# PIMRL: Physics-Informed Multi-Scale Recurrent Learning for Burst-Sampled Spatiotemporal Dynamics

arXiv: https://arxiv.org/abs/2503.10253 · HTML: https://mlsanity.com/paper/2503.10253/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 33 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Builds on (most cited first, 18 of 18)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [Encoding physics to learn reaction-diffusion processes](https://mlsanity.com/paper/2106.04781/) (2021)
- [Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers](https://mlsanity.com/paper/2302.10803/) (2023)
- [Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning](https://mlsanity.com/paper/2201.12354/) (2022)
- [A Neural PDE Solver with Temporal Stencil Modeling](https://mlsanity.com/paper/2302.08105/) (2023)
- [Deciphering and integrating invariants for neural operator learning with various physical mechanisms](https://mlsanity.com/paper/2311.14361/) (2023)
- [Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation](https://mlsanity.com/paper/2302.05104/) (2023)

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

- [NPSolver: Neural Poisson Solver with Iterative Physics Supervision](https://mlsanity.com/paper/2605.25786/) (2026)

## Abstract (arXiv)

Deep learning has shown strong potential in modeling complex spatiotemporal dynamics. However, most existing methods depend on densely and uniformly sampled data, which is often unavailable in practice due to sensor and cost limitations. In many real-world settings, such as mobile sensing and physical experiments, data are burst-sampled with short high-frequency segments followed by long gaps, making it difficult to learn accurate dynamics from sparse observations. To address this issue, we propose Physics-Informed Multi-Scale Recurrent Learning (PIMRL), a novel framework specifically designed for burst-sampled spatiotemporal data. PIMRL combines macro-scale latent dynamics inference with micro-scale adaptive refinement guided by incomplete prior information from partial differential equations (PDEs). It further introduces a temporal message-passing mechanism to effectively propagate information across burst intervals. This multi-scale architecture enables PIMRL to model complex systems accurately even under severe data scarcity. We evaluate our approach on five benchmark datasets involving 1D to 3D multi-scale PDEs. The results show that PIMRL consistently outperforms state-of-the-art baselines, achieving substantial improvements and reducing errors by up to 80% in the most challenging settings, which demonstrates the clear advantage of our model. Our work demonstrates the effectiveness of physics-informed recurrent learning for accurate and efficient modeling of sparse spatiotemporal systems.