Speakers: Max Hirsch, UC Berkeley

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy, room 134.

Abstract:

In this talk, we will introduce a novel hyper-reduction approach based on neural networks, the Neural Empirical Interpolation Method (NEIM), for reducing the time complexity of computing the nonlinear term in a reduced order model (ROM). NEIM is a non-intrusive greedy algorithm which accomplishes this reduction by approximating an affine decomposition of the nonlinear term of the ROM, where the vector terms of the expansion are given by neural networks depending on the ROM solution, and the coefficients are given by an interpolation of some "optimal'' coefficients. NEIM has the advantages of being easy to implement in models with automatic differentiation and of being a nonlinear projection of the ROM nonlinearity. We will show the effectiveness of the methodology in several examples, including an elliptic example with a nonlinear forcing term and a nonlinear parabolic model of liquid crystals.