Learning Heat-based Equations in Self-similar variables
The study introduces a training method using self-similar variables (SSV) to learn heat-based equations like Navier–Stokes and Burgers' equation. By transforming the problem into a coordinate system that reflects long-time scaling, SSV training yields significantly more accurate and stable predictions outside the training data compared to standard methods. This proves that adapting the input coordinates to the equation's inherent scaling structure is key for reliable long-term forecasting.