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

Wedler, Mathies; Stender, Merten; Klein, Marco; Ehlers, Svenja; Hoffmann, Norbert

doi:10.1016/j.neunet.2022.09.023

Cited by 10 publications

(3 citation statements)

References 26 publications

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“…For example, minimizing the absolute error in water-level prediction will not always yield the best tidal estimate and vice versa. The results reported in this work only use the mean absolute error (MAE) as the chosen loss function though we note that early testing has shown the Surface Similarity Parameter [30] can yield superior pure tidal estimates and is implemented in RTide. Unlike Mean Squared Error, MAE places less emphasis on outliars and is thus more robust.…”

Section: Training Proceduresmentioning

confidence: 99%

Response Framework: Tidal analysis and prediction through physics-informed ML

Monahan,

Tang,

Roberts

et al. 2024

Preprint

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Tides pose significant operational and engineering challenges to numerous industries and are critical drivers of many natural processes. Accurate tidal predictions are important for modelling these phenomena. Conventionally, tidal prediction is carried out using harmonic analysis which places severe restrictions on the minimum length of tidal records and cannot separate oceanography from astronomy. While Munk and Cartwright’s response method revolutionized tidal analysis, the difficulty of realistic input function selection has made its automated adaptation challenging. Here, we develop a new framework for tidal analysis and prediction based on embedding universal function approximators within Munk and Cartwright’s response method. The new ML Response Framework overcomes the challenges imposed by the original method and demonstrates superior predictive accuracy over harmonic analysis, typically using 90% less data. We devise a method for obtaining physical insights from the learned model and apply this to quantify and predict the tidal response to meteorological and other non-tidal forcing. By disentangling oceanography from astronomy, the ML Response Framework makes straightforward the study of phenomena which heretofore could not be accounted for. These include storm surges, tidal rivers, and anthropogenic climate change. An open-source Python package (RTide) is provided, and shows promise in terms of application to storm-surge modelling.

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Section: Training Proceduresmentioning

confidence: 99%

Response Framework: Tidal analysis and prediction through physics-informed ML

Monahan,

Tang,

Roberts

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Established machine learning metrics based on Euclidean distances treat the deviation of two surfaces in frequency or phase as amplitude errors (Wedler et al, 2022). Therefore, we introduce the surface similarity parameter (SSP) proposed by Perlin and Bustamante (2014) as an additional performance metric…”

Section: Training and Evaluationmentioning

confidence: 99%

“…The SSP is a normalized error metric, with SSP 𝑖 = 0 indicating perfect agreement and SSP 𝑖 = 1 a comparison against zero or of phase-inverted surfaces. As the SSP combines phase-, amplitude-, and frequency errors in a single quantity, it is used in recent ocean wave prediction and reconstruction studies by Klein et al (2020Klein et al ( , 2022, Wedler et al (2022Wedler et al ( , 2023, Desmars et al (2021Desmars et al ( , 2022 and Lünser et al (2022). While metrics such as the nL2 𝑖 or SSP 𝑖 evaluate the average reconstruction quality of each ŷ𝑖 ∈ R 𝑛 𝑟 ×1 across the entire spatial domain…”

Section: Training and Evaluationmentioning

confidence: 99%