Data-driven learning of nonlocal models: bridging scales with nonlocality

Marta D’Elia

Meta Reality Labs

Wednesday 16th November 2022

09:30:00

Aula Saleri, VI piano

Nonlocal models are characterized by integral operators that embed lengthscales in their definition. As such, they are preferable to classical partial differential equation models in situations where the dynamics of a system is affected by the small scale behavior, yet the small scales would require prohibitive computational cost to be treated explicitly. In this sense, nonlocal models can be considered as coarse-grained, homogenized models that, without resolving the small scales, are still able to accurately capture the system’s global behavior. However, nonlocal models depend on “kernel functions” that are often hand tuned. We propose to learn optimal kernel functions from high fidelity data by combining machine learning algorithms, known physics, and nonlocal theory. This combination guarantees that the resulting model is mathematically well-posed and physically consistent. Furthermore, by learning the operator rather than a surrogate for the solution, these models generalize well to settings that are different from the ones used during training. We apply this learning technique to find homogenized nonlocal models for anomalous subsurface transport, molecular dynamics displacements, and wave propagation through heterogeneous materials. Contatto: luca.dede@polimi.it