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math.NA2026
Inertial Manifold Neural Operator for Dissipative Time-Dependent Partial Differential Equations
Xiaoyang Xie, Clarence W. Rowley
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 suc…
math.NA2025
Symmetry-reduced model reduction of shift-equivariant systems via operator inference
Yu Shuai, Clarence W. Rowley
We consider data-driven reduced-order models of partial differential equations with shift equivariance. Shift-equivariant systems typically admit traveling solutions, and the main…