Surface similarity parameter: A new machine learning loss metric for oscillatory spatio-temporal data

Area of Science:

• Applied Mathematics
• Machine Learning
• Dynamical Systems

Background:

• Supervised machine learning relies on loss functions for training.
• Conventional Euclidean distance-based loss functions struggle with smooth oscillatory sequential data.
• Existing methods often fail to penalize amplitude, frequency, and phase errors simultaneously, showing bias towards amplitude errors.

Purpose of the Study:

• Introduce a novel loss function, the Surface Similarity Parameter (SSP).
• Address limitations of traditional loss functions for smooth oscillatory sequences.
• Enhance machine learning model training for complex sequential data.

Main Methods:

• Developed the Surface Similarity Parameter (SSP) as a new loss function.
• Conducted extensive experiments on chaotic spatio-temporal dynamical systems.
• Compared SSP performance against classical loss functions.

Main Results:

• SSP accelerates training by shaping gradients effectively.
• Reduced final prediction errors compared to traditional methods.
• Improved weight initialization robustness and provided stronger regularization.
• Demonstrated benefits on nonlinear two-dimensional Kuramoto-Sivashinsky and dispersive surface gravity wave data.

Conclusions:

• The Surface Similarity Parameter (SSP) is a highly effective novel loss function for smooth oscillatory sequences.
• SSP offers significant advantages in training speed, prediction accuracy, and robustness for complex and chaotic data.
• This metric holds particular promise for analyzing intricate spatio-temporal dynamics in scientific research.