# PINP: Physics-Informed Neural Predictor with latent estimation of fluid flows

arXiv: https://arxiv.org/abs/2504.06070 · HTML: https://mlsanity.com/paper/2504.06070/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 8 Apr 2025.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [SimVP: Simpler yet Better Video Prediction](https://mlsanity.com/paper/2206.05099/) (2022)
- [PredRNN: A Recurrent Neural Network for Spatiotemporal Predictive Learning](https://mlsanity.com/paper/2103.09504/) (2021)
- [Earthformer: Exploring Space-Time Transformers for Earth System Forecasting](https://mlsanity.com/paper/2207.05833/) (2022)
- [Scalable Transformer for PDE Surrogate Modeling](https://mlsanity.com/paper/2305.17560/) (2023)
- [Solving High-Dimensional PDEs with Latent Spectral Models](https://mlsanity.com/paper/2301.12664/) (2023)
- [Encoding physics to learn reaction-diffusion processes](https://mlsanity.com/paper/2106.04781/) (2021)
- [Learning Vortex Dynamics for Fluid Inference and Prediction](https://mlsanity.com/paper/2301.11494/) (2023)
- [P2C2Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics](https://mlsanity.com/paper/2411.00040/) (2024)
- [HelmFluid: Learning Helmholtz Dynamics for Interpretable Fluid Prediction](https://mlsanity.com/paper/2310.10565/) (2023)
- [Learning to Estimate and Refine Fluid Motion with Physical Dynamics](https://mlsanity.com/paper/2206.10480/) (2022)

## Built on by (most cited first, 3 of 3)

- [RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data](https://mlsanity.com/paper/2601.01829/) (2026)
- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [PRIMS: Physics-guided Representation for Fluid Identification in Multimodal Sensing](https://mlsanity.com/paper/2607.22422/) (2026)

## Abstract (arXiv)

Accurately predicting fluid dynamics and evolution has been a long-standing challenge in physical sciences. Conventional deep learning methods often rely on the nonlinear modeling capabilities of neural networks to establish mappings between past and future states, overlooking the fluid dynamics, or only modeling the velocity field, neglecting the coupling of multiple physical quantities. In this paper, we propose a new physics-informed learning approach that incorporates coupled physical quantities into the prediction process to assist with forecasting. Central to our method lies in the discretization of physical equations, which are directly integrated into the model architecture and loss function. This integration enables the model to provide robust, long-term future predictions. By incorporating physical equations, our model demonstrates temporal extrapolation and spatial generalization capabilities. Experimental results show that our approach achieves the state-of-the-art performance in spatiotemporal prediction across both numerical simulations and real-world extreme-precipitation nowcasting benchmarks.