{"ID":2849825,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.23810","arxiv_id":"2510.23810","title":"A Physics-informed Multi-resolution Neural Operator","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2510.23810","url_pdf":"https://arxiv.org/pdf/2510.23810v1","authors":"[\"Sumanta Roy\",\"Bahador Bahmani\",\"Ioannis G. Kevrekidis\",\"Michael D. Shields\"]","published":"2025-10-27T19:50:02Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.AP\",\"physics.comp-ph\",\"stat.ML\"]","methods":"[]","has_code":false}