# Data-Free Learning of Reduced-Order Kinematics

arXiv: https://arxiv.org/abs/2305.03846 · HTML: https://mlsanity.com/paper/2305.03846/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 5 May 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [SNUG: Self-Supervised Neural Dynamic Garments](https://mlsanity.com/paper/2204.02219/) (2022)
- [Propagation Networks for Model-Based Control Under Partial Observation](https://mlsanity.com/paper/1809.11169/) (2018)
- [PBNS: Physically Based Neural Simulator for Unsupervised Garment Pose Space Deformation](https://mlsanity.com/paper/2012.11310/) (2020)
- [Learning Signal-Agnostic Manifolds of Neural Fields](https://mlsanity.com/paper/2111.06387/) (2021)
- [Neural Cloth Simulation](https://mlsanity.com/paper/2212.11220/) (2022)
- [High-order Differentiable Autoencoder for Nonlinear Model Reduction](https://mlsanity.com/paper/2102.11026/) (2021)
- [Dynamic Neural Garments](https://mlsanity.com/paper/2102.11811/) (2021)
- [A Deep Emulator for Secondary Motion of 3D Characters](https://mlsanity.com/paper/2103.01261/) (2021)

## Built on by (most cited first, 19 of 19)

- [Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation](https://mlsanity.com/paper/2407.09497/) (2024)
- [Neural Stress Fields for Reduced-order Elastoplasticity and Fracture](https://mlsanity.com/paper/2310.17790/) (2023)
- [ContourCraft: Learning to Resolve Intersections in Neural Multi-Garment Simulations](https://mlsanity.com/paper/2405.09522/) (2024)
- [Quaffure: Real-Time Quasi-Static Neural Hair Simulation](https://mlsanity.com/paper/2412.10061/) (2024)
- [Neural Modes: Self-supervised Learning of Nonlinear Modal Subspaces](https://mlsanity.com/paper/2404.17620/) (2024)
- [Accelerate Neural Subspace-Based Reduced-Order Solver of Deformable Simulation by Lipschitz Optimization](https://mlsanity.com/paper/2409.03807/) (2024)
- [Neuralocks: Real-Time Dynamic Neural Hair Simulation](https://mlsanity.com/paper/2507.05191/) (2025)
- [NeuROK: Generative 4D Neural Object Kinematics](https://mlsanity.com/paper/2605.30347/) (2026)
- [FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes](https://mlsanity.com/paper/2605.29318/) (2026)
- [Stabilizing and Solving Unique Continuation Problems by Parameterizing Data and Learning Finite Element Solution Operators](https://mlsanity.com/paper/2412.04409/) (2024)
- [Learning Nonlinear Finite Element Solution Operators using Multilayer Perceptrons and Energy Minimization](https://mlsanity.com/paper/2412.04596/) (2024)
- [Neural Kinematic Bases for Fluids](https://mlsanity.com/paper/2504.15657/) (2025)
- [Generalized Dynamics Generation towards Scannable Physical World Model](https://mlsanity.com/paper/2510.15041/) (2025)
- [PhysSkin: Real-Time and Generalizable Physics-Based Animation via Self-Supervised Neural Skinning](https://mlsanity.com/paper/2603.23194/) (2026)
- [Momentum-Conserving Graph Neural Networks for Deformable Objects](https://mlsanity.com/paper/2604.26097/) (2026)
- [Reduced-order Neural Modeling with Differentiable Simulation for High-Detail Tactile Perception](https://mlsanity.com/paper/2605.05053/) (2026)
- [Learning Orthonormal Bases for Function Spaces](https://mlsanity.com/paper/2605.19959/) (2026)
- [ODeform: Learning Continuous 4D Motion for Shape Deformation with Neural ODEs](https://mlsanity.com/paper/2607.20670/) (2026)
- [RealSimLoop: Online Real-to-Sim Adaptation via Differentiable Reduced-Order Simulation with Vision Feedback](https://mlsanity.com/paper/2609.09828/) (2026)

## Abstract (arXiv)

Physical systems ranging from elastic bodies to kinematic linkages are defined on high-dimensional configuration spaces, yet their typical low-energy configurations are concentrated on much lower-dimensional subspaces. This work addresses the challenge of identifying such subspaces automatically: given as input an energy function for a high-dimensional system, we produce a low-dimensional map whose image parameterizes a diverse yet low-energy submanifold of configurations. The only additional input needed is a single seed configuration for the system to initialize our procedure; no dataset of trajectories is required. We represent subspaces as neural networks that map a low-dimensional latent vector to the full configuration space, and propose a training scheme to fit network parameters to any system of interest. This formulation is effective across a very general range of physical systems; our experiments demonstrate not only nonlinear and very low-dimensional elastic body and cloth subspaces, but also more general systems like colliding rigid bodies and linkages. We briefly explore applications built on this formulation, including manipulation, latent interpolation, and sampling.