The Physics-Guided Transformer (PGT) embeds physical priors (like diffusion and causality) directly into the self-attention mechanism via heat-kernel biases.
March 31, 2026
Original Paper
Physics-Guided Transformer (PGT): Physics-Aware Attention Mechanism for PINNs
arXiv · 2603.27929
The Takeaway
It moves beyond treating physics as a soft penalty in the loss function (PINNs) and instead builds physical constraints into the architecture's inductive bias. This results in significantly more stable and physically consistent field reconstructions with sparse data.
From the abstract
Reconstructing continuous physical fields from sparse, irregular observations is a central challenge in scientific machine learning, particularly for systems governed by partial differential equations (PDEs). Existing physics-informed methods typically enforce governing equations as soft penalty terms during optimization, often leading to gradient imbalance, instability, and degraded physical consistency under limited data. We introduce the Physics-Guided Transformer (PGT), a neural architecture