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Inertial Manifold Neural Operator for Dissipative Time-Dependent Partial Differential Equations

ArXiv|Monday, August 24, 2026|21 days ago|Xiaoyang Xie

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In this paper, we introduce the Inertial Manifold Neural Operator (IMNO) for solving dissipative time-dependent partial differential equations (PDEs).

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Key Claims

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 furth...

Original description

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 furth...

arxiv math.NA cs.LG math.DS publisher:arxiv tier:research

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ID: http://arxiv.org/abs/2608.23546v1 · Indexed 21 days ago