CoNO: Complex neural operator for continous dynamical physical systems Article Swipe
Karn Tiwari
,
N. M. Anoop Krishnan
,
Prathosh AP
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1063/5.0254013
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1063/5.0254013
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.
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https://doi.org/10.1063/5.0254013Digital Object Identifier
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CoNO: Complex neural operator for continous dynamical physical systemsWork title
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articleOpenAlex work type
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enPrimary language
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2025Year of publication
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2025-04-01Full publication date if available
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Karn Tiwari, N. M. Anoop Krishnan, Prathosh APList of authors in order
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https://doi.org/10.1063/5.0254013Publisher landing page
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YesWhether a free full text is available
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diamondOpen access status per OpenAlex
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0Total citation count in OpenAlex
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| abstract_inverted_index.time | 19 |
| abstract_inverted_index.when | 28 |
| abstract_inverted_index.with | 40, 152 |
| abstract_inverted_index.CoNO. | 75 |
| abstract_inverted_index.Here, | 42 |
| abstract_inverted_index.While | 11 |
| abstract_inverted_index.data. | 158 |
| abstract_inverted_index.learn | 138 |
| abstract_inverted_index.model | 151, 166 |
| abstract_inverted_index.other | 119 |
| abstract_inverted_index.point | 96 |
| abstract_inverted_index.prove | 69 |
| abstract_inverted_index.seven | 85 |
| abstract_inverted_index.small | 140 |
| abstract_inverted_index.their | 23 |
| abstract_inverted_index.these | 12 |
| abstract_inverted_index.time. | 41 |
| abstract_inverted_index.using | 55 |
| abstract_inverted_index.whose | 36 |
| abstract_inverted_index.(CoNO) | 49 |
| abstract_inverted_index.10.9%. | 111 |
| abstract_inverted_index.Neural | 0, 47 |
| abstract_inverted_index.better | 59 |
| abstract_inverted_index.change | 39 |
| abstract_inverted_index.either | 17 |
| abstract_inverted_index.extend | 2 |
| abstract_inverted_index.fillip | 174 |
| abstract_inverted_index.grids, | 92 |
| abstract_inverted_index.kernel | 54 |
| abstract_inverted_index.models | 4, 120 |
| abstract_inverted_index.noise. | 131 |
| abstract_inverted_index.robust | 163 |
| abstract_inverted_index.tasks, | 123 |
| abstract_inverted_index.Complex | 46 |
| abstract_inverted_index.Fourier | 57 |
| abstract_inverted_index.ability | 136 |
| abstract_inverted_index.amounts | 141 |
| abstract_inverted_index.applied | 29 |
| abstract_inverted_index.attains | 101 |
| abstract_inverted_index.average | 107 |
| abstract_inverted_index.between | 7 |
| abstract_inverted_index.clouds. | 97 |
| abstract_inverted_index.domain, | 22 |
| abstract_inverted_index.domain. | 66 |
| abstract_inverted_index.limited | 27 |
| abstract_inverted_index.machine | 177 |
| abstract_inverted_index.meshes, | 94 |
| abstract_inverted_index.partial | 87 |
| abstract_inverted_index.perform | 14, 77 |
| abstract_inverted_index.regular | 91 |
| abstract_inverted_index.signals | 35, 62 |
| abstract_inverted_index.spaces. | 10 |
| abstract_inverted_index.spatial | 32 |
| abstract_inverted_index.Operator | 48 |
| abstract_inverted_index.exhibits | 114, 134 |
| abstract_inverted_index.integral | 53 |
| abstract_inverted_index.modeling | 168 |
| abstract_inverted_index.presents | 161 |
| abstract_inverted_index.relative | 108 |
| abstract_inverted_index.superior | 115, 165 |
| abstract_inverted_index.systems, | 171 |
| abstract_inverted_index.temporal | 34 |
| abstract_inverted_index.training | 157 |
| abstract_inverted_index.dynamical | 170 |
| abstract_inverted_index.empirical | 80 |
| abstract_inverted_index.extensive | 79 |
| abstract_inverted_index.frequency | 21, 37 |
| abstract_inverted_index.including | 90 |
| abstract_inverted_index.introduce | 44 |
| abstract_inverted_index.learning. | 178 |
| abstract_inverted_index.operators | 1, 13 |
| abstract_inverted_index.providing | 172 |
| abstract_inverted_index.universal | 71 |
| abstract_inverted_index.zero-shot | 126 |
| abstract_inverted_index.additional | 122 |
| abstract_inverted_index.capability | 73 |
| abstract_inverted_index.continuous | 169 |
| abstract_inverted_index.equations, | 89 |
| abstract_inverted_index.evaluation | 81 |
| abstract_inverted_index.fractional | 56 |
| abstract_inverted_index.functional | 9 |
| abstract_inverted_index.robustness | 129 |
| abstract_inverted_index.scientific | 176 |
| abstract_inverted_index.showcasing | 105 |
| abstract_inverted_index.structured | 93 |
| abstract_inverted_index.transform, | 58 |
| abstract_inverted_index.Altogether, | 159 |
| abstract_inverted_index.challenging | 86 |
| abstract_inverted_index.data-driven | 3 |
| abstract_inverted_index.effectively | 15 |
| abstract_inverted_index.performance | 24, 146 |
| abstract_inverted_index.Empirically, | 98 |
| abstract_inverted_index.Furthermore, | 112 |
| abstract_inverted_index.consistently | 100 |
| abstract_inverted_index.differential | 88 |
| abstract_inverted_index.performance, | 104, 116 |
| abstract_inverted_index.representing | 60 |
| abstract_inverted_index.approximation | 72 |
| abstract_inverted_index.data—giving | 143 |
| abstract_inverted_index.outperforming | 117 |
| abstract_inverted_index.parameterizes | 51 |
| abstract_inverted_index.Theoretically, | 67 |
| abstract_inverted_index.complex-valued | 65 |
| abstract_inverted_index.non-stationary | 31, 61 |
| abstract_inverted_index.characteristics | 38 |
| abstract_inverted_index.state-of-the-art | 103 |
| abstract_inverted_index.super-resolution | 127 |
| abstract_inverted_index.infinite-dimensional | 8 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.04202236 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |