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PAPM: A Physics-aware Proxy Model for Process Systems
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Proposes PAPM, a physics-aware proxy model for process systems that embeds multiple input conditions and the general conservation-law form (diffusion, convection, source terms) into a neural ODE stepping module, evaluated on five 2D benchmarks under time-extrapolation tasks.
Problem
Data-driven proxy models for process systems need large labeled datasets and generalize poorly out-of-sample (e.g., time extrapolation), while existing physics-aware models use only spatial derivatives and are tailored to specific systems.
Approach
Embed the general conservation-law form (diffusive flow, convective flow, internal and external source terms) plus all input conditions (initial/boundary conditions, coefficients, external sources) into the network architecture, with a temporal-spatial stepping module that uses localized convolution, spectral, or hybrid operators and a Neural ODE time integrator.
Key results
- PAPM achieves an average 6.7% performance improvement over nine generalization tasks compared with the prior leading method PPNN.
- PAPM uses about 1% of PPNN's parameters (e.g., 0.014M vs 1.201M for localized) and 1.23M FLOPs vs 348.56M for PPNN.
- PAPM achieves the best error on Burgers2d C Ext. (0.101 vs 0.126 for CNO) and on RD2d C Int. (0.018 vs 0.021 for Dil-ResNet).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use PAPM rather than the strongest listed baseline | PAPM · Across nine time-extrapolation tasks | mean L2 relative error ε: average performance improvement of 6.7% | Helped |
| integrate coefficient data within conservation and constitutive relations | PAPM · Three coefficient-extrapolation tasks | mean L2 relative error ε: 9.6% performance boost | Helped |
| add diffusion flow (DF) (ablation) | PAPM · Burgers2d C Int. and C Ext. | mean L2 relative error ε: 0.067 -> 0.039; 0.207 -> 0.101 | Helped |
| add convection flow (CF) (ablation) | PAPM · Burgers2d C Int. and C Ext. | mean L2 relative error ε: 0.062 -> 0.039; 0.131 -> 0.101 | Helped |
| add diffusion and convection flows (ablation) | PAPM · Burgers2d C Int. and C Ext. | mean L2 relative error ε: 0.149 -> 0.039; 0.210 -> 0.101 | Helped |
| add explicit boundary-condition embedding (ablation) | PAPM · Burgers2d C Int. and C Ext. | mean L2 relative error ε: 0.068 -> 0.039; 0.136 -> 0.101 | Helped |
| use Neural ODE instead of Euler stepping (ablation) | PAPM · Burgers2d C Int. and C Ext. | mean L2 relative error ε: 0.053 -> 0.039; 0.150 -> 0.101 | Helped |
| add physics-aware components rather than use a purely data-driven approach (ablation) | PAPM · Burgers2d C Int. and C Ext. | mean L2 relative error ε: 0.162 -> 0.039; 0.216 -> 0.101 | Helped |
Surprising findings
- Pure data-driven baseline Dil-ResNet is competitive on RD2d, beating physics-aware PPNN in the C Int. setting (0.021 vs 0.030)
- PeRCNN, despite being physics-aware, performs poorly with limited accuracy in several tasks
Limitations
- Limited to 2D spatio-temporal dynamics; 3D and multi-physics settings not yet explored
- Assumes regular grids; irregular grid scenarios not handled
- Unknown source/constitutive terms still approximated by generic neural networks
Experimental setup
Datasets: Burgers2d RD2d NS2d Lid2d NSM2d
Benchmarks: Burgers2d RD2d NS2d Lid2d NSM2d
Metrics: mean L2 relative error FLOPs parameter count
Baselines: ConvLSTM Dil-ResNet time-FNO2D MIONet U-FNet CNO PeRCNN PPNN
Builds on: PPNN PeRCNN FNO Neural ODE DeepONet
Closest papers by meaning
- PARCv2: Physics-aware Recurrent Convolutional Neural Networks for Spatiotemporal Dynamics Modeling (ICML 2024 · similarity 0.83)
- Multiple Physics Pretraining for Spatiotemporal Surrogate Models (NeurIPS 2024 · similarity 0.83)
- PhysGuard: Fisher-Guided Gradient Projection for Sim-to-Real Neural PDE Surrogates (NeurIPS 2026 · similarity 0.82)
- How to Re-enable PDE Loss for Physical Systems Modeling Under Partial Observation (AAAI 2025 · similarity 0.82)
- GenPRM: Scaling Test-Time Compute of Process Reward Models via Generative Reasoning (AAAI 2026 · similarity 0.82)
- Learning Physics Informed Neural ODEs with Partial Measurements (AAAI 2025 · similarity 0.82)
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