11:00 AM - 1:00 PM
[MIS16-P09] Evaluation of uncertainty in the inverse analysis of sediment gravity flow deposits
Keywords:sediment gravity flow, inverse analysis, neural network
The inverse analysis of particulate gravity flows and tsunamis from their deposits has recently become a practical research method using neural networks. In the past, the computational load of the forward models was a barrier for reconstructing past hydraulic conditions from deposits. However, the recent studies indicated that a highly accurate inverse analysis model could be constructed by generating artificial depositional datasets using a numerical model and training a neural network on the relationship between hydraulic conditions and depositional characteristics. In this approach, the generation of artificial depositional data for training can be wholly parallelized so that even highly loaded forward models can be employed without any problems. The versatility of the neural network inversion method is broad. It has already been proved that this approach can be applied to turbidity currents and tsunamis, and debris flow deposits.
On the other hand, the method for estimating uncertainty in the inversion results has not yet been established. There is inevitably a certain degree of uncertainty in the inverse analysis, even when the past hydraulic conditions are appropriately reconstructed from deposits. Uncertainty in inverse analysis has two origins. One is the uncertainty of data. Measurement data is always subject to errors, and the effect of these errors on the inverse analysis results can be estimated in advance by adding noise to the input data. Another source of uncertainty in the inverse analysis is the lack of knowledge. The data given during training does not cover all situations, and when analyzing the actual deposits, the situations could not be given in the training data. In addition, the structure of the neural network is not perfect as an inverse analysis model, which leads to uncertainty in the inversion results. However, it is difficult to estimate the degree of uncertainty in the inverse analysis results caused by the lack of knowledge in the conventional inversion method using a neural network for gravity flow deposits.
In this presentation, we applied Bayesian Neural Network (BNN), which was developed based on Bayesian statistics, to estimate the degree of uncertainty in the inverse analysis results of gravity flow deposits. In the BNN, the weight coefficients of the NN are considered to have a probabilistic distribution, and by sampling these values, the uncertainty of the feed-forward calculation results can also be expressed. In order to approximate the sampling results from the distribution of weight coefficients, the Monte Carlo Dropout method (MC Dropout) has been proposed recently. In this study, we used the MC Dropout method to evaluate the uncertainty of the inverse analysis results. The target of the evaluation is the inverse analysis of turbidite performed by Naruse and Nakao (2021). In this study, 300 test data were generated by a numerical model, and the initial conditions of turbidity currents (length, height, concentration, and slope gradient of the suspension cloud) were estimated by the inverse analysis. As a result of the MC Dropout application, the MAP estimates of initial conditions were almost the same as those of existing studies. On the other hand, the 95% confidence intervals of the estimates varied greatly depending on the parameters. The geometry and concentration of the suspension cloud had an uncertainty of about 10-30%, while the slope was estimated with very low accuracy (> 80%).
Although the results of this study are only preliminary, it will be essential to estimate the uncertainty of the estimated values when the inverse analysis of event deposits is applied to disaster prevention in the future. The Bayesian network is expected to be a powerful method for this purpose.
On the other hand, the method for estimating uncertainty in the inversion results has not yet been established. There is inevitably a certain degree of uncertainty in the inverse analysis, even when the past hydraulic conditions are appropriately reconstructed from deposits. Uncertainty in inverse analysis has two origins. One is the uncertainty of data. Measurement data is always subject to errors, and the effect of these errors on the inverse analysis results can be estimated in advance by adding noise to the input data. Another source of uncertainty in the inverse analysis is the lack of knowledge. The data given during training does not cover all situations, and when analyzing the actual deposits, the situations could not be given in the training data. In addition, the structure of the neural network is not perfect as an inverse analysis model, which leads to uncertainty in the inversion results. However, it is difficult to estimate the degree of uncertainty in the inverse analysis results caused by the lack of knowledge in the conventional inversion method using a neural network for gravity flow deposits.
In this presentation, we applied Bayesian Neural Network (BNN), which was developed based on Bayesian statistics, to estimate the degree of uncertainty in the inverse analysis results of gravity flow deposits. In the BNN, the weight coefficients of the NN are considered to have a probabilistic distribution, and by sampling these values, the uncertainty of the feed-forward calculation results can also be expressed. In order to approximate the sampling results from the distribution of weight coefficients, the Monte Carlo Dropout method (MC Dropout) has been proposed recently. In this study, we used the MC Dropout method to evaluate the uncertainty of the inverse analysis results. The target of the evaluation is the inverse analysis of turbidite performed by Naruse and Nakao (2021). In this study, 300 test data were generated by a numerical model, and the initial conditions of turbidity currents (length, height, concentration, and slope gradient of the suspension cloud) were estimated by the inverse analysis. As a result of the MC Dropout application, the MAP estimates of initial conditions were almost the same as those of existing studies. On the other hand, the 95% confidence intervals of the estimates varied greatly depending on the parameters. The geometry and concentration of the suspension cloud had an uncertainty of about 10-30%, while the slope was estimated with very low accuracy (> 80%).
Although the results of this study are only preliminary, it will be essential to estimate the uncertainty of the estimated values when the inverse analysis of event deposits is applied to disaster prevention in the future. The Bayesian network is expected to be a powerful method for this purpose.