In this work, we study the impacts of the isospin-independent momentum-dependent interaction (MDI) and near-threshold \(NN\rightarrow N\Delta\) cross sections ( \(\sigma _{NN\rightarrow N\Delta }\) ) on the nucleonic flow and pion production observables in the ultra-relativistic quantum molecular dynamics (UrQMD) model. With the updated isospin-independent MDI and the near-threshold \(NN\rightarrow N\Delta\) cross sections in the UrQMD model, 17 observables, which are the directed flow ( \(v_1\) ) and elliptic flow ( \(v_2\) ) of neutrons, protons, Hydrogen (H), and charged particles as a function of transverse momentum ( \(p_\text {t}/A\) ) or normalized rapidity ( \(y_{0}^{\text {lab}}\) ), and the observables constructed from them, the charged pion multiplicity ( \(M(\pi )\) ) and its ratio ( \(M(\pi ^-)/M(\pi ^+)\) ), can be simultaneously described at certain forms of symmetry energy. The refinement of the UrQMD model provides a solid foundation for further understanding the effects of the missed physics, such as the threshold effect, the pion potential, and the momentum-dependent symmetry potential. Circumstantial constraints on the symmetry energy at the flow characteristic density \(1.2\pm 0.6 \rho _0\) and the pion characteristic density \(1.5\pm 0.5\rho _0\) were obtained with the current version of UrQMD, and the corresponding symmetry energies were \(S(1.2\rho _0)=34\pm 4\,\hbox {MeV}\) and \(S(1.5\rho _0)=36\pm 8\,\hbox {MeV}\) , respectively. Furthermore, the discrepancies between the data and the calculated results of \(v_2^\text {n}\) and \(v_2^\text {p}\) at high \(p_\text {t}\) (rapidity) imply that the roles of the missing ingredients, such as the threshold effect, the pion potential, and the momentum-dependent symmetry potential, should be investigated by differential observables, such as the momentum and rapidity distributions of the nucleonic and pionic probes over a wide beam energy range.
