  Physics-informed neural networks (PINNs) are a newly emerging research
frontier in machine learning, which incorporate certain physical laws that
govern a given data set, e.g., those described by partial differential
equations (PDEs), into the training of the neural network (NN) based on such a
data set. In PINNs, the NN acts as the solution approximator for the PDE while
the PDE acts as the prior knowledge to guide the NN training, leading to the
desired generalization performance of the NN when facing the limited
availability of training data. However, training PINNs is a non-trivial task
largely due to the complexity of the loss composed of both NN and physical law
parts. In this work, we propose a new PINN training framework based on the
multi-task optimization (MTO) paradigm. Under this framework, multiple
auxiliary tasks are created and solved together with the given (main) task,
where the useful knowledge from solving one task is transferred in an adaptive
mode to assist in solving some other tasks, aiming to uplift the performance of
solving the main task. We implement the proposed framework and apply it to
train the PINN for addressing the traffic density prediction problem.
Experimental results demonstrate that our proposed training framework leads to
significant performance improvement in comparison to the traditional way of
training the PINN.
