# Implicit Neural Representation for Physics-driven Actuated Soft Bodies

arXiv: https://arxiv.org/abs/2401.14861 · HTML: https://mlsanity.com/paper/2401.14861/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 26 Jan 2024.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [StyleSDF: High-Resolution 3D-Consistent Image and Geometry Generation](https://mlsanity.com/paper/2112.11427/) (2021)
- [3D Morphable Face Models -- Past, Present and Future](https://mlsanity.com/paper/1909.01815/) (2019)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [CIPS-3D: A 3D-Aware Generator of GANs Based on Conditionally-Independent Pixel Synthesis](https://mlsanity.com/paper/2110.09788/) (2021)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics](https://mlsanity.com/paper/1810.01054/) (2018)
- [Learning Formation of Physically-Based Face Attributes](https://mlsanity.com/paper/2004.03458/) (2020)
- [Scalable Differentiable Physics for Learning and Control](https://mlsanity.com/paper/2007.02168/) (2020)
- [DiffPD: Differentiable Projective Dynamics](https://mlsanity.com/paper/2101.05917/) (2021)
- [Differentiable Simulation of Soft Multi-body Systems](https://mlsanity.com/paper/2205.01758/) (2022)
- [SoftSMPL: Data-driven Modeling of Nonlinear Soft-tissue Dynamics for Parametric Humans](https://mlsanity.com/paper/2004.00326/) (2020)
- [High-Quality Face Capture Using Anatomical Muscles](https://mlsanity.com/paper/1812.02836/) (2018)

## Built on by (most cited first, 5 of 5)

- [Superpixel-informed Implicit Neural Representation for Multi-Dimensional Data](https://mlsanity.com/paper/2411.11356/) (2024)
- [Learning a Generalized Physical Face Model From Data](https://mlsanity.com/paper/2402.19477/) (2024)
- [An Implicit Physical Face Model Driven by Expression and Style](https://mlsanity.com/paper/2401.15414/) (2024)
- [BFSM: 3D Bidirectional Face-Skull Morphable Model](https://mlsanity.com/paper/2509.24577/) (2025)
- [GNM Head: A Generative aNthropometric Model of the human head](https://mlsanity.com/paper/2607.23687/) (2026)

## Abstract (arXiv)

Active soft bodies can affect their shape through an internal actuation mechanism that induces a deformation. Similar to recent work, this paper utilizes a differentiable, quasi-static, and physics-based simulation layer to optimize for actuation signals parameterized by neural networks. Our key contribution is a general and implicit formulation to control active soft bodies by defining a function that enables a continuous mapping from a spatial point in the material space to the actuation value. This property allows us to capture the signal's dominant frequencies, making the method discretization agnostic and widely applicable. We extend our implicit model to mandible kinematics for the particular case of facial animation and show that we can reliably reproduce facial expressions captured with high-quality capture systems. We apply the method to volumetric soft bodies, human poses, and facial expressions, demonstrating artist-friendly properties, such as simple control over the latent space and resolution invariance at test time.