Reduced Order Models based on Tensor Rank Decomposition: mathematical foundations and practical examples
Please login to view abstract download link
Tensor Rank Decomposition (TRD)-based Reduced Order Modelling (ROM) techniques are valuable tools for system interpretation, prediction and optimisation. If on one hand ROM allows complex systems simplification, its combination with TRD techniques produces real time and completely interpretable results, according to the following mathematical expression: F(v_1,…〖,v〗_D )=∑_(t=1)^T▒〖α_t ∏_(d=1)^D▒〖f_(t,d) (v_d)〗〗 (1) where: ft,d(vd) are one-dimensional functions each depending on a single system variable, D is the number of system dimensions, T is the model approximation order in the series expansion, and αt are weighting coefficients. Twinkle is an in-house developed library for TRD-based ROM applications, developed in C++, with a Python wrap, that allows decomposing a complex multivariable system into a product of one-dimensional functions, hence isolating the effect of each input variable, according to Equation (1) [1]. The ROM library has been applied to several use cases across different European projects, with outstanding results in system prediction, understanding, and optimisation. Moreover, the technique has been successfully applied to processes or products correction and improvement, using it for assessing acceptable ranges for nominal values variations by studying their impact on the expected outcome [2]. REFERENCES [1] Zambrano, V., Rodríguez-Barrachina, R., Calvo, S., & Izquierdo, S. (2020). TWINKLE: A digital twin-building kernel for real-time computer-aided engineering. SoftwareX, 11, 100419. https://doi.org/10.1016/j.softx.2020.100419 [2] Zambrano, V., Brase, M., Hernández-Gascón, B., Wangenheim, M., Gracia, L. A., Viejo, I., Izquierdo, S., & Valdés, J. R. (2021). A Digital Twin for Friction Prediction in Dynamic Rubber Applications with Surface Textures. Lubricants, 9(5), 57. https://doi.org/10.3390/lubricants9050057
