How to Train Your PINN: Pitfalls and the Perils of Low-Quality Data
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Physics-Informed Neural Networks (PINNs) are increasingly used to solve partial differential equations by embedding physical laws into neural network training. While physics-based constraints play a central role in this framework [1], the impact of data quality on training robustness and predictive accuracy is often underestimated. This work investigates how the quality of available data conditions the performance of PINNs. We analyze the interaction between data-driven supervision and physics-based constraints during training, using a data-driven warm-up stage to initialize the network before enforcing the governing equations. This strategy improves optimization robustness in the considered settings and allows for a clearer assessment of data-related limitations. The results show that the achievable accuracy of PINN predictions is fundamentally bounded by the quality, resolution, and precision of the data used during training. Even when the physical model is correctly imposed, low-quality data introduce an error floor that cannot be overcome through physics constraints alone. These findings highlight that PINNs are not data-agnostic and that realistic expectations on model accuracy must account for data fidelity. The analysis is illustrated with results for the steady Burgers equation and representative Navier–Stokes configurations, using a training and post-processing pipeline implemented with pyLOM [2].
