Solving inverse-PDE problems with physics-aware neural networks

• We present a novel hybrid framework that enables discovery of unknown fields in inverse partial differential problems. implement trainable finite discretization solver layers are composable with pre-existing neural layers. The network can be pre-trained self-supervised fashion and used on unseen data without further training. This consideration domain specific knowledge about the fields. In contrast to constrained optimization methods, loss function is simply difference between prediction. propose composite find context problems for equations (PDEs). blend high expressibility deep networks as universal estimators accuracy reliability existing numerical algorithms custom semantic autoencoders. Our design brings together techniques computational mathematics, machine learning pattern recognition under one umbrella incorporate domain-specific physical constraints discover underlying hidden explicitly aware governing physics through hard-coded PDE layer most methods or rely convolutional proper discretizations from data. subsequently focuses load only therefore more efficient. call this architecture Blended inverse-PDE (hereby dubbed BiPDE networks) demonstrate its applicability recovering variable diffusion coefficient Poisson two spatial dimensions, well time-dependent nonlinear Burgers' equation dimension. also show learned parameters robust added noise input