  The eigenvalue of a non-Hermitian Hamiltonian often forms a self-intersecting
Riemann surface, leading to a unique mode conversion phenomenon when the
Hamiltonian evolves along certain loop paths around an exceptional point (EP).
However, two fundamental problems exist with the conventional scheme of EP
encircling: the speed of mode conversion is restricted by the adiabatic
requirement, and the chirality cannot be freely controlled. Here, we introduce
a method which dynamically engineers the adiabaticity in the evolution of
non-Hermitian Hamiltonians that allows for both chiral and non-chiral mode
conversion on the same path. Our method is based on quantifying and controlling
the instantaneous adiabaticity, allowing for non-uniform evolution throughout
the entire path. We apply our method into the microwave waveguide system and by
optimizing the distributed adiabaticity along the evolution loop, we achieve
the same quality of mode conversion as conventional quasi-adiabatic evolution
in only one-fourth of the time. Our approach provides a comprehensive and
universal solution to address the speed and chirality challenges associated
with EP encircling. It also facilitates the dynamic manipulation and regulation
of non-adiabatic processes, thereby accelerating the operation and allowing for
a selection among various mode conversion patterns.
