Residual Learning With Multifactor Extreme Learning Machines for Waveheight Prediction

We explore the use of extreme learning machines (ELMs) for ocean waveheight prediction. Ocean waveheight variations are affected by multiple factors, such as air pressure, wind speed, and wind direction. To investigate the effects of these factors on waveheight prediction from a machine learning perspective, we develop a multifactor ELM (MFELM), which generalizes the vector inputs of existing ELMs into those of matrix inputs. The generalization enables the MFELM to admit the “multiple factor and multiple time” observed data (e.g., the air pressure, wind speed, and wind direction time sequences) for comprehensive waveheight prediction. Furthermore, we define the concept of numerical residuals in terms of the difference between observed data and waveheight numerical predictions, which are generated from equations of ocean dynamics. In contrast to the commonly used training schemes based on observed data, we propose to exploit numerical residuals for training the MFELM. The motivation for the training strategy arises from the observation that the numerical residuals follow an approximate Gaussian distribution and an ELM (or its generalization MFELM) can generate Gaussian random input layer weights and biases that have common distribution with the numerical residuals. This enhances the representational power of the ELM related methodologies in terms of effectively capturing numerical residual variations. The trained MFELM predicts future numerical residuals that are used for correcting numerical predictions, and finally result in more accurate predictions. Experimental results validate the effectiveness of our proposed method.