Quantification of Neural Network Uncertainties on the Hydrogeological Predictions by Probability Density Functions

International audienceThe risk of drought impacting the drinking water and agricultural production is worrying in the developed countries, especially in a changing climate context. To manage and prevent this phenomenon, real-time monitoring and predictive systems are emerging as the key solutions. In the field of artificial intelligence, neural networks are one of these predictive systems. This family of parameterized models is a composition of neuronal functions, which apply a non-linear transformation from their inputs to their outputs. These networks are able to learn a hydro(geo)logical system behaviour using a database composed of observed inputs (rainfall, evapotranspiration, etc.) and outputs (groundwater level, discharge, etc.), thanks to an algorithm minimizing a cost function between observed and simulated outputs. However, it remains difficult to assess the uncertainty generated by these models, possibly leading to misinterpretations by the end users. These uncertainties are mainly of three types. The first is related to the input data. Indeed, hydrosystems are surface elements whereas meteorological inputs are punctual elements. The interpolation error can, therefore, be significant because of the lack of knowledge between gauging stations. The second is the neural network model architecture itself. It is possible to deal with this source of uncertainty using regularization methods. Finally, the neural networks are submitted to uncertainties related to parameter initialization, before the training step. The initial parameters may have an important impact on the results. In this paper, we address the prediction of the Blavet groundwater level (Bretagne, France). In order to assess uncertainties, we will first focus on the parameters initialization of the model. Neuronal models are optimized using cross-validation and early stopping. Then, an ensemble model is realized, in which each member is the result of a unique set of parameters initialization. The purpose of the study is to define how many initializations are necessary to obtain a reasonable confidence interval for forecasts, with the smallest interval and the higher rate of observed points inside this interval. The best model will be determined using cross-validation scores thereby ensuring optimal robustness. We show that, in this case study, an ensemble model of 20 different initializations is sufficient to estimate uncertainty while preserving quality. In the second part, the resulting ensemble model will be used to estimate the global model uncertainty using probability density functions (pdf) applied to the distribution of groundwater level data and cross-validation scores of forecasts. It reveals that the groundwater level predictions are composed of two mixed distributions. Therefore, we will use the expectation-maximization algorithm (EM) to obtain parameters of mixed models. Mixed normal and mixed Gumbel laws, among five mixed distributions assessed, give the best groundwater distribution and are able to generate an abacus drawing uncertainty of mode

Long-term Oncological Outcome of Segmental Versus Extended Colectomy for Colorectal Cancer in Crohn's Disease: Results from an International Multicentre Study

Background and Aims Crohn's disease increases colorectal cancer risk, with high prevalence of synchronous and metachronous cancers. Current guidelines for colorectal cancer in Crohn's disease recommend pan-proctocolectomy. The aim of this study was to evaluate oncological outcomes of a less invasive surgical approach. Methods This was a retrospective database analysis of Crohn's disease patients with colorectal cancer undergoing surgery at selected European and US tertiary centres. Outcomes of segmental colectomy were compared with those of extended colectomy, total colectomy, and pan-proctocolectomy. Primary outcome was progression-free survival. Secondary outcomes included overall survival, synchronous and metachronous colorectal cancer, and major postoperative complications. Results Ninety-nine patients were included: 66 patients underwent segmental colectomy and 33 extended colectomy. Segmental colectomy patients were older [p = 0.0429], had less extensive colitis [p = 0.0002] and no preoperatively identified synchronous lesions [p = 0.0109]. Median follow-up was 43 [31-62] months. There was no difference in unadjusted progression-free survival [p = 0.2570] or in overall survival [p = 0.4191] between segmental and extended colectomy. Multivariate analysis adjusting for age, sex, ASA score, and AJCC staging, confirmed no difference for progression-free survival (hazard ratio [HR] 1.00, p = 0.9993) or overall survival [HR 0.77, p = 0.6654]. Synchronous and metachronous cancers incidence was 9% and 1.5%, respectively. Perioperative mortality was nil and major complications were comparable [7.58% vs 6.06%, p = 0.9998]. Conclusions Segmental colectomy seems to offer similar long-term outcomes to more extensive surgery. Incidence of synchronous and metachronous cancers appears much lower than previously described. Further prospective studies are warranted to confirm these results