In many settings, e.g. physical human-robot interaction, robotic behavior must be made robust against more or less spontaneous application of external forces. Typically, this problem is tackled by means of special purpose force sensors which are, however, not available on many robotic platforms. In contrast, we propose a machine learning approach suitable for more common, although often noisy sensors. This machine learning approach makes use of Dynamic Mode Decomposition (DMD) which is able to extract the dynamics of a nonlinear system. It is therefore well suited to separate noise from regular oscillations in sensor readings during cyclic robot movements under different behavior configurations. We demonstrate the feasibility of our approach with an example where physical forces are exerted on a humanoid robot during walking. In a training phase, a snapshot based DMD model for behavior specific parameter configurations is learned. During task execution the robot must detect and estimate the external forces exerted by a human interaction partner. We compare the DMD-based approach to other interpolation schemes and show that the former outperforms the latter particularly in the presence of sensor noise. We conclude that DMD which has so far been mostly used in other fields of science, particularly fluid mechanics, is also a highly promising method for robotics.