arXiv:2409.08958v3 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful deep learning approach for solving partial differential equations (PDEs) in the physical sciences, yet their behavior remains largely opaque and is typically understood through failure mode analyses rather than explicit interpretability. To address this issue, we introduce PINNfluence, a training data attribution framework for interpreting PINNs based on influence functions. By extending influence functions to composite physics-informed training objectives, we enable fine-gra
The increasing adoption of Physics-informed neural networks (PINNs) in scientific domains necessitates greater transparency and interpretability, particularly as their applications become more critical.
Improved interpretability of PINNs can accelerate scientific discovery and engineering design by providing insights into model behavior, thus fostering greater trust and enabling more robust applications across various physical sciences.
The introduction of PINNfluence shifts the understanding of PINNs from failure mode analyses to explicit, data-attribution-based interpretability, potentially broadening their reliable deployment in complex systems.
- · Researchers in computational physics
- · Deep learning engineers
- · Industries relying on PDE solutions (e.g., aerospace, energy)
- · Opaque black-box models
- · Trial-and-error engineering approaches
PINNfluence provides a novel framework for understanding how training data influences PINN predictions and performance.
This enhanced interpretability could lead to more efficient model debugging, targeted data collection strategies, and improved reliability of PINNs in real-world applications.
Ultimately, this could accelerate the development of scientific AI, leading to breakthroughs in areas such as materials science, climate modeling, and fluid dynamics by making advanced simulations more transparent and trustworthy.
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