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Chemical reaction neural network (CRNN), a recently developed tool for autonomous discovery of reaction models, has been successfully demonstrated on a variety of chemical engineering and biochemical systems. It leverages the extraordinary data-fitting capacity of modern deep neural networks (DNNs) while preserving high interpretability and robustness by embedding widely applicable physical laws such as the law of mass action and the Arrhenius law. In this paper, we further developed Bayesian CRNN to not only reconstruct but also quantify the uncertainty of chemical kinetic models from data. Two methods, the Markov chain Monte Carlo algorithm and variational inference, were used to perform the Bayesian CRNN, with the latter mainly adopted for its speed. We demonstrated the capability of Bayesian CRNN in the kinetic uncertainty quantification of different types of chemical systems and discussed the importance of embedding physical laws in data-driven modeling. Finally, we discussed the adaptation of Bayesian CRNN for incomplete measurements and model mixing for global uncertainty quantification. 

Abstract Easily portable, small-sized ocean wave energy converters (WECs) may be used in many situations where large-sized WEC devices are not necessary or practical. Power maximization for small-sized WECs amplifies challenges that are not as difficult with large-sized devices, especially tuning the device’s natural frequency to match the wave frequency and achieve resonance. In this study, power maximization is performed for a small-sized, two-body attenuator WEC with a footprint constraint of about 1m. A thin, submerged tuning plate is added to each body to increase added mass without significantly increasing hydrostatic stiffness in order to reach resonance. Three different body cross-section geometries are analyzed. Device power absorption is determined through time domain simulations using WEC-Sim with a simplified two-degree-of-freedom (2DOF) model and a more realistic three-degree-of-freedom (3DOF) model. Different drag coefficients are used for each geometry to explore the effect of drag. A mooring stiffness study is performed with the 3DOF model to investigate the mooring impact. Based on the 2DOF and 3DOF power results, there is not a significant difference in power between the shapes if the same drag coefficient is used, but the elliptical shape has the highest power after assigning a different approximate drag coefficient to each shape. The mooring stiffness study shows that mooring stiffness can be increased in order to increase relative motion between the two bodies and consequently increase the power.