  The classical approach to non-linear regression in physics, is to take a
mathematical model describing the functional dependence of the dependent
variable from a set of independent variables, and then, using non-linear
fitting algorithms, extract the parameters used in the modeling. Particularly
challenging are real systems, characterized by several additional influencing
factors related to specific components, like electronics or optical parts. In
such cases, to make the model reproduce the data, empirically determined terms
are built-in the models to compensate for the impossibility of modeling things
that are, by construction, impossible to model. A new approach to solve this
issue is to use neural networks, particularly feed-forward architectures with a
sufficient number of hidden layers and an appropriate number of output neurons,
each responsible for predicting the desired variables. Unfortunately,
feed-forward neural networks (FFNNs) usually perform less efficiently when
applied to multi-dimensional regression problems, that is when they are
required to predict simultaneously multiple variables that depend from the
input dataset in fundamentally different ways. To address this problem, we
propose multi-task learning (MTL) architectures. These are characterized by
multiple branches of task-specific layers, which have as input the output of a
common set of layers. To demonstrate the power of this approach for
multi-dimensional regression, the method is applied to luminescence sensing.
Here the MTL architecture allows predicting multiple parameters, the oxygen
concentration and the temperature, from a single set of measurements.
