# SLIDE: A machine-learning based method for forced dynamic response estimation of multibody systems

arXiv: https://arxiv.org/abs/2409.18272 · HTML: https://mlsanity.com/paper/2409.18272/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 42 references that are in the map.
- First posted on arXiv 26 Sep 2024.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2109.14545/) (2021)
- [Data-driven simulation for general purpose multibody dynamics using deep neural networks](https://mlsanity.com/paper/1909.02391/) (2019)
- [Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics](https://mlsanity.com/paper/2212.08989/) (2022)
- [MBD-NODE: Physics-informed data-driven modeling and simulation of constrained multibody systems](https://mlsanity.com/paper/2407.08664/) (2024)

## Built on by (most cited first, 1 of 1)

- [Real-Time Structural Deflection Estimation in Hydraulically Actuated Systems Using 3D Flexible Multibody Simulation and DNNs](https://mlsanity.com/paper/2503.07528/) (2025)

## Abstract (arXiv)

In computational engineering, enhancing the simulation speed and efficiency is a perpetual goal. To fully take advantage of neural network techniques and hardware, we present the SLiding-window Initially-truncated Dynamic-response Estimator (SLIDE), a deep learning-based method designed to estimate output sequences of mechanical or multibody systems with primarily, but not exclusively, forced excitation. A key advantage of SLIDE is its ability to estimate the dynamic response of damped systems without requiring the full system state, making it particularly effective for flexible multibody systems. The method truncates the output window based on the decay of initial effects, such as damping, which is approximated by the complex eigenvalues of the systems linearized equations. In addition, a second neural network is trained to provide an error estimation, further enhancing the methods applicability. The method is applied to a diverse selection of systems, including the Duffing oscillator, a flexible slider-crank system, and an industrial 6R manipulator, mounted on a flexible socket. Our results demonstrate significant speedups from the simulation up to several millions, exceeding real-time performance substantially.