# Breaking the Discretization Barrier of Continuous Physics Simulation Learning

arXiv: https://arxiv.org/abs/2509.17955 · HTML: https://mlsanity.com/paper/2509.17955/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 58 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 30 of 38)

- [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)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [WeatherBench 2: A benchmark for the next generation of data-driven global weather models](https://mlsanity.com/paper/2308.15560/) (2023)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Earthformer: Exploring Space-Time Transformers for Earth System Forecasting](https://mlsanity.com/paper/2207.05833/) (2022)
- [Variational Physics-Informed Neural Networks For Solving Partial Differential Equations](https://mlsanity.com/paper/1912.00873/) (2019)
- [Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks](https://mlsanity.com/paper/1906.05747/) (2019)
- [Neural Flows: Efficient Alternative to Neural ODEs](https://mlsanity.com/paper/2110.13040/) (2021)
- [Temporal Attention Unit: Towards Efficient Spatiotemporal Predictive Learning](https://mlsanity.com/paper/2206.12126/) (2022)
- [Continuous PDE Dynamics Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2209.14855/) (2022)
- [DeepSphere: a graph-based spherical CNN](https://mlsanity.com/paper/2012.15000/) (2020)
- [Learning Visual Predictive Models of Physics for Playing Billiards](https://mlsanity.com/paper/1511.07404/) (2015)
- [Learning continuous-time PDEs from sparse data with graph neural networks](https://mlsanity.com/paper/2006.08956/) (2020)
- [PastNet: Introducing Physical Inductive Biases for Spatio-temporal Video Prediction](https://mlsanity.com/paper/2305.11421/) (2023)
- [OneForecast: A Universal Framework for Global and Regional Weather Forecasting](https://mlsanity.com/paper/2502.00338/) (2025)
- [Generalised Implicit Neural Representations](https://mlsanity.com/paper/2205.15674/) (2022)
- [MAgNet: Mesh Agnostic Neural PDE Solver](https://mlsanity.com/paper/2210.05495/) (2022)
- [Probabilistic ODE Solvers with Runge-Kutta Means](https://mlsanity.com/paper/1406.2582/) (2014)

## Built on by (most cited first, 4 of 4)

- [Differential-Integral Neural Operator for Long-Term Turbulence Forecasting](https://mlsanity.com/paper/2509.21196/) (2025)
- [Spatiotemporal Forecasting as Planning: A Model-Based Reinforcement Learning Approach with Generative World Models](https://mlsanity.com/paper/2510.04020/) (2025)
- [Advanced Global Wildfire Activity Modeling with Hierarchical Graph ODE](https://mlsanity.com/paper/2601.01501/) (2026)
- [Unlocking Out-of-Distribution Generalization in Dynamics through Physics-Guided Augmentation](https://mlsanity.com/paper/2510.24216/) (2025)

## Abstract (arXiv)

The modeling of complicated time-evolving physical dynamics from partial observations is a long-standing challenge. Particularly, observations can be sparsely distributed in a seemingly random or unstructured manner, making it difficult to capture highly nonlinear features in a variety of scientific and engineering problems. However, existing data-driven approaches are often constrained by fixed spatial and temporal discretization. While some researchers attempt to achieve spatio-temporal continuity by designing novel strategies, they either overly rely on traditional numerical methods or fail to truly overcome the limitations imposed by discretization. To address these, we propose CoPS, a purely data-driven methods, to effectively model continuous physics simulation from partial observations. Specifically, we employ multiplicative filter network to fuse and encode spatial information with the corresponding observations. Then we customize geometric grids and use message-passing mechanism to map features from original spatial domain to the customized grids. Subsequently, CoPS models continuous-time dynamics by designing multi-scale graph ODEs, while introducing a Markov-based neural auto-correction module to assist and constrain the continuous extrapolations. Comprehensive experiments demonstrate that CoPS advances the state-of-the-art methods in space-time continuous modeling across various scenarios.