Source-linked AI summary
A Machine Learning Framework to Forecast Wave Conditions
Scott C. James, Yushan Zhang, Fearghal O'Donncha
TL;DR
Predicting wave conditions is important, but computational expense limits real-time forecasting. This paper presents machine-learning models using rapid matrix operations as surrogates for physics-based modeling, achieving over three orders of magnitude faster execution with similarly accurate results, while requiring retraining beyond Monterey Bay.
Problem
Predicting wave conditions is important, but computational expense is often a major limitation of real-time forecasting.
Method
Machine-learning models are trained to provide surrogate wave-condition predictions, with matrix multiplication used for rapid input-to-output transformations.
Results
485,833% faster than the full physics-based SWAN models, while yielding similarly accurate results.
Takeaways & Limitations
The presented technology provides a faster machine-learning alternative to physics-based wave modeling.
Takeaways & Limitations
The machine-learning models are specific to the Monterey Bay region and require re-training for other locations.
Abstract
from arXiv · showhide
A~machine learning framework is developed to estimate ocean-wave conditions. By supervised training of machine learning models on many thousands of iterations of a physics-based wave model, accurate representations of significant wave heights and period can be used to predict ocean conditions. A model of Monterey Bay was used as the example test site; it was forced by measured wave conditions, ocean-current nowcasts, and reported winds. These input data along with model outputs of spatially variable wave heights and characteristic period were aggregated into supervised learning training and test data sets, which were supplied to machine learning models. These machine learning models replicated wave heights with a root-mean-squared error of 9cm and correctly identify over 90% of the characteristic periods for the test-data sets. Impressively, transforming model inputs to outputs through matrix operations requires only a fraction (<1/1,000) of the computation time compared to forecasting with the physics-based model.
1. Introduction
The introduction motivates fast, accurate wave-condition prediction for energy, maritime, and operational applications, then presents machine learning as a surrogate for computationally expensive physics-based forecasting.
- Motivation: Accurate wave-condition forecasts support renewable-energy planning, power-production estimates, shipping optimization, aquaculture, and military or amphibious operations.The introduction links wave knowledge to intermittent renewable generation, potential WEC arrays, rough-sea avoidance, harvesting operations, and littoral operations.
- Forecasting requirements: A representative, calibrated, validated model must also run rapidly and incorporate relevant forecast data.These requirements are presented as prerequisites for useful forecasting systems.
- Method and contribution: The framework trains machine learning models on many realizations of a physics-based wave model to represent significant wave heights and characteristic periods.The surrogate is trained using historical atmospheric and sea states and targets spatially variable wave conditions.
- Method and contribution: Computational expense limits real-time forecasting, motivating machine learning to replace intensive physics-based models with matrix operations.The proposed approach maps input vectors through matrices resulting from trained models.
- Method and contribution: The resulting machine-learning technique is described as comparable in accuracy to the physics-based model at a fraction of its computational cost.The introduction also identifies the surrogate-model application as distinct from earlier machine-learning work on wave-condition prediction.
- Data requirements: Machine-learning surrogates can be supplied with sufficient training data by repeatedly running the physics-based model.This addresses the unusually large data appetite of machine-learning applications in this setting.
2. Wave Modeling
SWAN is a physics-based coastal wave model that represents wave-energy evolution under boundary waves, currents, winds, and physical sources and sinks. The Monterey Bay configuration was driven by observational and forecast inputs, verified against NOAA data, and judged suitable for generating machine-learning training data.
- Numerical model: SWAN computes coastal wave fields from boundary wave conditions, ocean currents, and winds.It models wave energy as it propagates and disperses through the domain.
- Numerical model: Action density N = E/σ is conserved during propagation along wave characteristics in the presence of ambient current.Its evolution in space and time is governed by the action balance equation.
- Numerical model: SWAN represents wave-energy sources and sinks from wind growth, nonlinear interactions, white-capping, bottom friction, and depth-induced breaking.These terms account for processes that generate, dissipate, or redistribute wave energy.
- Wave-energy characteristics: Significant wave height Hs and peak wave period T are needed to estimate wave power density because wave power is quadratically related to wave height.These quantities therefore provide key wave-energy-resource characteristics.
- Model verification: The Monterey Bay SWAN model used NOAA wave conditions, CeNCOOS ocean-current nowcasts, and Weather Company wind data as forcing inputs.The model domain used 0.001° horizontal resolution and was assembled into steady-state runs at three-hour intervals over six days.
- Computational considerations: The refined physics-based model required minutes and 224,163 active nodes, whereas the reduced model could run in under 10 seconds.This comparison motivates the computational advantage of the surrogate-modeling approach.
3. Machine Learning
The framework uses supervised machine learning to approximate SWAN wave-model outputs, applying regression to significant wave height and classification to characteristic period. Trained mappings transform wave, current, and wind inputs into spatially variable predictions, reproducing SWAN results with low error while enabling rapid matrix-based computation.
- Two supervised tasks are used: regression analysis for wave height and classification analysis for characteristic period.
- Wave-characteristic boundary conditions, spatially variable ocean currents, and wind speeds are transformed into spatially variable significant wave heights and characteristic periods.
- A sufficiently trained model produces a mapping matrix Θ that acts as a surrogate for SWAN, replacing partial-differential-equation solution with vector-matrix operations.
- 11,078 SWAN model runs supplied the design matrices used to assemble supervised training data.
- 9 cm RMSE was achieved for significant wave height with three layers of 20 nodes each, less than 5% of average Hs.
- 90.1% of characteristic periods were correctly identified by the OvO model, with an overall-data RMSE below 0.1 s.
4. Discussion
The framework uses forecast inputs and matrix mappings to rapidly generate wave-height and characteristic-period forecasts as a surrogate for SWAN. Its models are region-specific, but preloaded mapping matrices could make forecasts nearly instantaneous.
- Forecast-mode framework: Forecast inputs are assembled into a vector and multiplied by a machine-learning mapping matrix to yield the Hs field and characteristic T.The inputs are the same model inputs used to force SWAN, and forecast data can replace historical data in forecast mode.
- Computational performance: 0.12 s was required on a single processor for the machine-learning equivalent to calculate the Hs field and characteristic T.The Hs and characteristic-T calculations took 0.086 s and 0.034 s, respectively.
- Computational performance: 485,833% faster than the full physics-based SWAN models, the machine-learning equivalent required far less computation time.SWAN required 583 s on a single core, or 112 s on eight cores, for the same 48-hour forecast.
- Computational performance: Preloading mapping matrices into memory could result in nearly instantaneous wave-field forecasts.Loading the machine-learning matrix files was the operation requiring the most wall-clock time.
- Scope and limitations: The presented machine-learning models are specific to Monterey Bay and require retraining for application to other locations.Applying the physics-based model at a new site also requires grid generation and assembling boundary and forcing conditions.
- Scope and limitations: The framework for developing this data-centric machine-learning technology was presented for wave modeling for the first time.The authors expect such approaches to become increasingly common.
5. Conclusions
The study develops machine-learning surrogates for SWAN wave modeling that provide accurate, computationally efficient wave-condition forecasts. The conclusions also identify spatial-information limitations of the MLP approach and potential extensions using CNNs and locally updated models.
- Model performance: Appropriately trained mapping matrices produce accurate surrogate representations of significant wave-height fields and characteristic period.The surrogates operate through matrix multiplication after supervised training.
- Computational efficiency: Over 4,000 times faster, the matrix-based surrogates run substantially more quickly than the physics-based SWAN model.The reported speedup concerns surrogate calculations compared with the physics-based model.
- Applications: The machine-learning models can act as a rapid, efficient wave-condition forecast system for estimating wave-related conditions.The forecasted conditions are also described as useful for estimating wave-energy-converter power-generation potential or surf conditions.
- Applications: A locally installed model could let a wave-energy converter operate its own forecast system and use buoy-collected wave data to update the model.The paper describes continuous local data and available forecasts as inputs for evolving model parameters through online learning.
- Model limitations and extensions: The MLP approach does not account for spatial information, while a CNN design could incorporate node coordinates and bathymetry to represent spatial wave effects.The proposed inputs include latitude, longitude, and bathymetric depth at 3,104 SWAN nodes, supporting representation of bathymetric effects and coastline diffraction.