Near-future electric distribution grids operation will have to rely on demand-side flexibility, both by implementation of demand response strategies and by taking advantage of the intelligent management of increasingly common small-scale energy storage. The Home energy management system (HEMS), installed at low voltage residential clients, will play a crucial role on the flexibility provision to both system operators and market players like aggregators. Modeling and forecasting multi-period flexibility from residential prosumers, such as battery storage and electric water heater, while complying with internal constraints (comfort levels, data privacy) and uncertainty is a complex task. This papers describes a computational method that is capable of efficiently learn and define the feasibility flexibility space from controllable resources connected to a HEMS. An Evolutionary Particle Swarm Optimization (EPSO) algorithm is adopted and reshaped to derive a set of feasible temporal trajectories for the residential net-load, considering storage, flexible appliances, and predefined costumer preferences, as well as load and photovoltaic (PV) forecast uncertainty. A support vector data description (SVDD) algorithm is used to build models capable of classifying feasible and non-feasible HEMS operating trajectories upon request from an optimization/control algorithm operated by a DSO or market player. (C)2017 Elsevier Ltd. All rights reserved.