During the landing of a shipboard aircraft, the impact load on the ship deck has a short duration and a limited area of action. The impact load is essential for the safety assessment of the aircraft and landing deck. However, it is difficult to measure directly due to the limited measurements applicable to this scenario. In this paper, the data-driven regression method is proposed by constructing the transfer matrix of the kernel functions and the regularization norm, which can be seemed as a physical-informed method of machine learning. The sparse deconvolution equations from structural response to impact load are discretized to construct inverse models in terms of the kernel function. L1 norm regularization of the solution norm and residual norm is applied to overcome large deviations in the data-driven regression. The log-barrier interior-point method is used to replace the inequality constraints on the upper and lower bounds to quickly find reasonable solutions. The optimal search direction is determined by the conjugate gradient method. A stiffened panel of one ship landing deck is selected as the research objective for a series of impact experiments, where the impact load is applied by a force hammer to measure the structural response. The proposed method is shown to have advantages over the conventional method in identifying the impact load amplitude and its historical shape. The effect of sampling frequency and hammerhead of various materials on load identification is also discussed. Subsequently, drop-impact experiments of one aircraft tire are performed on the same stiffened panel to analyze the applicability of the proposed method in the tire impact load. The proposed method is also able to effectively identify the impact load when the actual impact location slightly deviates from the expected one. The analysis results show that the proposed method has excellent stability and robustness for the impact load identification. The conclusions will provide guidance for impact load identification in deck structures.