Physics-Informed Neural Networks with Hard Linear Equality Constraints

Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are data-driven models and devoid of any physics. The incorporation of physics into neural networks can improve generalization and data efficiency. The physics-informed neural network (PINN) is an approach to leverage known physical constraints present in the data, but it cannot strictly satisfy them in the predictions. This work proposes …

constraints cs.lg data data-driven efficiency equality linear math.oc modeling networks neural networks physics physics-informed simulations systems