RHYME-XT: A Neural Operator for Spatiotemporal Control Systems
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912972969869312 |
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| author | Ruiter, Marijn Aguiar, Miguel Rap, Jake Johansson, Karl H. Das, Amritam |
| author_facet | Ruiter, Marijn Aguiar, Miguel Rap, Jake Johansson, Karl H. Das, Amritam |
| contents | We propose RHYME-XT, an operator-learning framework for surrogate modeling of spatiotemporal control systems governed by input-affine nonlinear partial integro-differential equations (PIDEs) with localized rhythmic behavior. RHYME-XT uses a Galerkin projection to approximate the infinite-dimensional PIDE on a learned finite-dimensional subspace with spatial basis functions parameterized by a neural network. This yields a projected system of ODEs driven by projected inputs. Instead of integrating this non-autonomous system, we directly learn its flow map using an architecture for learning flow functions, avoiding costly computations while obtaining a continuous-time and discretization-invariant representation. Experiments on a neural field PIDE show that RHYME-XT outperforms a state-of-the-art neural operator and is able to transfer knowledge effectively across models trained on different datasets, through a fine-tuning process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17867 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | RHYME-XT: A Neural Operator for Spatiotemporal Control Systems Ruiter, Marijn Aguiar, Miguel Rap, Jake Johansson, Karl H. Das, Amritam Machine Learning Systems and Control Optimization and Control We propose RHYME-XT, an operator-learning framework for surrogate modeling of spatiotemporal control systems governed by input-affine nonlinear partial integro-differential equations (PIDEs) with localized rhythmic behavior. RHYME-XT uses a Galerkin projection to approximate the infinite-dimensional PIDE on a learned finite-dimensional subspace with spatial basis functions parameterized by a neural network. This yields a projected system of ODEs driven by projected inputs. Instead of integrating this non-autonomous system, we directly learn its flow map using an architecture for learning flow functions, avoiding costly computations while obtaining a continuous-time and discretization-invariant representation. Experiments on a neural field PIDE show that RHYME-XT outperforms a state-of-the-art neural operator and is able to transfer knowledge effectively across models trained on different datasets, through a fine-tuning process. |
| title | RHYME-XT: A Neural Operator for Spatiotemporal Control Systems |
| topic | Machine Learning Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2603.17867 |