Neural Network Emulation of Spatio temporal Data Using Linear and Nonlinear Dimensionality Reduction
A statistical emulator of a high fidelity computer model is based on the application of machine learning algorithms to input output data generated by the model at selected design points. Applications include real time control, design optimization and inverse parameter estimation. In many of these applications, the outputs are spatial or spatio temporal fields. In such cases, standard emulation methods are computationally impractical due to the curse of dimensionality, or are limited in their applicability by simplifying assumptions in relation to the correlation structure. In this work, we combine linear and nonlinear dimensionality reduction with artificial neural networks to develop an efficient approach to emulating high dimensional spatio temporal models, without making ad hoc assumptions regarding correlations. The approach is tested on models of electromagnetic wave propagation. The necessity of nonlinear dimensionality reduction is highlighted.