5 papers
Long-Time Trajectory Approximation via SA-NODEs: Model Predictive and Floquet Strategies
Ziqian Li, Nikolaos M. Matzakos
We study the approximation of dynamical systems by semi-autonomous neural ordinary differential equations (SA-NODEs) over long time horizons. For a single network trained on the wh…
Hamiltonian Interface Dynamics for Reduced-Order Optimization of Incompressible Mixing
Ziqian Li, Enrique Zuazua
We develop a reduced-order framework for optimizing mixing in two-dimensional incompressible flows. Instead of optimizing the full transport PDE, the method maximizes the length of…
Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications
Ziqian Li, Kang Liu, Lorenzo Liverani +1
In this paper, we introduce semi-autonomous neural ordinary differential equations (SA-NODEs), a variation of the vanilla NODEs, employing fewer parameters. We investigate the univ…
A Structure-Preserving Numerical Scheme for Optimal Control and Design of Mixing in Incompressible Flows
Weiwei Hu, Ziqian Li, Yubiao Zhang +1
We develop a structure-preserving computational framework for optimal mixing control in incompressible flows. Our approach exactly conserves the continuous system's key invariants…
Deep Neural ODE Operator Networks for PDEs
Ziqian Li, Kang Liu, Yongcun Song +2
Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often o…