# PAPM: A Physics-aware Proxy Model for Process Systems

arXiv: https://arxiv.org/abs/2407.05232 · HTML: https://mlsanity.com/paper/2407.05232/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 47 references that are in the map.
- First posted on arXiv 7 Jul 2024.

## Builds on (most cited first, 30 of 35)

- [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)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Dilated Residual Networks](https://mlsanity.com/paper/1705.09914/) (2017)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [MIONet: Learning multiple-input operators via tensor product](https://mlsanity.com/paper/2202.06137/) (2022)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [Learned Coarse Models for Efficient Turbulence Simulation](https://mlsanity.com/paper/2112.15275/) (2021)
- [PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs](https://mlsanity.com/paper/2306.08827/) (2023)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Encoding physics to learn reaction-diffusion processes](https://mlsanity.com/paper/2106.04781/) (2021)
- [Physics-Informed Multi-LSTM Networks for Metamodeling of Nonlinear Structures](https://mlsanity.com/paper/2002.10253/) (2020)
- [Learning to correct spectral methods for simulating turbulent flows](https://mlsanity.com/paper/2207.00556/) (2022)
- [Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics](https://mlsanity.com/paper/2205.03990/) (2022)
- [A Neural PDE Solver with Temporal Stencil Modeling](https://mlsanity.com/paper/2302.08105/) (2023)
- [Composing Partial Differential Equations with Physics-Aware Neural Networks](https://mlsanity.com/paper/2111.11798/) (2021)

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

- [Holistic Physics Solver: Learning PDEs in a Unified Spectral-Physical Space](https://mlsanity.com/paper/2410.11382/) (2024)
- [Accelerating Eigenvalue Dataset Generation via Chebyshev Subspace Filter](https://mlsanity.com/paper/2510.23215/) (2025)
- [NEMSim: Learning Control-Conditioned Multi-Event Physical Dynamics via Executable Event-Mechanism Priors](https://mlsanity.com/paper/2609.30718/) (2026)
- [Neural Constitutive Learning for Generalized Reaction-Diffusion Systems](https://mlsanity.com/paper/2609.37113/) (2026)

## Abstract (arXiv)

In the context of proxy modeling for process systems, traditional data-driven deep learning approaches frequently encounter significant challenges, such as substantial training costs induced by large amounts of data, and limited generalization capabilities. As a promising alternative, physics-aware models incorporate partial physics knowledge to ameliorate these challenges. Although demonstrating efficacy, they fall short in terms of exploration depth and universality. To address these shortcomings, we introduce a physics-aware proxy model (PAPM) that fully incorporates partial prior physics of process systems, which includes multiple input conditions and the general form of conservation relations, resulting in better out-of-sample generalization. Additionally, PAPM contains a holistic temporal-spatial stepping module for flexible adaptation across various process systems. Through systematic comparisons with state-of-the-art pure data-driven and physics-aware models across five two-dimensional benchmarks in nine generalization tasks, PAPM notably achieves an average performance improvement of 6.7%, while requiring fewer FLOPs, and just 1% of the parameters compared to the prior leading method. The code is available at https://github.com/pengwei07/PAPM.