A common technique in high energy physics is to characterize the response of a detector by means of models tuned to data which build parametric maps from the physical parameters of the system to the expected signal of the detector. When the underlying model is unknown it is difficult to apply this method, and often, simplifying assumptions are made introducing modeling errors. In this article, using a waveform toy model we present how deep learning in the form of constrained bottleneck autoencoders can be used to learn the underlying unknown detector response model directly from data. The results show that excellent performance results can be achieved even when the signals are significantly affected by random noise. The trained algorithm can be used simultaneously to perform estimations on the physical parameters of the model, simulate the detector response with high fidelity and to denoise detector signals.