2 citations · 3 across the 16 of their papers we have counts for
5 papers · 1 filter
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…
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…
Moments, Time-Inversion and Source Identification for the Heat Equation
Kang Liu, Enrique Zuazua
We address the initial source identification problem for the heat equation, a notably ill-posed inverse problem characterized by exponential instability. Departing from classical T…
Random Batch Methods for Discretized PDEs on Graphs
Martin Hernandez, Martín Hernández, Enrique Zuazua
Diffusion and transport processes on networks arise in applications such as pipeline systems, traffic and information flow, and energy and thermal networks. In these settings the d…
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…