# SlotPi: Physics-informed Object-centric Reasoning Models

arXiv: https://arxiv.org/abs/2506.10778 · HTML: https://mlsanity.com/paper/2506.10778/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 81 references that are in the map.
- First posted on arXiv 12 Jun 2025.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 25 of 25)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [CLEVRER: CoLlision Events for Video REpresentation and Reasoning](https://mlsanity.com/paper/1910.01442/) (2019)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [Physion: Evaluating Physical Prediction from Vision in Humans and Machines](https://mlsanity.com/paper/2106.08261/) (2021)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [A Compositional Object-Based Approach to Learning Physical Dynamics](https://mlsanity.com/paper/1612.00341/) (2016)
- [SCALOR: Generative World Models with Scalable Object Representations](https://mlsanity.com/paper/1910.02384/) (2019)
- [VDT: General-purpose Video Diffusion Transformers via Mask Modeling](https://mlsanity.com/paper/2305.13311/) (2023)
- [Learned Coarse Models for Efficient Turbulence Simulation](https://mlsanity.com/paper/2112.15275/) (2021)
- [Generalization and Robustness Implications in Object-Centric Learning](https://mlsanity.com/paper/2107.00637/) (2021)
- [IntPhys: A Framework and Benchmark for Visual Intuitive Physics Reasoning](https://mlsanity.com/paper/1803.07616/) (2018)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers](https://mlsanity.com/paper/2302.10803/) (2023)
- [Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately](https://mlsanity.com/paper/2201.10085/) (2022)
- [Visual Attention Methods in Deep Learning: An In-Depth Survey](https://mlsanity.com/paper/2204.07756/) (2022)
- [Benchmarking Unsupervised Object Representations for Video Sequences](https://mlsanity.com/paper/2006.07034/) (2020)
- [Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning](https://mlsanity.com/paper/2201.12354/) (2022)
- [R-SQAIR: Relational Sequential Attend, Infer, Repeat](https://mlsanity.com/paper/1910.05231/) (2019)
- [Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs](https://mlsanity.com/paper/2305.18702/) (2023)
- [Learning Neural Hamiltonian Dynamics: A Methodological Overview](https://mlsanity.com/paper/2203.00128/) (2022)
- [Reasoning-Enhanced Object-Centric Learning for Videos](https://mlsanity.com/paper/2403.15245/) (2024)

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

- [Predicting Video Slot Attention Queries from Random Slot-Feature Pairs](https://mlsanity.com/paper/2508.01345/) (2025)
- [Smoothing Slot Attention Iterations and Recurrences](https://mlsanity.com/paper/2508.05417/) (2025)
- [PhysMind: From Video to Executable Worlds for Training-Free Physical Reasoning](https://mlsanity.com/paper/2608.04575/) (2026)
- [CloDS: Visual-Only Unsupervised Cloth Dynamics Learning in Unknown Conditions](https://mlsanity.com/paper/2602.01844/) (2026)
- [Asking the World: Generalist Physical Reasoning through Agentic World Modeling and Probing](https://mlsanity.com/paper/2609.39135/) (2026)

## Abstract (arXiv)

Understanding and reasoning about dynamics governed by physical laws through visual observation, akin to human capabilities in the real world, poses significant challenges. Currently, object-centric dynamic simulation methods, which emulate human behavior, have achieved notable progress but overlook two critical aspects: 1) the integration of physical knowledge into models. Humans gain physical insights by observing the world and apply this knowledge to accurately reason about various dynamic scenarios; 2) the validation of model adaptability across diverse scenarios. Real-world dynamics, especially those involving fluids and objects, demand models that not only capture object interactions but also simulate fluid flow characteristics. To address these gaps, we introduce SlotPi, a slot-based physics-informed object-centric reasoning model. SlotPi integrates a physical module based on Hamiltonian principles with a spatio-temporal prediction module for dynamic forecasting. Our experiments highlight the model's strengths in tasks such as prediction and Visual Question Answering (VQA) on benchmark and fluid datasets. Furthermore, we have created a real-world dataset encompassing object interactions, fluid dynamics, and fluid-object interactions, on which we validated our model's capabilities. The model's robust performance across all datasets underscores its strong adaptability, laying a foundation for developing more advanced world models.