This paper proposes and analyzes an ultra-weak local discontinuous Galerkin scheme for one-dimensional nonlinear biharmonic Schr{o}dinger equations. We develop the paradigm of the local discontinuous Galerkin method by introducing the second-order sp
atial derivative as an auxiliary variable instead of the conventional first-order derivative. The proposed semi-discrete scheme preserves a few physically relevant properties such as the conservation of mass and the conservation of Hamiltonian accompanied by its stability for the targeted nonlinear biharmonic Schr{o}dinger equations. We also derive optimal $L^2$-error estimates of the scheme that measure both the solution and the auxiliary variable. Several numerical studies demonstrate and support our theoretical findings.
In this paper, an energy-based discontinuous Galerkin method for dynamic Euler-Bernoulli beam equations is developed. The resulting method is energy-dissipating or energy-conserving depending on the simple, mesh-independent choice of numerical fluxes
. By introducing a velocity field, the original problem is transformed into a first-order in time system. In our formulation, the discontinuous Galerkin approximations for the original displacement field and the auxiliary velocity field are not restricted to be in the same space. In particular, a given accuracy can be achieved with the fewest degrees of freedom when the degree for the approximation space of the velocity field is two orders lower than the degree of approximation space for the displacement field. In addition, we establish the error estimates in an energy norm and demonstrate the corresponding optimal convergence in numerical experiments.
Variable selection on the large-scale networks has been extensively studied in the literature. While most of the existing methods are limited to the local functionals especially the graph edges, this paper focuses on selecting the discrete hub struct
ures of the networks. Specifically, we propose an inferential method, called StarTrek filter, to select the hub nodes with degrees larger than a certain thresholding level in the high dimensional graphical models and control the false discovery rate (FDR). Discovering hub nodes in the networks is challenging: there is no straightforward statistic for testing the degree of a node due to the combinatorial structures; complicated dependence in the multiple testing problem is hard to characterize and control. In methodology, the StarTrek filter overcomes this by constructing p-values based on the maximum test statistics via the Gaussian multiplier bootstrap. In theory, we show that the StarTrek filter can control the FDR by providing accurate bounds on the approximation errors of the quantile estimation and addressing the dependence structures among the maximal statistics. To this end, we establish novel Cramer-type comparison bounds for the high dimensional Gaussian random vectors. Comparing to the Gaussian comparison bound via the Kolmogorov distance established by citet{chernozhukov2014anti}, our Cramer-type comparison bounds establish the relative difference between the distribution functions of two high dimensional Gaussian random vectors. We illustrate the validity of the StarTrek filter in a series of numerical experiments and apply it to the genotype-tissue expression dataset to discover central regulator genes.
Learning RAW-to-sRGB mapping has drawn increasing attention in recent years, wherein an input raw image is trained to imitate the target sRGB image captured by another camera. However, the severe color inconsistency makes it very challenging to gener
ate well-aligned training pairs of input raw and target sRGB images. While learning with inaccurately aligned supervision is prone to causing pixel shift and producing blurry results. In this paper, we circumvent such issue by presenting a joint learning model for image alignment and RAW-to-sRGB mapping. To diminish the effect of color inconsistency in image alignment, we introduce to use a global color mapping (GCM) module to generate an initial sRGB image given the input raw image, which can keep the spatial location of the pixels unchanged, and the target sRGB image is utilized to guide GCM for converting the color towards it. Then a pre-trained optical flow estimation network (e.g., PWC-Net) is deployed to warp the target sRGB image to align with the GCM output. To alleviate the effect of inaccurately aligned supervision, the warped target sRGB image is leveraged to learn RAW-to-sRGB mapping. When training is done, the GCM module and optical flow network can be detached, thereby bringing no extra computation cost for inference. Experiments show that our method performs favorably against state-of-the-arts on ZRR and SR-RAW datasets. With our joint learning model, a light-weight backbone can achieve better quantitative and qualitative performance on ZRR dataset. Codes are available at https://github.com/cszhilu1998/RAW-to-sRGB.
In this paper, we present an Efficient Planning System for automated vehicles In highLy interactive envirONments (EPSILON). EPSILON is an efficient interaction-aware planning system for automated driving, and is extensively validated in both simulati
on and real-world dense city traffic. It follows a hierarchical structure with an interactive behavior planning layer and an optimization-based motion planning layer. The behavior planning is formulated from a partially observable Markov decision process (POMDP), but is much more efficient than naively applying a POMDP to the decision-making problem. The key to efficiency is guided branching in both the action space and observation space, which decomposes the original problem into a limited number of closed-loop policy evaluations. Moreover, we introduce a new driver model with a safety mechanism to overcome the risk induced by the potential imperfectness of prior knowledge. For motion planning, we employ a spatio-temporal semantic corridor (SSC) to model the constraints posed by complex driving environments in a unified way. Based on the SSC, a safe and smooth trajectory is optimized, complying with the decision provided by the behavior planner. We validate our planning system in both simulations and real-world dense traffic, and the experimental results show that our EPSILON achieves human-like driving behaviors in highly interactive traffic flow smoothly and safely without being over-conservative compared to the existing planning methods.
We introduce Pathfinder, a variational method for approximately sampling from differentiable log densities. Starting from a random initialization, Pathfinder locates normal approximations to the target density along a quasi-Newton optimization path,
with local covariance estimated using the inverse Hessian estimates produced by the optimizer. Pathfinder returns draws from the approximation with the lowest estimated Kullback-Leibler (KL) divergence to the true posterior. We evaluate Pathfinder on a wide range of posterior distributions, demonstrating that its approximate draws are better than those from automatic differentiation variational inference (ADVI) and comparable to those produced by short chains of dynamic Hamiltonian Monte Carlo (HMC), as measured by 1-Wasserstein distance. Compared to ADVI and short dynamic HMC runs, Pathfinder requires one to two orders of magnitude fewer log density and gradient evaluations, with greater reductions for more challenging posteriors. Importance resampling over multiple runs of Pathfinder improves the diversity of approximate draws, reducing 1-Wasserstein distance further and providing a measure of robustness to optimization failures on plateaus, saddle points, or in minor modes. The Monte Carlo KL-divergence estimates are embarrassingly parallelizable in the core Pathfinder algorithm, as are multiple runs in the resampling version, further increasing Pathfinders speed advantage with multiple cores.
Architecture performance predictors have been widely used in neural architecture search (NAS). Although they are shown to be simple and effective, the optimization objectives in previous arts (e.g., precise accuracy estimation or perfect ranking of a
ll architectures in the space) did not capture the ranking nature of NAS. In addition, a large number of ground-truth architecture-accuracy pairs are usually required to build a reliable predictor, making the process too computationally expensive. To overcome these, in this paper, we look at NAS from a novel point of view and introduce Learning to Rank (LTR) methods to select the best (ace) architectures from a space. Specifically, we propose to use Normalized Discounted Cumulative Gain (NDCG) as the target metric and LambdaRank as the training algorithm. We also propose to leverage weak supervision from weight sharing by pretraining architecture representation on weak labels obtained from the super-net and then finetuning the ranking model using a small number of architectures trained from scratch. Extensive experiments on NAS benchmarks and large-scale search spaces demonstrate that our approach outperforms SOTA with a significantly reduced search cost.
Complex design problems are common in the scientific and industrial fields. In practice, objective functions or constraints of these problems often do not have explicit formulas, and can be estimated only at a set of sampling points through experimen
ts or simulations. Such optimization problems are especially challenging when design parameters are high-dimensional due to the curse of dimensionality. In this work, we propose a data-informed deep optimization (DiDo) approach as follows: first, we use a deep neural network (DNN) classifier to learn the feasible region; second, we sample feasible points based on the DNN classifier for fitting of the objective function; finally, we find optimal points of the DNN-surrogate optimization problem by gradient descent. To demonstrate the effectiveness of our DiDo approach, we consider a practical design case in industry, in which our approach yields good solutions using limited size of training data. We further use a 100-dimension toy example to show the effectiveness of our model for higher dimensional problems. Our results indicate that the DiDo approach empowered by DNN is flexible and promising for solving general high-dimensional design problems in practice.
Automatic surgical instruction generation is a prerequisite towards intra-operative context-aware surgical assistance. However, generating instructions from surgical scenes is challenging, as it requires jointly understanding the surgical activity of
current view and modelling relationships between visual information and textual description. Inspired by the neural machine translation and imaging captioning tasks in open domain, we introduce a transformer-backboned encoder-decoder network with self-critical reinforcement learning to generate instructions from surgical images. We evaluate the effectiveness of our method on DAISI dataset, which includes 290 procedures from various medical disciplines. Our approach outperforms the existing baseline over all caption evaluation metrics. The results demonstrate the benefits of the encoder-decoder structure backboned by transformer in handling multimodal context.
Automatic segmentation of hepatocellular carcinoma (HCC) in Digital Subtraction Angiography (DSA) videos can assist radiologists in efficient diagnosis of HCC and accurate evaluation of tumors in clinical practice. Few studies have investigated HCC s
egmentation from DSA videos. It shows great challenging due to motion artifacts in filming, ambiguous boundaries of tumor regions and high similarity in imaging to other anatomical tissues. In this paper, we raise the problem of HCC segmentation in DSA videos, and build our own DSA dataset. We also propose a novel segmentation network called DSA-LTDNet, including a segmentation sub-network, a temporal difference learning (TDL) module and a liver region segmentation (LRS) sub-network for providing additional guidance. DSA-LTDNet is preferable for learning the latent motion information from DSA videos proactively and boosting segmentation performance. All of experiments are conducted on our self-collected dataset. Experimental results show that DSA-LTDNet increases the DICE score by nearly 4% compared to the U-Net baseline.
