Physics-driven Learning of the Steady Navier-Stokes Equations using Deep Convolutional Neural Networks

Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the physics-driven learning of complex flow fields with high resolutions. We propose the use of emph{Convolutional neural networks} (CNN) based U-net architectures to efficiently represent and reconstruct the input and output fields, respectively. By introducing Navier-Stokes equations and boundary conditions into loss functions, the physics-driven CNN is designed to predict corresponding steady flow fields directly. In particular, this prevents many of the difficulties associated with approaches employing fully connected neural networks. Several numerical experiments are conducted to investigate the behavior of the CNN approach, and the results indicate that a first-order accuracy has been achieved. Specifically for the case of a flow around a cylinder, different flow regimes can be learned and the adhered twin-vortices are predicted correctly. The numerical results also show that the training for multiple cases is accelerated significantly, especially for the difficult cases at low Reynolds numbers, and when limited reference solutions are used as supplementary learning targets.

Local and global integrability of Lie brackets

We survey recent results on the local and global integrability of a Lie algebroid, as well as the integrability of infinitesimal multiplicative geometric structures on it.

CelebHair: A New Large-Scale Dataset for Hairstyle Recommendation based on CelebA

In this paper, we present a new large-scale dataset for hairstyle recommendation, CelebHair, based on the celebrity facial attributes dataset, CelebA. Our dataset inherited the majority of facial images along with some beauty-related facial attributes from CelebA. Additionally, we employed facial landmark detection techniques to extract extra features such as nose length and pupillary distance, and deep convolutional neural networks for face shape and hairstyle classification. Empirical comparison has demonstrated the superiority of our dataset to other existing hairstyle-related datasets regarding variety, veracity, and volume. Analysis and experiments have been conducted on the dataset in order to evaluate its robustness and usability.

DatasetGAN: Efficient Labeled Data Factory with Minimal Human Effort

We introduce DatasetGAN: an automatic procedure to generate massive datasets of high-quality semantically segmented images requiring minimal human effort. Current deep networks are extremely data-hungry, benefiting from training on large-scale datasets, which are time consuming to annotate. Our method relies on the power of recent GANs to generate realistic images. We show how the GAN latent code can be decoded to produce a semantic segmentation of the image. Training the decoder only needs a few labeled examples to generalize to the rest of the latent space, resulting in an infinite annotated dataset generator! These generated datasets can then be used for training any computer vision architecture just as real datasets are. As only a few images need to be manually segmented, it becomes possible to annotate images in extreme detail and generate datasets with rich object and part segmentations. To showcase the power of our approach, we generated datasets for 7 image segmentation tasks which include pixel-level labels for 34 human face parts, and 32 car parts. Our approach outperforms all semi-supervised baselines significantly and is on par with fully supervised methods, which in some cases require as much as 100x more annotated data as our method.

Topological charge density waves at half-integer filling of a moire superlattice

At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and Hofstadter bands; in both cases, a large magnetic field is required to engineer the underlying flat band. The recent observation of quantum anomalous Hall effects (QAH) in narrow band moire systems has led to the theoretical prediction that such phases may be realized even at zero magnetic field. Here we report the experimental observation of insulators with Chern number $C=1$ in the zero magnetic field limit at $ u=3/2$ and $7/2$ filling of the moire superlattice unit cell in twisted monolayer-bilayer graphene (tMBG). Our observation of Chern insulators at half-integer values of $ u$ suggests spontaneous doubling of the superlattice unit cell, in addition to spin- and valley-ferromagnetism. This is confirmed by Hartree-Fock calculations, which find a topological charge density wave ground state at half filling of the underlying $C=2$ band, in which the Berry curvature is evenly partitioned between occupied and unoccupied states. We find the translation symmetry breaking order parameter is evenly distributed across the entire folded superlattice Brillouin zone, suggesting that the system is in the flat band, strongly correlated limit. Our findings show that the interplay of quantum geometry and Coulomb interactions in moire bands allows for topological phases at fractional superlattice filling that spontaneously break time-reversal symmetry, a prerequisite in pursuit of zero magnetic field phases harboring fractional statistics as elementary excitations or bound to lattice dislocations.

Laser-Assisted Metalorganic Chemical Vapor Deposition of GaN

Ammonia (NH3) is commonly used as group V precursor in gallium nitride (GaN) metalorganic chemical vapor deposition (MOCVD). The high background carbon (C) impurity in MOCVD GaN is related to the low pyrolysis efficiency of NH3, which represents one of the fundamental challenges hindering the development of high purity thick GaN for vertical high power device applications. This work uses a laser-assisted MOCVD (LA-MOCVD) growth technique to address the high-C issue in MOCVD GaN. Carbon dioxide (CO2) laser with wavelength of 9.219 um was utilized to facilitate NH3 decomposition via resonant vibrational excitation. The LA-MOCVD GaN growth rate (as high as 10 um/hr) shows a strong linear relationship with the trimethylgallium (TMGa) flow rate, indicating high effective V/III ratios and hence efficient NH3 decomposition. Pits-free surface morphology of LA-MOCVD GaN was demonstrated for films with growth rate as high as 8.5 um/hr. The background [C] in LA-MOCVD GaN films decreases monotonically as the laser power increases. A low [C] at 5.5E15 cm-3 was achieved in LA-MOCVD GaN film grown with the growth rate of 4 um/hr. Charge transport characterization of LA-MOCVD GaN films reveals high crystalline quality with room temperature mobility >1000 cm2/Vs. LA-MOCVD growth technique provides an enabling route to achieve high quality GaN epitaxy with low-C impurity and fast growth rate simultaneously. This technique can also be extended for epitaxy of other nitride-based semiconductors.

Adaptive Radar Detection and Classification Algorithms for Multiple Coherent Signals

In this paper, we address the problem of target detection in the presence of coherent (or fully correlated) signals, which can be due to multipath propagation effects or electronic attacks by smart jammers. To this end, we formulate the problem at hand as a multiple-hypothesis test that, besides the conventional radar alternative hypothesis, contains additional hypotheses accounting for the presence of an unknown number of interfering signals. In this context and leveraging the classification capabilities of the Model Order Selection rules, we devise penalized likelihood-ratio-based detection architectures that can establish, as a byproduct, which hypothesis is in force. Moreover, we propose a suboptimum procedure to estimate the angles of arrival of multiple coherent signals ensuring (at least for the considered parameters) almost the same performance as the exhaustive search. Finally, the performance assessment, conducted over simulated data and in comparison with conventional radar detectors, highlights that the proposed architectures can provide satisfactory performance in terms of probability of detection and correct classification.

A prognostic dynamic model applicable to infectious diseases providing easily visualized guides -- A case study of COVID-19 in the UK

A reasonable prediction of infectious diseases transmission process under different disease control strategies is an important reference point for policy makers. Here we established a dynamic transmission model via Python and realized comprehensive regulation of disease control measures. We classified government interventions into three categories and introduced three parameters as descriptions for the key points in disease control, these being intraregional growth rate, interregional communication rate, and detection rate of infectors. Our simulation predicts the infection by COVID-19 in the UK would be out of control in 73 days without any interventions; at the same time, herd immunity acquisition will begin from the epicentre. After we introduced government interventions, single intervention is effective in disease control but at huge expense while combined interventions would be more efficient, among which, enhancing detection number is crucial in control strategy of COVID-19. In addition, we calculated requirements for the most effective vaccination strategy based on infection number in real situation. Our model was programmed with iterative algorithms, and visualized via cellular automata, it can be applied to similar epidemics in other regions if the basic parameters are inputted, and is able to synthetically mimick the effect of multiple factors in infectious disease control.

Image GANs meet Differentiable Rendering for Inverse Graphics and Interpretable 3D Neural Rendering

Differentiable rendering has paved the way to training neural networks to perform inverse graphics tasks such as predicting 3D geometry from monocular photographs. To train high performing models, most of the current approaches rely on multi-view imagery which are not readily available in practice. Recent Generative Adversarial Networks (GANs) that synthesize images, in contrast, seem to acquire 3D knowledge implicitly during training: object viewpoints can be manipulated by simply manipulating the latent codes. However, these latent codes often lack further physical interpretation and thus GANs cannot easily be inverted to perform explicit 3D reasoning. In this paper, we aim to extract and disentangle 3D knowledge learned by generative models by utilizing differentiable renderers. Key to our approach is to exploit GANs as a multi-view data generator to train an inverse graphics network using an off-the-shelf differentiable renderer, and the trained inverse graphics network as a teacher to disentangle the GANs latent code into interpretable 3D properties. The entire architecture is trained iteratively using cycle consistency losses. We show that our approach significantly outperforms state-of-the-art inverse graphics networks trained on existing datasets, both quantitatively and via user studies. We further showcase the disentangled GAN as a controllable 3D neural renderer, complementing traditional graphics renderers.