  We introduce a novel continual learning method based on multifidelity deep
neural networks. This method learns the correlation between the output of
previously trained models and the desired output of the model on the current
training dataset, limiting catastrophic forgetting. On its own the
multifidelity continual learning method shows robust results that limit
forgetting across several datasets. Additionally, we show that the
multifidelity method can be combined with existing continual learning methods,
including replay and memory aware synapses, to further limit catastrophic
forgetting. The proposed continual learning method is especially suited for
physical problems where the data satisfy the same physical laws on each domain,
or for physics-informed neural networks, because in these cases we expect there
to be a strong correlation between the output of the previous model and the
model on the current training domain.
