PEINR: A Physics-enhanced Implicit Neural Representation for High-Fidelity Flow Field Reconstruction

Liming Shen, Liang Deng, Chongke Bi, Yu Wang, Xinhai Chen, Yueqing Wang, Jie Liu
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:54364-54380, 2025.

Abstract

Implicit neural representation (INR) has now been thrust into the limelight with its flexibility in high-fidelity flow field reconstruction tasks. However, the lack of standard benchmarking datasets and the grid independence assumption for INR-based methods hinder progress and adoption in real-world simulation scenarios. Moreover, naive adoptions of existing INR frameworks suffer from limited accuracy in capturing fine-scale structures and spatiotemporal dynamics. Tacking these issues, we first introduce HFR-Beach, a 5.4 TB public large-scale CFD dataset with 33,600 unsteady 2D and 3D vector fields for reconstructing high-fidelity flow fields. We further present PEINR, a physics-enhanced INR framework, to enrich the flow fields by concurrently enhancing numerical-precision and grid-resolution. Specifically, PEINR is mainly composed of physical encoding and transformer-based spatiotemporal fuser (TransSTF). Physical encoding decouples temporal and spatial components, employing Gaussian coordinate encoding and localized encoding techniques to capture the nonlinear characteristics of spatiotemporal dynamics and the stencil discretization of spatial dimensions, respectively. TransSTF fuses both spatial and temporal information via transformer for capturing long-range temporal dependencies. Qualitative and quantitative experiments and demonstrate that PEINR outperforms state-of-the-art INR-based methods in reconstruction quality.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-shen25a, title = {{PEINR}: A Physics-enhanced Implicit Neural Representation for High-Fidelity Flow Field Reconstruction}, author = {Shen, Liming and Deng, Liang and Bi, Chongke and Wang, Yu and Chen, Xinhai and Wang, Yueqing and Liu, Jie}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {54364--54380}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/shen25a/shen25a.pdf}, url = {https://proceedings.mlr.press/v267/shen25a.html}, abstract = {Implicit neural representation (INR) has now been thrust into the limelight with its flexibility in high-fidelity flow field reconstruction tasks. However, the lack of standard benchmarking datasets and the grid independence assumption for INR-based methods hinder progress and adoption in real-world simulation scenarios. Moreover, naive adoptions of existing INR frameworks suffer from limited accuracy in capturing fine-scale structures and spatiotemporal dynamics. Tacking these issues, we first introduce HFR-Beach, a 5.4 TB public large-scale CFD dataset with 33,600 unsteady 2D and 3D vector fields for reconstructing high-fidelity flow fields. We further present PEINR, a physics-enhanced INR framework, to enrich the flow fields by concurrently enhancing numerical-precision and grid-resolution. Specifically, PEINR is mainly composed of physical encoding and transformer-based spatiotemporal fuser (TransSTF). Physical encoding decouples temporal and spatial components, employing Gaussian coordinate encoding and localized encoding techniques to capture the nonlinear characteristics of spatiotemporal dynamics and the stencil discretization of spatial dimensions, respectively. TransSTF fuses both spatial and temporal information via transformer for capturing long-range temporal dependencies. Qualitative and quantitative experiments and demonstrate that PEINR outperforms state-of-the-art INR-based methods in reconstruction quality.} }
Endnote
%0 Conference Paper %T PEINR: A Physics-enhanced Implicit Neural Representation for High-Fidelity Flow Field Reconstruction %A Liming Shen %A Liang Deng %A Chongke Bi %A Yu Wang %A Xinhai Chen %A Yueqing Wang %A Jie Liu %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-shen25a %I PMLR %P 54364--54380 %U https://proceedings.mlr.press/v267/shen25a.html %V 267 %X Implicit neural representation (INR) has now been thrust into the limelight with its flexibility in high-fidelity flow field reconstruction tasks. However, the lack of standard benchmarking datasets and the grid independence assumption for INR-based methods hinder progress and adoption in real-world simulation scenarios. Moreover, naive adoptions of existing INR frameworks suffer from limited accuracy in capturing fine-scale structures and spatiotemporal dynamics. Tacking these issues, we first introduce HFR-Beach, a 5.4 TB public large-scale CFD dataset with 33,600 unsteady 2D and 3D vector fields for reconstructing high-fidelity flow fields. We further present PEINR, a physics-enhanced INR framework, to enrich the flow fields by concurrently enhancing numerical-precision and grid-resolution. Specifically, PEINR is mainly composed of physical encoding and transformer-based spatiotemporal fuser (TransSTF). Physical encoding decouples temporal and spatial components, employing Gaussian coordinate encoding and localized encoding techniques to capture the nonlinear characteristics of spatiotemporal dynamics and the stencil discretization of spatial dimensions, respectively. TransSTF fuses both spatial and temporal information via transformer for capturing long-range temporal dependencies. Qualitative and quantitative experiments and demonstrate that PEINR outperforms state-of-the-art INR-based methods in reconstruction quality.
APA
Shen, L., Deng, L., Bi, C., Wang, Y., Chen, X., Wang, Y. & Liu, J.. (2025). PEINR: A Physics-enhanced Implicit Neural Representation for High-Fidelity Flow Field Reconstruction. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:54364-54380 Available from https://proceedings.mlr.press/v267/shen25a.html.

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