Learning of Spatio-temporal Dynamics in Thermal Engineering
Thermal engineering deals with the estimation of the temperature at different points and instants for a given set of boundary and initial conditions. For this, an analytic model replaces accurate but time-expensive numerical simulation models; it is independent of the boundary conditions and parameterized by the statistical learning of multidimensional temporal trajectories. This black-box model is a recursive neural network emulating the temperatures of interest over time from the only knowledge of initial conditions and exogenous variables.
The number of hidden neurons is selected by a non-asymptotic approach based upon the minimization of a penalyzed criterion. Methods like the slope heuristic and the dimension jump enable the calibration of the penalty constant in presence of a n-sample. In practice, their extrapolation to dependent data gives accurate results in the sense of the mean square error.
The surrogate model and the model selection are successfully applied to an industrial benchmark.
Keywordsrecursive neural network nonuniform time step model selection penalized criterion thermal engineering
Unable to display preview. Download preview PDF.
- 3.Ljung, L.: System identification: theory for the user, 2nd edn. Prentice Hall PTR (1999)Google Scholar
- 5.Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press (1995)Google Scholar
- 6.Igel, C., Hüsken, M.: Improving the Rprop Learning Algorithm. In: Proceedings of the Second International Symposium on Neural Computation (2000)Google Scholar
- 7.Nguyen, D., Widrow, B.: Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights. In: Proceedings of the International Joint Conference on Neural Networks, vol. 3, pp. 21–26 (1990)Google Scholar
- 8.Arlot, S., Massart, P.: Data-driven Calibration of Penalties for Least-Squares Regression, vol. 10, pp. 245–279 (2009)Google Scholar