High-order differentiable autoencoder for nonlinear model reduction

@article{Shen2021HighorderDA,
  title={High-order differentiable autoencoder for nonlinear model reduction},
  author={Siyuan Shen and Yin Yang and Tianjia Shao and He Wang and Chenfanfu Jiang and Lei Lan and Kun Zhou},
  journal={ACM Transactions on Graphics (TOG)},
  year={2021},
  volume={40},
  pages={1 - 15}
}
This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable solids. Due to the inertia effect, the dynamic equilibrium cannot be established without evaluating the second-order derivatives of the deep autoencoder network. This is beyond the capability of off-the-shelf automatic differentiation packages and algorithms… 
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