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.