Combined grey-black-box (GBB) model identification.

Mathematical models are fundamental in most fields of science and technology, such as physics, chemistry, biology, mechanics, control, electrical, automotive and aerospace engineering, finance and economy, weather and climate, signal processing, etc.

Models can be used for system design, prediction, simulation, control, filtering, fault detection, decision making, etc., and are constructed on the basis of prior knowledge about the system of interest and experimental observations. In standard modeling approaches, white-box or grey-box models are typically used, i.e., models obtained from the physical laws governing the system to control. However, due to imprecise knowledge about the system, these kinds of models may be over-simplified, resulting in inaccurate predictions. Trying to include details that are not completely known or too complex may lead to more inaccurate or even completely wrong results.

On the other hand, black-box models, like neural networks, can be trained to optimize the prediction accuracy.

However, these kinds of models may be affected by several problems:

  1. need of large amounts of data, which may require expensive and time-consuming experiments;
  2. energy and time-consuming identification/training processes;
  3. high complexity, in terms of number of parameters and basis functions;
  4. trapping in low-quality local minima;
  5. low/null physical interpretability;
  6. poor generalization capability.

In this research activity, new model identification methods are developed, optimizing the combined use of prior knowledge and data, allowing us to overcome the aforementioned issues. On one side, these methods are based on the physical information available on the system (grey-box part).

On the other side, they incorporate a black-box part, identified by means of machine learning techniques, allowing us to capture the unmodeled dynamics.

Erc Sector:

  • PE7_1 Control engineering
  • PE7_3 Simulation engineering and modelling
  • PE1_19 Control theory and optimisation


  • System identification
  • Nonlinear systems

Research groups