The development of a reliable and robust surrogate model is often constrained by the dimensionality of the problem. For a system with high‐dimensional inputs/outputs (I/O), conventional approaches usually use a low‐dimensional manifold to describe the high‐dimensional system, where the I/O data are first reduced to more manageable dimensions and then the condensed representation is used for surrogate modeling. In this study, a new solution scheme for this type of problem based on a deep learning approach is presented. The proposed surrogate is based on a particular network architecture, that is, convolutional neural networks. The surrogate architecture is designed in a hierarchical style containing three different levels of model structures, advancing the efficiency and effectiveness of the model in the aspect of training. To assess the model performance, uncertainty quantification is carried out in a continuum mechanics benchmark problem. Numerical results suggest the proposed model is capable of directly inferring a wide variety of I/O mapping relationships. Uncertainty analysis results obtained via the proposed surrogate have successfully characterized the statistical properties of the output fields compared to the Monte Carlo estimates.
in improving predictive performance using contaminated data, and various examples are provided to illustrate concepts, methodologies, and algorithms of this proposed BDL modeling technique.
The climate system consists of diverse yet interconnected components, such as the atmosphere, oceans, etc., and each can exhibit complex, multiscale, and chaotic behaviors. Additional interactions and feedbacks among these subsystems drive dynamic evolution over an enormous range of spatial and temporal scales in the climate system (Canadell et al., 2021;IPCC, 2007;Masson-Delmotte, 2021). In this setting, comprehensive climate models have emerged as a powerful tool in helping unravel and better comprehend the myriad processes underlying climate and climate change. Moreover, studies using such models have greatly improved the understanding of climate system processes over the past few decades (Masson-Delmotte, 2021). Importantly, comprehensive climate models have helped to better anticipate the climate system's response to external forcings, such as those stemming from increased greenhouse gases that typically are realized on a timescale of a few decades or longer. At shorter timescales at which natural variability plays an increasingly important role, however, improvements in the ability to predict climate are not commensurate with advances in understanding dynamics and processes (
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