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This paper presents a PINN training framework that employs (1) pre-trainingsteps that accelerates and improve the robustness of the training ofphysics-informed neural network with auxiliary data stored in point clouds, (2)a net-to-net knowledge transfer algorithm that improves the weightinitialization of the neural network and (3) a multi-objective optimizationalgorithm that may improve the performance of a physical-informed neuralnetwork with competing constraints. We consider the training and transfer andmulti-task learning of physics-informed neural network (PINN) asmulti-objective problems where the physics constraints such as the governingequation, boundary conditions, thermodynamic inequality, symmetry, andinvariant properties, as well as point cloud used for pre-training cansometimes lead to conflicts and necessitating the seek of the Pareto optimalsolution. In these situations, weighted norms commonly used to handle multipleconstraints may lead to poor performance, while other multi-objectivealgorithms may scale poorly with increasing dimensionality. To overcome thistechnical barrier, we adopt the concept of vectorized objective function andmodify a gradient descent approach to handle the issue of conflictinggradients. Numerical experiments are compared the benchmark boundary valueproblems solved via PINN. The performance of the proposed paradigm is comparedagainst the classical equal-weighted norm approach. Our numerical experimentsindicate that the brittleness and lack of robustness demonstrated in some PINNimplementations can be overcome with the proposed strategy.

Training multi-objective/multi-task collocation physics-informed neural network with student/teachers transfer learnings