A Physics-informed Multi-resolution Neural Operator
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911236167303168 |
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| author | Roy, Sumanta Bahmani, Bahador Kevrekidis, Ioannis G. Shields, Michael D. |
| author_facet | Roy, Sumanta Bahmani, Bahador Kevrekidis, Ioannis G. Shields, Michael D. |
| contents | The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to obtain in some real-world engineering applications. These datasets may be unevenly discretized from one realization to another, with the grid resolution varying across samples. In this study, we introduce a physics-informed operator learning approach by extending the Resolution Independent Neural Operator (RINO) framework to a fully data-free setup, addressing both challenges simultaneously. Here, the arbitrarily (but sufficiently finely) discretized input functions are projected onto a latent embedding space (i.e., a vector space of finite dimensions), using pre-trained basis functions. The operator associated with the underlying partial differential equations (PDEs) is then approximated by a simple multi-layer perceptron (MLP), which takes as input a latent code along with spatiotemporal coordinates to produce the solution in the physical space. The PDEs are enforced via a finite difference solver in the physical space. The validation and performance of the proposed method are benchmarked on several numerical examples with multi-resolution data, where input functions are sampled at varying resolutions, including both coarse and fine discretizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Physics-informed Multi-resolution Neural Operator Roy, Sumanta Bahmani, Bahador Kevrekidis, Ioannis G. Shields, Michael D. Machine Learning Analysis of PDEs Computational Physics The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to obtain in some real-world engineering applications. These datasets may be unevenly discretized from one realization to another, with the grid resolution varying across samples. In this study, we introduce a physics-informed operator learning approach by extending the Resolution Independent Neural Operator (RINO) framework to a fully data-free setup, addressing both challenges simultaneously. Here, the arbitrarily (but sufficiently finely) discretized input functions are projected onto a latent embedding space (i.e., a vector space of finite dimensions), using pre-trained basis functions. The operator associated with the underlying partial differential equations (PDEs) is then approximated by a simple multi-layer perceptron (MLP), which takes as input a latent code along with spatiotemporal coordinates to produce the solution in the physical space. The PDEs are enforced via a finite difference solver in the physical space. The validation and performance of the proposed method are benchmarked on several numerical examples with multi-resolution data, where input functions are sampled at varying resolutions, including both coarse and fine discretizations. |
| title | A Physics-informed Multi-resolution Neural Operator |
| topic | Machine Learning Analysis of PDEs Computational Physics |
| url | https://arxiv.org/abs/2510.23810 |