Learning stable reduced-order models for hybrid twins

Abstract

The concept of “hybrid twin” (HT) has recently received a growing interest thanks to the availability of powerful machine learning techniques. This twin concept combines physics-based models within a model order reduction framework—to obtain real-time feedback rates—and data science. Thus, the main idea of the HT is to develop on-the-fly data-driven models to correct possible deviations between measurements and physics-based model predictions. This paper is focused on the computation of stable, fast, and accurate corrections in the HT framework. Furthermore, regarding the delicate and important problem of stability, a new approach is proposed, introducing several subvariants and guaranteeing a low computational cost as well as the achievement of a stable time-integration.

A Regularized Real-Time Integrator for Data-Driven Control of Heating Channels

“…The input of the network is a 3D tensor of dimension (20 × 5 × 1), for 20 time steps and 5 variables as inputs. The selected optimization algorithm is Adam with the loss function being the mean square errors, modified to add a regularization similar to the DMD regularization [36,37], to perform integration in time without increasing the error significantly. For instance, the loss function J in this section reads:…”

Empowering engineering with data, machine learning and artificial intelligence: a short introductive review

“…The best constant matrix enabling the representation of all the available data is computed accordingly in general in a least-squares sense. Some constraints can be added during the learning process in order to ensure the stability of the resulting time integrator (related to the spectral radius of the matrix that is being learned) [109].…”

“…Hybrid models consist of two contributions. It is the result of a physics-based model and the data-driven model, which takes into account the deviation between the measured physical reality and the physics-based model prediction [3,24,92,108,109]. The main advantages of the augmented framework is double.…”

Engineering empowered by physics-based and data-driven hybrid models: A methodological overview

“…-In some cases, when the model captures most of the solution complexity, the correction must describe a discrepancy that could exhibits much smaller nonlinearities, as was the case treated in [40,41], where the same amount of data performed better within the hybrid than within the fully data-driven framework. -Sometimes the physics-based model operates very accurately in a part of the domain, whereas the nonlinear behavior localizes in a very small region that can, in that case, be captured by a data-driven learned model, as considered in [39] for addressing the inelastic behavior of spot-welds.…”