<p>Due to physical environment restrictions or equipment failures, engineering systems can only obtain partial variable observation data. If ignored or simply interpolated, state estimation bias and control strategy failure are easy to result. Therefore, the developed inference algorithm can reconstruct the complete state of the system from the limited observations, and can provide data support for accurate modeling, dynamic analysis and real-time control. Special neural network reservoir computing (RC) can achieve this goal by virtue of its own unique reservoir pool to infinitely approximate the dynamical system. In this paper, combined with the homotopy idea in topology theory, a novel model-free inference method based on RC is proposed, called reservoir computing of homotopy function (HFRC). Firstly, we proved the echo state property of HFRC, which is the theoretical guarantee for the model to conduct experiments. In the experiment, the hyperchaotic system, which is more complex than chaos, is selected as the experimental object. The complex internal relationship of the hyperchaotic system is successfully learned by using the proposed model HFRC, and the hyperchaotic attractor is derived based on the partial observations. At the same time, we demonstrate the excellent performance of the model in the case of very small amount of system data. More importantly, we also study the effects of regularization parameters and noise on the model. The results show that the model is a very effective and robust model-free inference tool, which can be used to reconstruct the internal relations of dynamic systems.</p>