Computational Learning

The MOX Research Group of Computational Learning creates a concrete bridge and synergies between Machine/Deep Learning and Scientific Computing. The goal is to complement physics-based methods and data-driven models, to improve knowledge of real phenomena.

The activities of the Computational Learning MOX Group focus on the following research topics.

Data-driven reduced-order and surrogate models.

The numerical approximation of differential models typically calls for large computational resources and significant resolution times, which are often not compatible with the needs of real-life applications. Hence, we develop reduced models and emulators, based on Machine and Deep Learning tools, that surrogate high-fidelity solvers of differential equations.

Black-box and grey-box discovery of differential equations.

By combining prior physical knowledge and data, Machine Learning represents a promising approach to generating descriptions of real phenomena in terms of differential equations and constitutive laws. The combination between black-box Machine Learning tools and mathematical models boosts interpretability and enhances generalization accuracy.

Neural Network-based acceleration of numerical methods.

Classical numerical techniques often call for improvements in accuracy and efficiency. By leveraging its capability to extract knowledge from large datasets, Machine Learning offers an opportunity to enhance the trade-off between computational cost and accuracy of traditional numerical methods, e.g. by learning the optimal values of stabilization parameters, by finding optimal refinements of computational meshes, or by optimising the convergence rate of algebraic solvers.

Machine Learning methods for the approximation of differential problems.

 Thanks to the universal approximation property of Artificial Neural Networks, the latter can approximate the solution of differential equations. For example, Physics Informed Neural Networks represent a flexible tool to solve forward and inverse problems for real-life applications, in which available data and physical knowledge are balanced in the learning phase.