This paper studies 3D dense shape correspondence, a key shape analysis application in computer vision and graphics. We introduce a novel hybrid geometric deep learning-based model that learns geometrically meaningful and discretization-independent features with a U-Net model as the primary node feature extraction module, followed by a successive spectral-based graph convolutional network. To create a diverse set of filters, we use anisotropic wavelet basis filters, being sensitive to both different directions and band-passes. This filter set overcomes the over-smoothing behavior of conventional graph neural networks. To further improve the model's performance, we add a function that perturbs the feature maps in the last layer ahead of fully connected layers, forcing the network to learn more discriminative features overall. The resulting correspondence maps show state-of-the-art performance on the benchmark datasets based on average geodesic errors and superior robustness to discretization in 3D meshes. Our approach provides new insights and practical solutions to the dense shape correspondence research.

Lean combustion is environment friendly with low NOx emissions and also provides better fuel efficiency in a combustion system. However, approaching towards lean combustion can make engines more susceptible to lean blowout. Lean blowout (LBO) is an undesirable phenomenon that can cause sudden flame extinction leading to sudden loss of power. During the design stage, it is quite challenging for the scientists to accurately determine the optimal operating limits to avoid sudden LBO occurrence. Therefore, it is crucial to develop accurate and computationally tractable frameworks for online LBO detection in low NOx emission engines. To the best of our knowledge, for the first time, we propose a deep learning approach to detect lean blowout in combustion systems. In this work, we utilize a laboratory-scale combustor to collect data for different protocols. We start far from LBO for each protocol and gradually move towards the LBO regime, capturing a quasi-static time series dataset at each condition. Using one of the protocols in our dataset as the reference protocol and with conditions annotated by domain experts, we find a transition state metric for our trained deep learning model to detect LBO in the other test protocols. We find that our proposed approach is more accurate and computationally faster than other baseline models to detect the transitions to LBO. Therefore, we recommend this method for real-time performance monitoring in lean combustion engines.

Automatic Machine Learning (Auto-ML) systems tackle the problem of automating the design of prediction models or pipelines for data science. In this paper, we present Lifelong Bayesian Optimization (LBO), an online, multitask Bayesian optimization (BO) algorithm designed to solve the problem of model selection for datasets arriving and evolving over time. To be suitable for Lifelong Bayesian Optimization, an algorithm needs to scale with the ever-increasing size of the dataset, and should be able to leverage past optimizations in learning the current best model. We cast the problem of model selection as a black-box function optimization problem. In LBO, we exploit the correlation between functions by using components of previously learned functions to speed up the learning process for newly arriving datasets. Experiments on real and synthetic data show that LBO outperforms standard BO algorithms applied repeatedly on the data.

Bayesian optimization and Lipschitz optimization have developed alternative techniques for optimizing black-box functions. They each exploit a different form of prior about the function. In this work, we explore strategies to combine these techniques for better global optimization. In particular, we propose ways to use the Lip-schitz continuity assumption within traditional BO algorithms, which we call Lips-chitz Bayesian optimization (LBO). This approach does not increase the asymptotic run-time and in some cases drastically improves the performance (while in the worst case the performance is similar). Indeed, in a particular setting, we prove that using the Lips-chitz information yields the same or a better bound on the regret compared to using Bayesian optimization on its own. Moreover, we propose a simple heuristics to estimate the Lipschitz constant, and prove that a growing estimate of the Lipschitz constant is in some sense "harmless". Our experiments on 15 datasets with 4 acquisition functions show that in the worst case LBO performs similar to the underlying BO method while in some cases it performs substantially better. Thompson sampling in particular typically saw drastic improvements (as the Lipschitz information corrected for its well-known "over-exploration" phenomenon) and its LBO variant often outperformed other acquisition functions.