Thermodynamically consistent data-driven computational mechanics
- 278 Downloads
In the paradigm of data-intensive science, automated, unsupervised discovering of governing equations for a given physical phenomenon has attracted a lot of attention in several branches of applied sciences. In this work, we propose a method able to avoid the identification of the constitutive equations of complex systems and rather work in a purely numerical manner by employing experimental data. In sharp contrast to most existing techniques, this method does not rely on the assumption on any particular form for the model (other than some fundamental restrictions placed by classical physics such as the second law of thermodynamics, for instance) nor forces the algorithm to find among a predefined set of operators those whose predictions fit best to the available data. Instead, the method is able to identify both the Hamiltonian (conservative) and dissipative parts of the dynamics while satisfying fundamental laws such as energy conservation or positive production of entropy, for instance. The proposed method is tested against some examples of discrete as well as continuum mechanics, whose accurate results demonstrate the validity of the proposed approach.
KeywordsData-driven computational mechanics GENERIC Governing equations
Unable to display preview. Download preview PDF.
This work has been supported by the Spanish Ministry of Economy and Competitiveness through Grants number DPI2017-85139-C2-1-R and DPI2015-72365-EXP and by the Regional Government of Aragon and the European Social Fund, research group T88.
- 13.Öttinger, H.C.: Nonequilibrium thermodynamics: a powerful tool for scientists and engineers. DYNA 79, 122–128 (2012)Google Scholar
- 16.Español, P.: Statistical Mechanics of Coarse-Graining, pp. 69–115. Springer, Berlin (2004)Google Scholar
- 19.Manzoni, A., Lassila, T., Quarteroni, A., Rozza, G.: A reduced-order strategy for solving inverse bayesian shape identification problems in physiological flows. In: Hans Georg B., Xuan Phu H., Rolf R., Johannes P. Schlöder, (eds.) Modeling, Simulation and Optimization of Complex Processes—HPSC 2012: In: Proceedings of the Fifth International Conference on High Performance Scientific Computing, March 5–9, 2012, Hanoi, Vietnam, pp. 145–155. Springer International Publishing, Cham, (2014)Google Scholar
- 25.Pasquali, Matteo., Scriven, L.E.: Theoretical modeling of microstructured liquids: a simple thermodynamic approach. Journal of Non-Newtonian Fluid Mechanics, 120(1):101 – 135, (2004). 3rd International workshop on Nonequilibrium Thermodynamics and Complex FluidsGoogle Scholar
- 30.Karhunen, K.: Uber lineare methoden in der wahrscheinlichkeitsrechnung. Ann. Acad. Sci. Fennicae, ser. Al. Math. Phys., 37, (1946)Google Scholar
- 32.Lorenz, E.N.: Empirical Orthogonal Functions and Statistical Weather Prediction. MIT, Departement of Meteorology, Scientific Report Number 1, Statistical Forecasting Project, (1956)Google Scholar