  Achieving precise preparation of quantum many-body states is crucial for the
practical implementation of quantum computation and quantum simulation.
However, the inherent challenges posed by unavoidable excitations at critical
points during quench processes necessitate careful design of control fields. In
this work, we introduce a promising and versatile dynamic control neural
network tailored to optimize control fields. We address the problem of
suppressing defect density and enhancing cat-state fidelity during the passage
across the critical point in the quantum Ising model. Our method facilitates
seamless transitions between different objective functions by adjusting the
{optimization strategy}. In comparison to gradient-based power-law quench
methods, our approach demonstrates significant advantages for both small system
sizes and long-term evolutions. We provide a detailed analysis of the specific
forms of control fields and summarize common features for experimental
implementation. Furthermore, numerical simulations demonstrate the robustness
of our proposal against random noise and spin number fluctuations. The
optimized defect density and cat-state fidelity exhibit a transition at a
critical ratio of the quench duration to the system size, coinciding with the
quantum speed limit for quantum evolution.
