Title: PIANO: Physics-Informed Autoregressive Networks
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: Physics-Informed Neural Networks, Autoregressive Networks

Abstract: Solving time-dependent partial differential equations (PDEs) is fundamental to modeling critical phenomena across science and engineering. Physics-Informed Neural Networks (PINNs) solve PDEs using deep learning. However, PINNs perform pointwise predictions that neglect the autoregressive property of dynamical systems, leading to instabilities and inaccurate predictions. We introduce Physics-Informed Autoregressive Networks (PIANO)---a framework that redesigns PINNs to model dynamical systems. PIANO operates autoregressively, explicitly conditioning future predictions on the past. It is trained through a self-supervised rollout mechanism while enforcing physical constraints. We present a rigorous theoretical analysis demonstrating that PINNs suffer from temporal instability, while PIANO achieves stability through autoregressive modeling. Extensive experiments on challenging time-dependent PDEs demonstrate that PIANO achieves state-of-the-art performance, significantly improving accuracy and stability over existing methods. We further show that PIANO outperforms existing methods in weather forecasting.

TL;DR: PIANO is a novel physics-informed autoregressive framework for time-dependent PDEs that conditions each prediction on prior states, improving stability and accuracy over existing methods.