Learning the accurate dynamics of robotic systems directly from the trajectory data is currently a prominent research focus. Recent physics-enforced networks, exemplified by Hamiltonian neural networks and Lagrangian neural networks, demonstrate proficiency in modeling ideal physical systems, but face limitations when applied to systems with uncertain non-conservative dynamics due to the inherent constraints of the conservation laws foundation. In this paper, we present a novel augmented deep Lagrangian network, which seamlessly integrates a deep Lagrangian network with a standard deep network. This fusion aims to effectively model uncertainties that surpass the limitations of conventional Lagrangian mechanics. The proposed network is applied to learn inverse dynamics model of two multi-degree manipulators including a 6-dof UR-5 robot and a 7-dof SARCOS manipulator under uncertainties. The experimental results clearly demonstrate that our approach exhibits superior modeling precision and enhanced physical credibility.