  Dynamics of the (sub-)Ohmic spin-boson model under various bath initial
conditions is investigated by employing the Dirac-Frenkel time-dependent
variational approach with the multiple Davydov $\mathrm{D_1}$ ansatz in the
interaction picture. The validity of our approach is carefully checked by
comparing results with those of the hierarchy equations of motion method. By
analyzing the features of nonequilibrium dynamics, we identify the phase
diagrams for different bath initial conditions. We find that for spectral
exponent $s<s_c$, there exists a transition from coherent to quasicoherent
dynamics with increasing the coupling strengths. For $s_c<s\leq{1}$, the
coherent to incoherent crossover occurs at a certain coupling strength, and the
quasicoherent dynamics emerges at much larger couplings. The initial
preparation of the bath has considerable influence on the dynamics.
