When deploying machine learning estimators in science and engineering (SAE) domains, it is critical to avoid failed estimations that can have disastrous consequences, e.g., in aero engine design. This work focuses on detecting and correcting failed state estimations before adopting them in SAE inverse problems, by utilizing simulations and performance metrics guided by physical laws. We suggest to flag a machine learning estimation when its physical model error exceeds a feasible threshold, and propose a novel approach, GEESE, to correct it through optimization, aiming at delivering both low error and high efficiency. The key designs of GEESE include (1) a hybrid surrogate error model to provide fast error estimations to reduce simulation cost and to enable gradient based backpropagation of error feedback, and (2) two generative models to approximate the probability distributions of the candidate states for simulating the exploitation and exploration behaviours. All three models are constructed as neural networks. GEESE is tested on three real-world SAE inverse problems and compared to a number of state-of-the-art optimization/search approaches. Results show that it fails the least number of times in terms of finding a feasible state correction, and requires physical evaluations less frequently in general.

A methodology is proposed, which addresses the caveat that line-of-sight emission spectroscopy presents in that it cannot provide spatially resolved temperature measurements in nonhomogeneous temperature fields. The aim of this research is to explore the use of data-driven models in measuring temperature distributions in a spatially resolved manner using emission spectroscopy data. Two categories of data-driven methods are analyzed: (i) Feature engineering and classical machine learning algorithms, and (ii) end-to-end convolutional neural networks (CNN). In total, combinations of fifteen feature groups and fifteen classical machine learning models, and eleven CNN models are considered and their performances explored. The results indicate that the combination of feature engineering and machine learning provides better performance than the direct use of CNN. Notably, feature engineering which is comprised of physics-guided transformation, signal representation-based feature extraction and Principal Component Analysis is found to be the most effective. Moreover, it is shown that when using the extracted features, the ensemble-based, light blender learning model offers the best performance with RMSE, RE, RRMSE and R values of 64.3, 0.017, 0.025 and 0.994, respectively. The proposed method, based on feature engineering and the light blender model, is capable of measuring nonuniform temperature distributions from low-resolution spectra, even when the species concentration distribution in the gas mixtures is unknown.