CoNO: Complex neural operator for continous dynamical physical systems
Neural operators extend data-driven models to map between infinite-dimensional functional spaces. While these operators perform effectively in either the time or frequency domain, their performance may be limited when applied to non-stationary spatial or temporal signals whose frequency characterist...
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2025-06-01
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| Series: | APL Machine Learning |
| Online Access: | http://dx.doi.org/10.1063/5.0254013 |
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| author | Karn Tiwari N. M. Anoop Krishnan Prathosh A. P. |
| author_facet | Karn Tiwari N. M. Anoop Krishnan Prathosh A. P. |
| author_sort | Karn Tiwari |
| collection | DOAJ |
| description | Neural operators extend data-driven models to map between infinite-dimensional functional spaces. While these operators perform effectively in either the time or frequency domain, their performance may be limited when applied to non-stationary spatial or temporal signals whose frequency characteristics change with time. Here, we introduce a Complex Neural Operator (CoNO) that parameterizes the integral kernel using fractional Fourier transform, better representing non-stationary signals in a complex-valued domain. Theoretically, we prove the universal approximation capability of CoNO. We perform an extensive empirical evaluation of CoNO on seven challenging partial differential equations, including regular grids, structured meshes, and point clouds. Empirically, CoNO consistently attains a state-of-the-art performance, showcasing an average relative gain of 10.9%. Furthermore, CoNO exhibits superior performance, outperforming all other models in additional tasks, such as zero-shot super-resolution and robustness to noise. CoNO also exhibits the ability to learn from small amounts of data—giving the same performance as the next best model with just 60% of the training data. Altogether, CoNO presents a robust and superior model for modeling continuous dynamical systems, providing a fillip to scientific machine learning. |
| format | Article |
| id | doaj-art-ca2b1166b96f4e6da6633071cbf2be5d |
| institution | DOAJ |
| issn | 2770-9019 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | APL Machine Learning |
| spelling | doaj-art-ca2b1166b96f4e6da6633071cbf2be5d2025-08-20T03:14:57ZengAIP Publishing LLCAPL Machine Learning2770-90192025-06-0132026101026101-1410.1063/5.0254013CoNO: Complex neural operator for continous dynamical physical systemsKarn Tiwari0N. M. Anoop Krishnan1Prathosh A. P.2Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, Bengaluru 560012, IndiaYardi School of Artificial Intelligence Indian Institute of Technology, Delhi, New Delhi 110016, IndiaDepartment of Electrical Communication Engineering, Indian Institute of Science, Bangalore, Bengaluru 560012, IndiaNeural operators extend data-driven models to map between infinite-dimensional functional spaces. While these operators perform effectively in either the time or frequency domain, their performance may be limited when applied to non-stationary spatial or temporal signals whose frequency characteristics change with time. Here, we introduce a Complex Neural Operator (CoNO) that parameterizes the integral kernel using fractional Fourier transform, better representing non-stationary signals in a complex-valued domain. Theoretically, we prove the universal approximation capability of CoNO. We perform an extensive empirical evaluation of CoNO on seven challenging partial differential equations, including regular grids, structured meshes, and point clouds. Empirically, CoNO consistently attains a state-of-the-art performance, showcasing an average relative gain of 10.9%. Furthermore, CoNO exhibits superior performance, outperforming all other models in additional tasks, such as zero-shot super-resolution and robustness to noise. CoNO also exhibits the ability to learn from small amounts of data—giving the same performance as the next best model with just 60% of the training data. Altogether, CoNO presents a robust and superior model for modeling continuous dynamical systems, providing a fillip to scientific machine learning.http://dx.doi.org/10.1063/5.0254013 |
| spellingShingle | Karn Tiwari N. M. Anoop Krishnan Prathosh A. P. CoNO: Complex neural operator for continous dynamical physical systems APL Machine Learning |
| title | CoNO: Complex neural operator for continous dynamical physical systems |
| title_full | CoNO: Complex neural operator for continous dynamical physical systems |
| title_fullStr | CoNO: Complex neural operator for continous dynamical physical systems |
| title_full_unstemmed | CoNO: Complex neural operator for continous dynamical physical systems |
| title_short | CoNO: Complex neural operator for continous dynamical physical systems |
| title_sort | cono complex neural operator for continous dynamical physical systems |
| url | http://dx.doi.org/10.1063/5.0254013 |
| work_keys_str_mv | AT karntiwari conocomplexneuraloperatorforcontinousdynamicalphysicalsystems AT nmanoopkrishnan conocomplexneuraloperatorforcontinousdynamicalphysicalsystems AT prathoshap conocomplexneuraloperatorforcontinousdynamicalphysicalsystems |