  With several advantages and as an alternative to predict physics field,
machine learning methods can be classified into two distinct types: data-driven
relying on training data and physics-driven using physics law. Choosing heat
conduction problem as an example, we compared the data- and physics-driven
learning process with deep Convolutional Neural Networks (CNN). It shows that
the convergences of the error to ground truth solution and the residual of heat
conduction equation exhibit remarkable differences. Based on this observation,
we propose a combined-driven method for learning acceleration and more accurate
solutions. With a weighted loss function, reference data and physical equation
are able to simultaneously drive the learning. Several numerical experiments
are conducted to investigate the effectiveness of the combined method. For the
data-driven based method, the introduction of physical equation not only is
able to speed up the convergence, but also produces physically more consistent
solutions. For the physics-driven based method, it is observed that the
combined method is able to speed up the convergence up to 49.0\% by using a not
very restrictive coarse reference.
