## 4 Neural Network Implementation to Speed-Up Satellite Data Processing  
The SRT inversion approach uses an optimization method that is applied pixel by pixel, which can be highly time consuming. As an example, the processing of the study area (500 \(\times\) 500 pixels) could take 1 h10 for computational time. The hardware used to estimate the computational time is an intel Core i7 processor, 2.60 Ghz \(\times\) 12 CPU and 31 Gio RAM. Thus, the processing of an OLCI typical scene (4090 \(\times\) 4865 pixels) would require about 10 days to retrieve the bio-optical parameters. A neural network approach was then implemented to reduce the computational time and to make more operational the application of the proposed method at larger scale. Neural network techniques have been previously implemented to detect the presence of _Sargassum_ in the open ocean [16; 17]; their training phase, which consists in recognizing _Sargassum_ using spectral and spatial features, is performed using either the application of indexes such as AFAI and MCI. Neural networks can detect the presence of _Sargassum_ and/or assess their abundance per pixels. However, they are not able yet to consider the _Sargassum_ immersion depth. Here, the neural network was trained using a simulated dataset because in situ data of the immersion depth of the _Sargassum_ aggregation are not available. The forward SRT model was used to create such a training dataset which links the bio-optical parameters to their associated surface reflectances. A noise is added to the simulated surface reflectances using the same method as described Section 3.1 to obtain OLCI-like surface reflectances. The artificial neural network is trained to estimate the five bio-optical parameters (Chl, NAP, CDOM, FC and z) from the simulated OLCI-like surface reflectances (12 spectral bands). It is then able to perform the inversion of the SRT model for the OLCI surface derived reflectances image, pixel by pixel. The artificial neural network is based on a multi-layer perceptron model (MLP) which enables to approximate non-linear functions to estimate continuous outputs [36].The neural network was built using 4 hidden layers of 50 neurons fully connected (Figure 10a). The training phase, the test phase, and the validation phase were applied using, respectively, 70%, 15%, and 15% of the dataset. The training phase duration is 12 h when using 100,000 samples composed by the set of reflectances and associated water constituents. It should be highlighted that the training phase is performed only once. Then, the neural network can be applied to any OLCI scene within a few minutes, thus significantly decreasing the computational time. The metric used to evaluate the learning performances for each phase (training, test, and validation) is the mean squared error (MSE) which is expressed as follows (Equation (9)):  
\[\text{MSE}=\frac{1}{\text{N}}\sum(\text{C}_{\text{reference}}-\text{C}_{ \text{estimation}})^{2} \tag{9}\]  
where N is the number of evaluated parameters for each phase. One epoch is defined as one training cycle for which the dataset is processed by the algorithm. The variation of the MSE with the epoch number for each step of the learning process (training, test, and  
Figure 9: Histogram of the probability of occurrence (in %) of FC (in %) retrieved by the SRT inversion method (red) and by the \(\delta\)MCI (blue) for the study area of the scene acquired on 8 July 2017.  
validation phase) is shown Figure 10b. A similar shape is observed for the training and the test phase. The epoch number for which MSE of the test phase is minimum points out the number of training cycle that is sufficient for stopping the learning process. Here, the value of this epoch number is 42. The learning process could lead to overfitting of a given neural network when MSE for the validation phase increases with respect to the epoch number prior to that of the MSE for the test phase.