| _version_ | 1866902316046614528 |
|---|---|
| author | SÉRGIO DE ANDRADE, PAULO |
| author_facet | SÉRGIO DE ANDRADE, PAULO |
| contents | Modeling complex physical systems characterized by multiscale spatiotemporal dynamics remains a formidable challenge for traditional numerical solvers due to prohibitive computational costs. This paper introduces a comprehensive framework based on Physics-Informed Neural Operators (PINOs) designed to address this challenge. By synergizing the function-space learning capabilities of neural operators, such as the Fourier Neural Operator (FNO), with the robust regularization provided by physical laws, our approach learns the solution operator of parametric partial differential equations (PDEs) that govern such systems. We detail a methodology where the model is trained on a hybrid loss function, combining a data-fidelity term from coarse-resolution simulation data with a physics-based residual term evaluated on a much finer grid. This strategy enables zero-shot super-resolution, allowing the trained operator to make accurate predictions at resolutions not seen during training. The proposed PINO framework demonstrates superior performance in terms of accuracy, computational efficiency, and generalization across a range of canonical problems exhibiting multiscale phenomena, including turbulent flows and reaction-diffusion systems. We show that by embedding physical constraints directly into the operator learning paradigm, PINOs not only overcome the spectral bias limitations of traditional Physics-Informed Neural Networks (PINNs) but also reduce the reliance on large, high-fidelity datasets, which are often expensive or infeasible to obtain. The results establish PINOs as a powerful and scalable tool for real-time prediction and surrogate modeling of complex, multiscale spatiotemporal systems. |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17480275 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Physics-Informed Neural Operators for Multiscale Spatiotemporal Prediction SÉRGIO DE ANDRADE, PAULO Neural Operators Physics-Informed Machine Learning Fourier Neural Operator Multiscale Modeling Spatiotemporal Prediction Partial Differential Equations Modeling complex physical systems characterized by multiscale spatiotemporal dynamics remains a formidable challenge for traditional numerical solvers due to prohibitive computational costs. This paper introduces a comprehensive framework based on Physics-Informed Neural Operators (PINOs) designed to address this challenge. By synergizing the function-space learning capabilities of neural operators, such as the Fourier Neural Operator (FNO), with the robust regularization provided by physical laws, our approach learns the solution operator of parametric partial differential equations (PDEs) that govern such systems. We detail a methodology where the model is trained on a hybrid loss function, combining a data-fidelity term from coarse-resolution simulation data with a physics-based residual term evaluated on a much finer grid. This strategy enables zero-shot super-resolution, allowing the trained operator to make accurate predictions at resolutions not seen during training. The proposed PINO framework demonstrates superior performance in terms of accuracy, computational efficiency, and generalization across a range of canonical problems exhibiting multiscale phenomena, including turbulent flows and reaction-diffusion systems. We show that by embedding physical constraints directly into the operator learning paradigm, PINOs not only overcome the spectral bias limitations of traditional Physics-Informed Neural Networks (PINNs) but also reduce the reliance on large, high-fidelity datasets, which are often expensive or infeasible to obtain. The results establish PINOs as a powerful and scalable tool for real-time prediction and surrogate modeling of complex, multiscale spatiotemporal systems. |
| title | Physics-Informed Neural Operators for Multiscale Spatiotemporal Prediction |
| topic | Neural Operators Physics-Informed Machine Learning Fourier Neural Operator Multiscale Modeling Spatiotemporal Prediction Partial Differential Equations |
| url | https://doi.org/10.5281/zenodo.17480275 |