RHYME-XT: A Neural Operator for Spatiotemporal Control Systems
This work addresses surrogate modeling for spatiotemporal control systems, which is incremental as it builds on existing neural operator methods with specific architectural improvements.
The authors tackled surrogate modeling of spatiotemporal control systems governed by complex equations with localized rhythmic behavior, proposing RHYME-XT, which outperformed a state-of-the-art neural operator in experiments on a neural field PIDE and enabled effective knowledge transfer across datasets through fine-tuning.
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.