A Sequential Meta-Transfer (SMT) Learning to Combat Complexities of
  Physics-Informed Neural Networks: Application to Composites Autoclave
  Processing
Milad Ramezankhani Abbas S. Milani
Physics-Informed Neural Networks (PINNs) have gained popularity in solving
nonlinear partial differential equations (PDEs) via integrating physical laws
into the training of neural networks, making them superior in many scientific
and engineering applications. However, conventional PINNs still fall short in
accurately approximating the solution of complex systems with strong
nonlinearity, especially in long temporal domains. Besides, since PINNs are
designed to approximate a specific realization of a given PDE system, they lack
the necessary generalizability to efficiently adapt to new system
configurations. This entails computationally expensive re-training from scratch
for any new change in the system. To address these shortfalls, in this work a
novel sequential meta-transfer (SMT) learning framework is proposed, offering a
unified solution for both fast training and efficient adaptation of PINNs in
highly nonlinear systems with long temporal domains. Specifically, the
framework decomposes PDE's time domain into smaller time segments to create
"easier" PDE problems for PINNs training. Then for each time interval, a
meta-learner is assigned and trained to achieve an optimal initial state for
rapid adaptation to a range of related tasks. Transfer learning principles are
then leveraged across time intervals to further reduce the computational
cost.Through a composites autoclave processing case study, it is shown that SMT
is clearly able to enhance the adaptability of PINNs while significantly
reducing computational cost, by a factor of 100.