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The ensemble data assimilation of computational fluid dynamics simulations based on the lattice Boltzmann method (LBM) and the local ensemble transform Kalman filter (LETKF) is implemented and optimized on a GPU supercomputer based on NVIDIA A100 GPUs. To connect the LBM and LETKF parts, data transpose communication is optimized by overlapping computation, file I/O, and communication based on data dependency in each LETKF kernel. In two dimensional forced isotropic turbulence simulations with the ensemble size of $M=64$ and the number of grid points of $N_x=128^2$, the optimized implementation achieved $\times3.80$ speedup from the naive implementation, in which the LETKF part is not parallelized. The main computing kernel of the local problem is the eigenvalue decomposition (EVD) of $M\times M$ real symmetric dense matrices, which is computed by a newly developed batched EVD in $\verb|EigenG|$. The batched EVD in $\verb|EigenG|$ outperforms that in $\verb|cuSOLVER|$, and $\times65.3$ speedup was achieved.

In this letter, we propose a model parameter identification method via a hyperparameter optimization scheme (MI-HPO). Our method adopts an efficient explore-exploit strategy to identify the parameters of dynamic models in a data-driven optimization manner. We utilize our method for model parameter identification of the AV-21, a full-scaled autonomous race vehicle. We then incorporate the optimized parameters for the design of model-based planning and control systems of our platform. In experiments, MI-HPO exhibits more than 13 times faster convergence than traditional parameter identification methods. Furthermore, the parametric models learned via MI-HPO demonstrate good fitness to the given datasets and show generalization ability in unseen dynamic scenarios. We further conduct extensive field tests to validate our model-based system, demonstrating stable obstacle avoidance and high-speed driving up to 217 km/h at the Indianapolis Motor Speedway and Las Vegas Motor Speedway. The source code for our work and videos of the tests are available at //github.com/hynkis/MI-HPO.

We investigate to what extent it is possible to solve linear inverse problems with $ReLu$ networks. Due to the scaling invariance arising from the linearity, an optimal reconstruction function $f$ for such a problem is positive homogeneous, i.e., satisfies $f(\lambda x) = \lambda f(x)$ for all non-negative $\lambda$. In a $ReLu$ network, this condition translates to considering networks without bias terms. We first consider recovery of sparse vectors from few linear measurements. We prove that $ReLu$- networks with only one hidden layer cannot even recover $1$-sparse vectors, not even approximately, and regardless of the width of the network. However, with two hidden layers, approximate recovery with arbitrary precision and arbitrary sparsity level $s$ is possible in a stable way. We then extend our results to a wider class of recovery problems including low-rank matrix recovery and phase retrieval. Furthermore, we also consider the approximation of general positive homogeneous functions with neural networks. Extending previous work, we establish new results explaining under which conditions such functions can be approximated with neural networks. Our results also shed some light on the seeming contradiction between previous works showing that neural networks for inverse problems typically have very large Lipschitz constants, but still perform very well also for adversarial noise. Namely, the error bounds in our expressivity results include a combination of a small constant term and a term that is linear in the noise level, indicating that robustness issues may occur only for very small noise levels.

The problem of bandit with graph feedback generalizes both the multi-armed bandit (MAB) problem and the learning with expert advice problem by encoding in a directed graph how the loss vector can be observed in each round of the game. The mini-max regret is closely related to the structure of the feedback graph and their connection is far from being fully understood. We propose a new algorithmic framework for the problem based on a partition of the feedback graph. Our analysis reveals the interplay between various parts of the graph by decomposing the regret to the sum of the regret caused by small parts and the regret caused by their interaction. As a result, our algorithm can be viewed as an interpolation and generalization of the optimal algorithms for MAB and learning with expert advice. Our framework unifies previous algorithms for both strongly observable graphs and weakly observable graphs, resulting in improved and optimal regret bounds on a wide range of graph families including graphs of bounded degree and strongly observable graphs with a few corrupted arms.

Matching has been widely used to mimic a randomized experiment with observational data. Ideally, treated subjects are exactly matched with controls for the covariates, and randomization-based estimation can then be conducted as in a randomized experiment (assuming no unobserved covariates). However, when there exists continuous covariates or many covariates, matching typically should be inexact. Previous studies have routinely ignored inexact matching in the downstream randomization-based estimation as long as some covariate balance criteria are satisfied, which can cause severe estimation bias. Built on the covariate-adaptive randomization inference framework, in this research note, we propose two new classes of bias-corrected randomization-based estimators to reduce estimation bias due to inexact matching: the bias-corrected maximum $p$-value estimator for the constant treatment effect and the bias-corrected difference-in-means estimator for the average treatment effect. Our simulation results show that the proposed bias-corrected estimators can effectively reduce estimation bias due to inexact matching.

The diffusion model is capable of generating high-quality data through a probabilistic approach. However, it suffers from the drawback of slow generation speed due to the requirement of a large number of time steps. To address this limitation, recent models such as denoising diffusion implicit models (DDIM) focus on generating samples without directly modeling the probability distribution, while models like denoising diffusion generative adversarial networks (GAN) combine diffusion processes with GANs. In the field of speech synthesis, a recent diffusion speech synthesis model called DiffGAN-TTS, utilizing the structure of GANs, has been introduced and demonstrates superior performance in both speech quality and generation speed. In this paper, to further enhance the performance of DiffGAN-TTS, we propose a speech synthesis model with two discriminators: a diffusion discriminator for learning the distribution of the reverse process and a spectrogram discriminator for learning the distribution of the generated data. Objective metrics such as structural similarity index measure (SSIM), mel-cepstral distortion (MCD), F0 root mean squared error (F0 RMSE), short-time objective intelligibility (STOI), perceptual evaluation of speech quality (PESQ), as well as subjective metrics like mean opinion score (MOS), are used to evaluate the performance of the proposed model. The evaluation results show that the proposed model outperforms recent state-of-the-art models such as FastSpeech2 and DiffGAN-TTS in various metrics. Our implementation and audio samples are located on GitHub.

We introduce Compartmentalized Diffusion Models (CDM), a method to train different diffusion models (or prompts) on distinct data sources and arbitrarily compose them at inference time. The individual models can be trained in isolation, at different times, and on different distributions and domains and can be later composed to achieve performance comparable to a paragon model trained on all data simultaneously. Furthermore, each model only contains information about the subset of the data it was exposed to during training, enabling several forms of training data protection. In particular, CDMs are the first method to enable both selective forgetting and continual learning for large-scale diffusion models, as well as allowing serving customized models based on the user's access rights. CDMs also allow determining the importance of a subset of the data in generating particular samples.

In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.

In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax