Lorentzian geometrical structures with global time, Gravity and Electrodynamics

We investigate Lorentzian structures in the four-dimensionalspace-time, supplemented either by a covector field of thetime-direction or by a scalar field of the global time. Furthermore,we propose a new metrizable model of the gravity. In contrast to theusual Theory of General Relativity where all ten components of thesymmetric pseudo-metrics are independent variables, the presentedhere model of the gravity essentially depend only on singlefour-covector field, restricted to have only three-independentcomponents. However, we prove that the Gravitational field, ruled bythe proposed model and generated by some massive body, resting andspherically symmetric in some coordinate system, is given by apseudo-metrics, which coincides with thewell known Schwarzschild metric from the General Relativity. TheMaxwell equations and Electrodynamics are also investigated in theframes of the proposed model. In particular, we derive the covariantformulation of Electrodynamics of moving dielectrics andpara/diamagnetic mediums.

Explaining Bad Forecasts in Global Time Series Models

While increasing empirical evidence suggests that global time series forecasting models can achieve better forecasting performance than local ones, there is a research void regarding when and why the global models fail to provide a good forecast. This paper uses anomaly detection algorithms and explainable artificial intelligence (XAI) to answer when and why a forecast should not be trusted. To address this issue, a dashboard was built to inform the user regarding (i) the relevance of the features for that particular forecast, (ii) which training samples most likely influenced the forecast outcome, (iii) why the forecast is considered an outlier, and (iv) provide a range of counterfactual examples to understand how value changes in the feature vector can lead to a different outcome. Moreover, a modular architecture and a methodology were developed to iteratively remove noisy data instances from the train set, to enhance the overall global time series forecasting model performance. Finally, to test the effectiveness of the proposed approach, it was validated on two publicly available real-world datasets.

Explaining Bad Forecasts in Global Time Series Models

While increasing empirical evidence suggests that global time series forecasting models can achieve better forecasting performance than local ones, there is a research void regarding when and why the global models fail to provide a good forecast. This paper uses anomaly detection algorithms and Explainable Artificial Intelligence (XAI) to answer when and why a forecast should not be trusted. To address this issue, a dashboard was built to inform the user regarding (i) the relevance of the features for that particular forecast, (ii) which training samples most likely influenced the forecast outcome, (iii) why the forecast is considered an outlier, and (iv) provide a range of counterfactual examples to understand value changes, in the feature vector or the predicted value, can lead to a different outcome. Moreover, a modular architecture and a methodology were developed to iteratively remove noisy data instances from the train set, to enhance the overall global time series forecasting model performance. Finally, to test the effectiveness of the proposed approach, it was validated on two publicly available real-world datasets.