RHYME-XT: A Neural Operator for Spatiotemporal Control Systems

• URL: http://arxiv.org/abs/2603.17867v1
• Date: Wed, 18 Mar 2026 15:55:26 GMT
• Title: RHYME-XT: A Neural Operator for Spatiotemporal Control Systems
• Abstract summary: We propose RHYME-XT, an operator-learning framework for governed control systems by input-affine nonlinear partial integro-differential equations (PIDEs)<n>RHYME-XT uses a Galerkin projection to approximate the infinite-dimensional subspace with basis functions parameterized by a neural network.<n> 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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