  A common technique in high energy physics is to characterize the response of
a detector by means of models tunned 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.
