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This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most $n$ supports and its applications in various AI tasks such as color transfer or domain adaptation. There is hence the need for fast approximations of POT with increasingly large problem sizes in arising applications. We first theoretically and experimentally investigate the infeasibility of the state-of-the-art Sinkhorn algorithm for POT due to its incompatible rounding procedure, which consequently degrades its qualitative performance in real world applications like point-cloud registration. To this end, we propose a novel rounding algorithm for POT, and then provide a feasible Sinkhorn procedure with a revised computation complexity of $\mathcal{\widetilde O}(n^2/\varepsilon^4)$. Our rounding algorithm also permits the development of two first-order methods to approximate the POT problem. The first algorithm, Adaptive Primal-Dual Accelerated Gradient Descent (APDAGD), finds an $\varepsilon$-approximate solution to the POT problem in $\mathcal{\widetilde O}(n^{2.5}/\varepsilon)$, which is better in $\varepsilon$ than revised Sinkhorn. The second method, Dual Extrapolation, achieves the computation complexity of $\mathcal{\widetilde O}(n^2/\varepsilon)$, thereby being the best in the literature. We further demonstrate the flexibility of POT compared to standard OT as well as the practicality of our algorithms on real applications where two marginal distributions are unbalanced., Comment: Accepted to AAAI 2024

Shape optimization with respect to eigenvalues of a cavity plays an important role in the design of new resonators or in the optimization of existing ones. In our paper, we propose a gradient-based optimization scheme, which we enhance with closed-form shape derivatives of the system matrices. Based on these, we can compute accurate derivatives of eigenvalues, eigenmodes and the cost function with respect to the geometry, which significantly reduces the computational effort of the optimizer. We demonstrate our work by applying it to the 9-cell TESLA cavity, for which we tune the design parameters of the computational model to match the design criteria for devices in realistic use cases. Since eigenvalues may cross during the shape optimization of a cavity, we propose a new algorithm based on an eigenvalue matching procedure, to ensure the optimization of the desired mode in order to also enable successful matching along large shape variations.

In this paper, we present a novel deep method to reconstruct a point cloud of an object from a single still image. Prior arts in the field struggle to reconstruct an accurate and scalable 3D model due to either the inefficient and expensive 3D representations, the dependency between the output and number of model parameters or the lack of a suitable computing operation. We propose to overcome these by deforming a random point cloud to the object shape through two steps: feature blending and deformation. In the first step, the global and point-specific shape features extracted from a 2D object image are blended with the encoded feature of a randomly generated point cloud, and then this mixture is sent to the deformation step to produce the final representative point set of the object. In the deformation process, we introduce a new layer termed as GraphX that considers the inter-relationship between points like common graph convolutions but operates on unordered sets. Moreover, with a simple trick, the proposed model can generate an arbitrary-sized point cloud, which is the first deep method to do so. Extensive experiments verify that we outperform existing models and halve the state-of-the-art distance score in single image 3D reconstruction., Comment: In Proceedings of the IEEE International Conference on Computer Vision 2019. Fixed minor details and added some updates. Project page: https://git.io/JeovA

Controlling the interconnection of neighboring seeds (nanoflakes) to full coverage of the textured substrate is the main challenge for the large-scale conformal growth of atomic-thick transition metal dichalcogenides by chemical vapor deposition. Herein, we report on a controllable method for the conformal growth of monolayer MoS2 on not only planar but also micro- and nano-rugged SiO2/Si substrates via metal-organic chemical vapor deposition. The continuity of monolayer MoS2 on the rugged surface is evidenced by scanning electron microscopy, cross-section high-resolution transmission electron microscopy, photoluminescence (PL) mapping, and Raman mapping. Interestingly, the photo-responsivity (~254.5 mA/W) of as-grown MoS2 on the nano-rugged substrate exhibits 59 times higher than that of the planar sample (4.3 mA/W) under a small applied bias of 0.1 V. This value is record high when compared with all previous MoS2-based photocurrent generation under low or zero bias. Such a large enhancement in the photo-responsivity arises from a large active area for light-matter interaction and local strain for PL quenching, where the latter effect is the key factor and unique in the conformally grown monolayer on the nano-rugged surface. The result is a step toward the batch fabrication of modern atomic-thick optoelectronic devices., Comment: 25 pages, 5 figures

We propose a generative framework which takes on the video frame interpolation problem. Our framework, which we call Deep Locally Linear Embedding (DeepLLE), is powered by a deep convolutional neural network (CNN) while it can be used instantly like conventional models. DeepLLE fits an auto-encoding CNN to a set of several consecutive frames and embeds a linearity constraint on the latent codes so that new frames can be generated by interpolating new latent codes. Different from the current deep learning paradigm which requires training on large datasets, DeepLLE works in a plug-and-play and unsupervised manner, and is able to generate an arbitrary number of frames. Thorough experiments demonstrate that without bells and whistles, our method is highly competitive among current state-of-the-art models., Comment: 16 pages