# Analytically Integratable Zero-restlength Springs for Capturing Dynamic Modes unrepresented by Quasistatic Neural Networks

arXiv: https://arxiv.org/abs/2201.10122 · HTML: https://mlsanity.com/paper/2201.10122/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 75 references that are in the map.
- First posted on arXiv 25 Jan 2022.

## Builds on (most cited first, 23 of 23)

- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [TailorNet: Predicting Clothing in 3D as a Function of Human Pose, Shape and Garment Style](https://mlsanity.com/paper/2003.04583/) (2020)
- [Latent-space Physics: Towards Learning the Temporal Evolution of Fluid Flow](https://mlsanity.com/paper/1802.10123/) (2018)
- [DeepWrinkles: Accurate and Realistic Clothing Modeling](https://mlsanity.com/paper/1808.03417/) (2018)
- [Gradients are Not All You Need](https://mlsanity.com/paper/2111.05803/) (2021)
- [PBNS: Physically Based Neural Simulator for Unsupervised Garment Pose Space Deformation](https://mlsanity.com/paper/2012.11310/) (2020)
- [Simulation of hyperelastic materials in real-time using Deep Learning](https://mlsanity.com/paper/1904.06197/) (2019)
- [A Pixel-Based Framework for Data-Driven Clothing](https://mlsanity.com/paper/1812.01677/) (2018)
- [Dynamic Neural Garments](https://mlsanity.com/paper/2102.11811/) (2021)
- [PhysGNN: A Physics-Driven Graph Neural Network Based Model for Predicting Soft Tissue Deformation in Image-Guided Neurosurgery](https://mlsanity.com/paper/2109.04352/) (2021)
- [Learning Soft Tissue Behavior of Organs for Surgical Navigation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.00722/) (2019)
- [SoftSMPL: Data-driven Modeling of Nonlinear Soft-tissue Dynamics for Parametric Humans](https://mlsanity.com/paper/2004.00326/) (2020)
- [A Deep Emulator for Secondary Motion of 3D Characters](https://mlsanity.com/paper/2103.01261/) (2021)
- [Coercing Machine Learning to Output Physically Accurate Results](https://mlsanity.com/paper/1910.09671/) (2019)
- [Realtime Simulation of Thin-Shell Deformable Materials using CNN-Based Mesh Embedding](https://mlsanity.com/paper/1909.12354/) (2019)
- [Complementary Dynamics](https://mlsanity.com/paper/2009.02462/) (2020)
- [Mesh-based Autoencoders for Localized Deformation Component Analysis](https://mlsanity.com/paper/1709.04304/) (2017)
- [Skinning a Parameterization of Three-Dimensional Space for Neural Network Cloth](https://mlsanity.com/paper/2006.04874/) (2020)
- [Alternating ConvLSTM: Learning Force Propagation with Alternate State Updates](https://mlsanity.com/paper/2006.07818/) (2020)
- [Recovering Geometric Information with Learned Texture Perturbations](https://mlsanity.com/paper/2001.07253/) (2020)
- [Volume Preserving Simulation of Soft Tissue with Skin](https://mlsanity.com/paper/2109.01170/) (2021)
- [DSNet: Dynamic Skin Deformation Prediction by Recurrent Neural Network](https://mlsanity.com/paper/2201.07660/) (2021)

## Built on by (most cited first, 2 of 2)

- [Software-based Automatic Differentiation is Flawed](https://mlsanity.com/paper/2305.03863/) (2023)
- [A Neural-Network-Based Approach for Loose-Fitting Clothing](https://mlsanity.com/paper/2404.16896/) (2024)

## Abstract (arXiv)

We present a novel paradigm for modeling certain types of dynamic simulation in real-time with the aid of neural networks. In order to significantly reduce the requirements on data (especially time-dependent data), as well as decrease generalization error, our approach utilizes a data-driven neural network only to capture quasistatic information (instead of dynamic or time-dependent information). Subsequently, we augment our quasistatic neural network (QNN) inference with a (real-time) dynamic simulation layer. Our key insight is that the dynamic modes lost when using a QNN approximation can be captured with a quite simple (and decoupled) zero-restlength spring model, which can be integrated analytically (as opposed to numerically) and thus has no time-step stability restrictions. Additionally, we demonstrate that the spring constitutive parameters can be robustly learned from a surprisingly small amount of dynamic simulation data. Although we illustrate the efficacy of our approach by considering soft-tissue dynamics on animated human bodies, the paradigm is extensible to many different simulation frameworks.