MINES ParisTech CAS - Centre automatique et systèmes

Complementary Deep - Reduced Order Model

Thursday 4th November 2021, 4pm – 5pm (Paris time).

Michele Alessandro Bucci INRIA-Saclay, France

Reducing simulation time is critical for applications such as closed loop control or iterative design optimization. In this context, model reduction techniques have become a growing area of research in the last decades. While research efforts have mainly been centered around feature based approaches like POD, BPOD or DMD, direct approaches leveraging Deep Neural Networks have been proposed in recent years with great success. Despite these promising results, neural network architectures provide little to no physical guarantees, and have limited interpretability. On the other hand, feature based methods often reconstruct the final solution through a linear combination of modes embedded with physical constraints. However, this often comes at the cost of loss of information and increased error rates. POD-Galerkin models are a perfect example of this trade-off between physical guarantees and performance loss. These models have been shown to be very efficient for the reduction of linear systems, but they are extremely limited when applied to nonlinear systems such as the Navier-Stokes equations. To address these shortcomings, we propose to add a closure term to POD-Galerkin models to correct their dynamics. We use simple neural networks in combination with delay differential equations to reconstruct the required correction. We show that a satisfactory model can be trained through the Neural ODE framework to learn a memory based correction from simulation data. We preserve the simple structure and low computational cost of Galerkin models while improving their performance.

Michele Alessandro Bucci is researcher in Machine Learning and Dynamical systems at TAU team in INRIA-Saclay, France. He got a PhD in Arts et Métiers ParisTech in 2017 with a research on passive control of unstable fluid mechanics mechanisms leading to laminar to turbulent transition in boundary layer flows. With a particular focus on spectral analysis of dynamical systems, he studied the capability of data driven methods to predict and control chaotic systems. Notably, his research has focused on the link between deep reinforcement learning and optimal control theory. More recently, his research is devoted to the acceleration of numerical simulations with machine learning models, both replacing standard numerical solvers or hybridizing existing CFD codes with Deep Learning solutions.