-orders of time-differentiated dynamics. For evaluation, the numerical study of metamodeling high-dimensional virtual vehicle acceleration is performed with two different types of competing networks: the conventional network that directly maps the input to the second-order derivative in a common way and the autogradient network that first maps the input to the zeroth-order time derivative and then employs an automatic differentiation engine to compute time differentiations of its output. The proposed composite neural net shows the outperformance for predicting unknown impulsive accelerations more than the other baseline models. Although the presented numerical study focuses only on mechanical dynamics, the proposed methodology can be applied to any other domain that deals with massively fluctuating responses by changing the differentiation domain variable from time to space, frequency, or any other variables.

Original language | English |
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Title of host publication | Data Science in Engineering, Volume 10 - Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics 2023 |

Editors | Ramin Madarshahian, François Hemez |

Publisher | Springer |

Pages | 165-168 |

Number of pages | 4 |

ISBN (Print) | 9783031349454 |

DOIs | |

Publication status | Published - 2023 |

Event | 41st IMAC, A Conference and Exposition on Structural Dynamics, 2023 - Austin, United States Duration: 13 Feb 2023 → 16 Feb 2023 |

### Publication series

Name | Conference Proceedings of the Society for Experimental Mechanics Series |
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ISSN (Print) | 2191-5644 |

ISSN (Electronic) | 2191-5652 |

### Conference

Conference | 41st IMAC, A Conference and Exposition on Structural Dynamics, 2023 |
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Country/Territory | United States |

City | Austin |

Period | 13/02/23 → 16/02/23 |

### Bibliographical note

Publisher Copyright:© 2023, The Society for Experimental Mechanics, Inc.

## Keywords

- Composite neural network
- Data-driven modeling
- Impulse dynamics
- Machine learning
- Nonlinear dynamics