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math.NA2025
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…
math.NA2024★ 1 cited
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…