Physics-informed neural networks can be made dramatically faster and more generalizable by learning shared representations across PDE families and using closed-form adaptation, enabling accurate predictions on new problems without retraining.
This paper introduces Pi-PINN, a physics-informed neural network that learns reusable representations for solving different partial differential equations (PDEs). Instead of training separate models for each PDE, Pi-PINN learns a shared representation and adapts quickly to new PDEs using a mathematical technique called pseudoinverse, achieving 100-1000x faster predictions than standard PINNs.