Can Data-Driven Dynamics Reveal Hidden Physics? There Is A Need for Interpretable Neural Operators
This work addresses the need for interpretable neural operators in physics simulations, but it is incremental as it builds on existing methods with limited generalizability.
The paper tackles the problem of understanding and improving neural operators for data-driven dynamics by classifying them into spatial and functional domain types, proposing an explanation method for predictions, and showing that a dual-space multi-scale model achieves state-of-the-art performance.
Recently, neural operators have emerged as powerful tools for learning mappings between function spaces, enabling data-driven simulations of complex dynamics. Despite their successes, a deeper understanding of their learning mechanisms remains underexplored. In this work, we classify neural operators into two types: (1) Spatial domain models that learn on grids and (2) Functional domain models that learn with function bases. We present several viewpoints based on this classification and focus on learning data-driven dynamics adhering to physical principles. Specifically, we provide a way to explain the prediction-making process of neural operators and show that neural operator can learn hidden physical patterns from data. However, this explanation method is limited to specific situations, highlighting the urgent need for generalizable explanation methods. Next, we show that a simple dual-space multi-scale model can achieve SOTA performance and we believe that dual-space multi-spatio-scale models hold significant potential to learn complex physics and require further investigation. Lastly, we discuss the critical need for principled frameworks to incorporate known physics into neural operators, enabling better generalization and uncovering more hidden physical phenomena.