Graduate Student Rutgers university, New Jersey, United States
Abstract Submission: Deep learning has demonstrated significant potential in solving partial differential equations (PDEs). However, the rapid decay of prediction accuracy in many models underscores the urgent need to comprehend the underlying mechanisms of deep learning-based PDE solvers. Such understanding is crucial not only for designing more effective models but also for potentially uncovering new physics from trained models. Our ongoing study addresses this knowledge gap by visualizing benchmark PDE models across varying levels of complexity. Initial findings reveal intricate patterns within model weights and biases, suggesting a complex relationship with the underlying PDEs. We aim to develop an inverse symbolic model to establish correlations between model structures and their represented PDEs. This presentation will showcase our preliminary findings and discuss the challenges encountered in this innovative approach to PDE solver interpretation and design.
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