Gokul Radhakrishnan, Rahul Sundar, Nishant Parashar et al.
The sparse and spatio-temporally discontinuous nature of precipitation data presents significant challenges for simulation and statistical processing for bias correction and downscaling. These include incorrect representation of intermittency and extreme values (critical for hydrology applications), Gibbs phenomenon upon regridding, and lack of fine scales details. To address these challenges, a common approach is to transform the precipitation variable nonlinearly into one that is more malleable. In this work, we explore how deep learning can be used to generate a smooth, spatio-temporally continuous variable as a proxy for simulation of precipitation data. We develop a normally distributed field called pseudo-precipitation (PP) as an alternative for simulating precipitation. The practical applicability of this variable is investigated by applying it for downscaling precipitation from \(1\degree\) (\(\sim\) 100 km) to \(0.25\degree\) (\(\sim\) 25 km).
An unmanned autonomous vehicle (UAV) is sent on a mission to explore and reconstruct an unknown environment from a series of measurements collected by Bayesian optimization. The success of the mission is judged by the UAV's ability to faithfully reconstruct any anomalous features present in the environment, with emphasis on the extremes (e.g., extreme topographic depressions or abnormal chemical concentrations). We show that the criteria commonly used for determining which locations the UAV should visit are ill-suited for this task. We introduce a number of novel criteria that guide the UAV towards regions of strong anomalies by leveraging previously collected information in a mathematically elegant and computationally tractable manner. We demonstrate superiority of the proposed approach in several applications, including reconstruction of seafloor topography from real-world bathymetry data, as well as tracking of dynamic anomalies. A particularly attractive property of our approach is its ability to overcome adversarial conditions, that is, situations in which prior beliefs about the locations of the extremes are imprecise or erroneous.
In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy estimations. We approach the problem from the perspective of importance-sampling theory, and advocate the use of the likelihood ratio to guide the search algorithm towards regions of the input space where the objective function to be minimized assumes abnormally small values. The likelihood ratio acts as a sampling weight and can be computed at each iteration without severely deteriorating the overall efficiency of the algorithm. In particular, it can be approximated in a way that makes the approach tractable in high dimensions. The "likelihood-weighted" acquisition functions introduced in this work are found to outperform their unweighted counterparts in a number of applications.
For a large class of dynamical systems, the optimally time-dependent (OTD) modes, a set of deformable orthonormal tangent vectors that track directions of instabilities along any trajectory, are known to depend "pointwise" on the state of the system on the attractor, and not on the history of the trajectory. We leverage the power of neural networks to learn this "pointwise" mapping from phase space to OTD space directly from data. The result of the learning process is a cartography of directions associated with strongest instabilities in phase space. Implications for data-driven prediction and control of dynamical instabilities are discussed.