Fig. 3: Diagram of a PINN.
From: Machine Learning in Acoustics: A Review and Open-source Repository
The neural network inputs are the coordinates x, y, t, and the output is the physical quantity of interest u(x, y, t). Automatic differentiation is used to compute the partial derivatives of the output with respect to the inputs. A physics loss term, \({{\mathcal{L}}}_{{\rm{pde}}}\), that contains the underlying PDE is formed, and added to loss terms that account for initial/boundary conditions, \({{\mathcal{L}}}_{{\rm{ic/bc}}}\), and/or observed data, \({{\mathcal{L}}}_{{\rm{data}}}\), to compute the total loss, \({{\mathcal{L}}}_{{\rm{total}}}\).
