Inertial Manifold Neural Operator for Dissipative Time-Dependent Partial Differential Equations
In this paper, we introduce the Inertial Manifold Neural Operator (IMNO) for solving dissipative time-dependent partial differential equations (PDEs). The long-time dynamics of such systems often exhibit an effective low-dimensional structure due to dissipation. Unlike standard neural operator architectures such as the Fourier Neural Operator (FNO), IMNO explicitly leverages the low-dimensional structure to achieve better physical interpretability, accuracy, and stability in long-horizon autoregressive training and prediction for nonlinear dissipative PDEs. For shift-equivariant PDEs, we further introduce a shift-equivariant variant (IMNO-SE) of the proposed neural operator, ensuring that...
| Authors | Xiaoyang Xie, Clarence W. Rowley |
|---|---|
| Primary category | math.NA |
| Published | 24 August 2026 |
| Last updated at source | 24 August 2026 |
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