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Rapid advancement in inverse modeling methods have brought into light their susceptibility to imperfect data. This has made it imperative to obtain more explainable and trustworthy estimates from these models. In hydrology, basin characteristics can be noisy or missing, impacting streamflow prediction. We propose a probabilistic inverse model framework that can reconstruct robust hydrology basin characteristics from dynamic input weather driver and streamflow response data. We address two aspects of building more explainable inverse models, uncertainty estimation (uncertainty due to imperfect data and imperfect model) and robustness. This can help improve the trust of water managers, handling of noisy data and reduce costs. We also propose an uncertainty based loss regularization that offers removal of 17% of temporal artifacts in reconstructions, 36% reduction in uncertainty and 4% higher coverage rate for basin characteristics. The forward model performance (streamflow estimation) is also improved by 6% using these uncertainty learning based reconstructions. 

We present an overview of four challenging research areas in multiscale physics and engineering as well as four data science topics that may be developed for addressing these challenges. We focus on multiscale spatiotemporal problems in light of the importance of understanding the accompanying scientific processes and engineering ideas, where “multiscale” refers to concurrent, non-trivial and coupled models over scales separated by orders of magnitude in either space, time, energy, momenta, or any other relevant parameter. Specifically, we consider problems where the data may be obtained at various resolutions; analyzing such data and constructing coupled models led to open research questions in various applications of data science. Numeric studies are reported for one of the data science techniques discussed here for illustration, namely, on approximate Bayesian computations.