The process is similar to how human babies learn that bowls and spoons are used to eat. Breakthroughs, discoveries, and DIY tips sent every weekday. We've long known that dogs are pretty smart. They may "picture" objects in their heads just like us, communicate with button boards, and can even understand fairly complicated words . They also appear to categorize objects by function, understanding how similar types of toys work, even if they don't look alike.

Long-term groundwater level (GWL) measurement is vital for effective policymaking and recharge estimation using annual maxima and minima. However, current methods prioritize short-term predictions and lack multi-year applicability, limiting their utility. Moreover, sparse in-situ measurements lead to reliance on low-resolution satellite data like GLDAS as the ground truth for Machine Learning models, further constraining accuracy. To overcome these challenges, we first develop an ML model to mitigate data gaps, achieving $R^2$ scores of 0.855 and 0.963 for maximum and minimum GWL predictions, respectively. Subsequently, using these predictions and well observations as ground truth, we train an Upsampling Model that uses low-resolution (25 km) GLDAS data as input to produce high-resolution (2 km) GWLs, achieving an excellent $R^2$ score of 0.96. Our approach successfully upscales GLDAS data for 2003-2024, allowing high-resolution recharge estimations and revealing critical trends for proactive resource management. Our method allows upsampling of groundwater storage (GWS) from GLDAS to high-resolution GWLs for any points independently of officially curated piezometer data, making it a valuable tool for decision-making.

Usually standard algorithms employ a loss where each error is the mere absolute difference between the true value and the prediction, in case of a regression task. In the present, we introduce several error weighting schemes that are a generalization of the consolidated routine. We study both a binary classification model for Support Vector Classification and a regression net for Multi-layer Perceptron. Results proves that the error is never worse than the standard procedure and several times it is better.

The output distribution of a neural network (NN) over the entire input space captures the complete input-output mapping relationship, offering insights toward a more comprehensive NN understanding. Exhaustive enumeration or traditional Monte Carlo methods for the entire input space can exhibit impractical sampling time, especially for high-dimensional inputs. To make such difficult sampling computationally feasible, in this paper, we propose a novel Gradient-based Wang-Landau (GWL) sampler. We first draw the connection between the output distribution of a NN and the density of states (DOS) of a physical system. Then, we renovate the classic sampler for the DOS problem, the Wang-Landau algorithm, by replacing its random proposals with gradient-based Monte Carlo proposals. This way, our GWL sampler investigates the under-explored subsets of the input space much more efficiently. Extensive experiments have verified the accuracy of the output distribution generated by GWL and also showcased several interesting findings - for example, in a binary image classification task, both CNN and ResNet mapped the majority of human unrecognizable images to very negative logit values.

In the present study, six meta-heuristic schemes are hybridized with artificial neural network (ANN), adaptive neuro-fuzzy interface system (ANFIS), and support vector machine (SVM), to predict monthly groundwater level (GWL), evaluate uncertainty analysis of predictions and spatial variation analysis. The six schemes, including grasshopper optimization algorithm (GOA), cat swarm optimization (CSO), weed algorithm (WA), genetic algorithm (GA), krill algorithm (KA), and particle swarm optimization (PSO), were used to hybridize for improving the performance of ANN, SVM, and ANFIS models. Groundwater level (GWL) data of Ardebil plain (Iran) for a period of 144 months were selected to evaluate the hybrid models. The pre-processing technique of principal component analysis (PCA) was applied to reduce input combinations from monthly time series up to 12-month prediction intervals. The results showed that the ANFIS-GOA was superior to the other hybrid models for predicting GWL in the first piezometer and third piezometer in the testing stage. The performance of hybrid models with optimization algorithms was far better than that of classical ANN, ANFIS, and SVM models without hybridization. The percent of improvements in the ANFIS-GOA versus standalone ANFIS in piezometer 10 were 14.4%, 3%, 17.8%, and 181% for RMSE, MAE, NSE, and PBIAS in the training stage and 40.7%, 55%, 25%, and 132% in testing stage, respectively. The improvements for piezometer 6 in train step were 15%, 4%, 13%, and 208% and in the test step were 33%, 44.6%, 16.3%, and 173%, respectively, that clearly confirm the superiority of developed hybridization schemes in GWL modeling. Uncertainty analysis showed that ANFIS-GOA and SVM had, respectively, the best and worst performances among other models. In general, GOA enhanced the accuracy of the ANFIS, ANN, and SVM models.