# LiCROM: Linear-Subspace Continuous Reduced Order Modeling with Neural Fields

arXiv: https://arxiv.org/abs/2310.15907 · HTML: https://mlsanity.com/paper/2310.15907/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2023.

## Built on by (most cited first, 9 of 9)

- [Make-It-Animatable: An Efficient Framework for Authoring Animation-Ready 3D Characters](https://mlsanity.com/paper/2411.18197/) (2024)
- [ClothTransformer: Unified Latent-Space Transformers for Scalable Cloth Simulation](https://mlsanity.com/paper/2605.27852/) (2026)
- [NeuROK: Generative 4D Neural Object Kinematics](https://mlsanity.com/paper/2605.30347/) (2026)
- [Learning Lagrangian Interaction Dynamics with Sampling-Based Model Order Reduction](https://mlsanity.com/paper/2407.03925/) (2024)
- [Tube Diffusion Policy: Reactive Visual-Tactile Policy Learning for Contact-rich Manipulation](https://mlsanity.com/paper/2604.23609/) (2026)
- [FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes](https://mlsanity.com/paper/2605.29318/) (2026)
- [Neural Kinematic Bases for Fluids](https://mlsanity.com/paper/2504.15657/) (2025)
- [PhysSkin: Real-Time and Generalizable Physics-Based Animation via Self-Supervised Neural Skinning](https://mlsanity.com/paper/2603.23194/) (2026)
- [RealSimLoop: Online Real-to-Sim Adaptation via Differentiable Reduced-Order Simulation with Vision Feedback](https://mlsanity.com/paper/2609.09828/) (2026)

## Abstract (arXiv)

Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial discretization, and then serves to accelerate simulations with the same discretization. This discretization-dependence is restrictive. Becoming independent of a specific discretization would provide flexibility to mix and match mesh resolutions, connectivity, and type (tetrahedral, hexahedral) in training data; to accelerate simulations with novel discretizations unseen during training; and to accelerate adaptive simulations that temporally or parametrically change the discretization. We present a flexible, discretization-independent approach to reduced-order modeling. Like traditional ROM, we represent the configuration as a linear combination of displacement fields. Unlike traditional ROM, our displacement fields are continuous maps from every point on the reference domain to a corresponding displacement vector; these maps are represented as implicit neural fields. With linear continuous ROM (LiCROM), our training set can include multiple geometries undergoing multiple loading conditions, independent of their discretization. This opens the door to novel applications of reduced order modeling. We can now accelerate simulations that modify the geometry at runtime, for instance via cutting, hole punching, and even swapping the entire mesh. We can also accelerate simulations of geometries unseen during training. We demonstrate one-shot generalization, training on a single geometry and subsequently simulating various unseen geometries.