# Surface Similarity Parameter: A New Machine Learning Loss Metric for Oscillatory Spatio-Temporal Data

arXiv: https://arxiv.org/abs/2204.06843 · HTML: https://mlsanity.com/paper/2204.06843/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 14 Apr 2022.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Highly comparative feature-based time-series classification](https://mlsanity.com/paper/1401.3531/) (2014)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [Highly comparative time-series analysis: The empirical structure of time series and their methods](https://mlsanity.com/paper/1304.1209/) (2013)
- [Machine Learning for Spatiotemporal Sequence Forecasting: A Survey](https://mlsanity.com/paper/1808.06865/) (2018)
- [Deep learning for time series classification](https://mlsanity.com/paper/2010.00567/) (2020)
- [Deep learning for brake squeal: vibration detection, characterization and prediction](https://mlsanity.com/paper/2001.01596/) (2020)

## Built on by (most cited first, 2 of 2)

- [Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data](https://mlsanity.com/paper/2305.11913/) (2023)
- [Data assimilation and parameter identification for water waves using the nonlinear Schr"odinger equation and physics-informed neural networks](https://mlsanity.com/paper/2401.03708/) (2024)

## Abstract (arXiv)

Supervised machine learning approaches require the formulation of a loss functional to be minimized in the training phase. Sequential data are ubiquitous across many fields of research, and are often treated with Euclidean distance-based loss functions that were designed for tabular data. For smooth oscillatory data, those conventional approaches lack the ability to penalize amplitude, frequency and phase prediction errors at the same time, and tend to be biased towards amplitude errors. We introduce the surface similarity parameter (SSP) as a novel loss function that is especially useful for training machine learning models on smooth oscillatory sequences. Our extensive experiments on chaotic spatio-temporal dynamics systems indicate that the SSP is beneficial for shaping gradients, thereby accelerating the training process, reducing the final prediction error, increasing weight initialization robustness, and implementing a stronger regularization effect compared to using classical loss functions. The results indicate the potential of the novel loss metric particularly for highly complex and chaotic data, such as data stemming from the nonlinear two-dimensional Kuramoto-Sivashinsky equation and the linear propagation of dispersive surface gravity waves in fluids.