# Neural Force Field: Few-shot Learning of Generalized Physical Reasoning

arXiv: https://arxiv.org/abs/2502.08987 · HTML: https://mlsanity.com/paper/2502.08987/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 70 references that are in the map.
- First posted on arXiv 13 Feb 2025.

## Builds on (most cited first, 30 of 42)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Is Space-Time Attention All You Need for Video Understanding?](https://mlsanity.com/paper/2102.05095/) (2021)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [How Far is Video Generation from World Model: A Physical Law Perspective](https://mlsanity.com/paper/2411.02385/) (2024)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [PredRNN: A Recurrent Neural Network for Spatiotemporal Predictive Learning](https://mlsanity.com/paper/2103.09504/) (2021)
- [PhysGen: Rigid-Body Physics-Grounded Image-to-Video Generation](https://mlsanity.com/paper/2409.18964/) (2024)
- [Do generative video models understand physical principles?](https://mlsanity.com/paper/2501.09038/) (2025)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Physion: Evaluating Physical Prediction from Vision in Humans and Machines](https://mlsanity.com/paper/2106.08261/) (2021)
- [SlotFormer: Unsupervised Visual Dynamics Simulation with Object-Centric Models](https://mlsanity.com/paper/2210.05861/) (2022)
- [PHYRE: A New Benchmark for Physical Reasoning](https://mlsanity.com/paper/1908.05656/) (2019)
- [On Second Order Behaviour in Augmented Neural ODEs](https://mlsanity.com/paper/2006.07220/) (2020)
- [Dark, Beyond Deep: A Paradigm Shift to Cognitive AI with Humanlike Common Sense](https://mlsanity.com/paper/2004.09044/) (2020)
- [Rapid trial-and-error learning with simulation supports flexible tool use and physical reasoning](https://mlsanity.com/paper/1907.09620/) (2019)
- [Physics Informed Neural Fields for Smoke Reconstruction with Sparse Data](https://mlsanity.com/paper/2206.06577/) (2022)
- [Learning Long-term Visual Dynamics with Region Proposal Interaction Networks](https://mlsanity.com/paper/2008.02265/) (2020)
- [Learning rigid dynamics with face interaction graph networks](https://mlsanity.com/paper/2212.03574/) (2022)

## Built on by (most cited first, 1 of 1)

- [Overhang Tower: Resource-Rational Adaptation in Sequential Physical Planning](https://mlsanity.com/paper/2604.09072/) (2026)

## Abstract (arXiv)

Physical reasoning is a remarkable human ability that enables rapid learning and generalization from limited experience. Current AI models, despite extensive training, still struggle to achieve similar generalization, especially in Out-of-distribution (OOD) settings. This limitation stems from their inability to abstract core physical principles from observations. A key challenge is developing representations that can efficiently learn and generalize physical dynamics from minimal data. Here we present Neural Force Field (NFF), a framework extending Neural Ordinary Differential Equation (NODE) to learn complex object interactions through force field representations, which can be efficiently integrated through an Ordinary Differential Equation (ODE) solver to predict object trajectories. Unlike existing approaches that rely on discrete latent spaces, NFF captures fundamental physical concepts such as gravity, support, and collision in continuous explicit force fields. Experiments on three challenging physical reasoning tasks demonstrate that NFF, trained with only a few examples, achieves strong generalization to unseen scenarios. This physics-grounded representation enables efficient forward-backward planning and rapid adaptation through interactive refinement. Our work suggests that incorporating physics-inspired representations into learning systems can help bridge the gap between artificial and human physical reasoning capabilities.