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Boundary conditions (BCs) are a key component in every Physics-InformedNeural Network (PINN). By defining the solution to partial differentialequations (PDEs) along domain boundaries, BCs constrain the underlying boundaryvalue problem (BVP) that a PINN tries to approximate. Without them, unique PDEsolutions may not exist and finding approximations with PINNs would be achallenging, if not impossible task. This study examines how soft loss-basedand exact distance function-based BC imposition approaches differ when appliedin PINNs. The well known variable coefficient Poisson equation serves as thetarget PDE for all PINN models trained in this work. Besides comparing BCimposition approaches, the goal of this work is to also provide resources onhow to implement these PINNs in practice. To this end, Keras models withTensorflow backend as well as a Python notebook with code examples andstep-by-step explanations on how to build soft/exact BC PINNs are publishedalongside this review.

Exact and soft boundary conditions in Physics-Informed Neural Networks for the Variable Coefficient Poisson equation