Professor Dr. Angelo Iollo, head of the Memphis Team of INRIA, and Dr. Haysam Telib, CEO of Optimad Engineering, were guest speakers in the IT'IS Brown-Bag-Lunch Seminar series with a presentation on Thursday, October 11 on the topic of “Convergence Between Data and High-Fidelity Numerical Models”.
Model reduction is a powerful tool that is applied throughout many different disciplines, including controls, fluid dynamics, structural dynamics, and biological flows. In many situations, high-order, complicated numerical models accurately represent the problem at hand, but are unsuitable for many applications – e.g., optimization, control design, systems with real-time requirements – that require fast simulations. The use of reduced-order models (ROMs) that significantly reduce the computational complexity is a trade-off of accuracy for speed and scalability. The construction of ROMs for design, optimization, control, and data-driven systems is not a trivial task because often there is no guarantee that the ROM will effectively model the physical phenomenon given a particular choice of the empirical modes.
The focus of Prof. Iollo's talk was on the mathematical foundation of numerical methods based on the proper orthogonal decomposition (POD) method for low-order modeling (LOM) of non-linear multiscale phenomena. POD is a mathematical technique designed to extract the relevant features of the problem at hand from an existing database of solution snapshots under the form of global modes. These are used to represent the far-field solution, while the high-fidelity model is solved only on a smaller portion of the computational domain, with considerable reduction in computational effort and preservation of local accuracy.
Among the many topics discussed by Prof. Iollo were the basic derivation of the POD method, estimates of error and of the upper/lower bounds on error estimates, and reconstruction of POD modes for advection-dominated phenomena, e.g., the solution of optimized transportation problems.
Dr. Telib provided some examples of real-life applications of POD-based LOM for, e.g., optimization of shape for aerodynamics in the automotive industry, prediction of tumor growth based on magnetic resonance imaging data, and optimization via LOM of a turbine blade in an aeronautics engine.