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• The Physics-Guided Transformer (PGT) achieves a relative L2 error of 5.9e-3 in sparse 1D heat equation reconstruction with 100 observations, representing a 38-fold reduction over physics-informed neural networks (PINNs).result 95%
• PGT uniquely achieves both low PDE residual (8.3e-4) and competitive relative error (0.034) in the 2D cylinder wake problem, outperforming methods that optimize only one objective.result 90%
• PGT embeds physical structure directly into the self-attention mechanism by incorporating a heat-kernel-derived additive bias into attention logits, encoding diffusion dynamics and temporal causality.method 85%
• Existing physics-informed methods that enforce governing equations as soft penalty terms often lead to gradient imbalance, instability, and degraded physical consistency under limited data.limitation 80%
• PGT uses a FiLM-modulated sinusoidal implicit network decoder that adaptively controls spectral response.technical 75%
• PGT is trained with a composite loss that includes data fidelity, PDE residuals, boundary conditions, and initial conditions, using uncertainty-based weighting to avoid manual tuning.method 90%
• Operator-learning frameworks like Fourier Neural Operators and DeepONets often lack explicit awareness of underlying physical constraints, relying instead on purely spectral priors.limitation 70%
• PGT maintains relative errors on the order of 10^-3 even as the number of sparse observation points increases to 500, while PINN and SIREN remain two orders of magnitude higher.result 85%

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