  Temperature field prediction is of great importance in the thermal design of
systems engineering, and building the surrogate model is an effective way for
the task. Generally, large amounts of labeled data are required to guarantee a
good prediction performance of the surrogate model, especially the deep
learning model, which have more parameters and better representational ability.
However, labeled data, especially high-fidelity labeled data, are usually
expensive to obtain and sometimes even impossible. To solve this problem, this
paper proposes a pithy deep multi-fidelity model (DMFM) for temperature field
prediction, which takes advantage of low-fidelity data to boost the performance
with less high-fidelity data. First, a pre-train and fine-tune paradigm are
developed in DMFM to train the low-fidelity and high-fidelity data, which
significantly reduces the complexity of the deep surrogate model. Then, a
self-supervised learning method for training the physics-driven deep
multi-fidelity model (PD-DMFM) is proposed, which fully utilizes the physics
characteristics of the engineering systems and reduces the dependence on large
amounts of labeled low-fidelity data in the training process. Two diverse
temperature field prediction problems are constructed to validate the
effectiveness of DMFM and PD-DMFM, and the result shows that the proposed
method can greatly reduce the dependence of the model on high-fidelity data.
