  Optimal decision-making compels us to anticipate the future at different
horizons. However, in many domains connecting together predictions from
multiple time horizons and abstractions levels across their organization
becomes all the more important, else decision-makers would be planning using
separate and possibly conflicting views of the future. This notably applies to
smart grid operation. To optimally manage energy flows in such systems,
accurate and coherent predictions must be made across varying aggregation
levels and horizons. With this work, we propose a novel multi-dimensional
hierarchical forecasting method built upon structurally-informed
machine-learning regressors and established hierarchical reconciliation
taxonomy. A generic formulation of multi-dimensional hierarchies, reconciling
spatial and temporal hierarchies under a common frame is initially defined.
Next, a coherency-informed hierarchical learner is developed built upon a
custom loss function leveraging optimal reconciliation methods. Coherency of
the produced hierarchical forecasts is then secured using similar
reconciliation technics. The outcome is a unified and coherent forecast across
all examined dimensions. The method is evaluated on two different case studies
to predict building electrical loads across spatial, temporal, and
spatio-temporal hierarchies. Although the regressor natively profits from
computationally efficient learning, results displayed disparate performances,
demonstrating the value of hierarchical-coherent learning in only one setting.
Yet, supported by a comprehensive result analysis, existing obstacles were
clearly delineated, presenting distinct pathways for future work. Overall, the
paper expands and unites traditionally disjointed hierarchical forecasting
methods providing a fertile route toward a novel generation of forecasting
regressors.
