Uncertainty quantification of two-phase flow in porous media via coupled-TgNN surrogate model

Uncertainty quantification (UQ) of subsurface two-phase flow usually requires numerous executions of forward simulations under varying conditions. In this work, a novel coupled theory-guided neural network (TgNN) based surrogate model is built to facilitate computation efficiency under the premise of satisfactory accuracy. The core notion of this proposed method is to bridge two separate blocks on top of an overall network. They underlie the TgNN model in a coupled form, which reflects the coupling nature of pressure and water saturation in the two-phase flow equation. The TgNN model not only relies on labeled data, but also incorporates underlying scientific theory and experiential rules (e.g., governing equations, stochastic parameter fields, boundary and initial conditions, well conditions, and expert knowledge) as additional components into the loss function. The performance of the TgNN-based surrogate model for two-phase flow problems is tested by different numbers of labeled data and collocation points, as well as the existence of data noise. The proposed TgNN-based surrogate model offers an effective way to solve the coupled nonlinear two-phase flow problem and demonstrates good accuracy and strong robustness when compared with the purely data-driven surrogate model. By combining the accurate TgNN-based surrogate model with the Monte Carlo method, UQ tasks can be performed at a minimum cost to evaluate statistical quantities. Since the heterogeneity of the random fields strongly impacts the results of the surrogate model, corresponding variance and correlation length are added to the input of the neural network to maintain its predictive capacity. The results show that the TgNN-based surrogate model achieves satisfactory accuracy, stability, and efficiency in UQ problems of subsurface two-phase flow.

ImGCL: Revisiting Graph Contrastive Learning on Imbalanced Node Classification

Graph contrastive learning (GCL) has attracted a surge of attention due to its superior performance for learning node/graph representations without labels. However, in practice, unlabeled nodes for the given graph usually follow an implicit imbalanced class distribution, where the majority of nodes belong to a small fraction of classes (a.k.a., head class) and the rest classes occupy only a few samples (a.k.a., tail classes). This highly imbalanced class distribution inevitably deteriorates the quality of learned node representations in GCL. Indeed, we empirically find that most state-of-the-art GCL methods exhibit poor performance on imbalanced node classification. Motivated by this observation, we propose a principled GCL framework on Imbalanced node classification (ImGCL), which automatically and adaptively balances the representation learned from GCL without knowing the labels. Our main inspiration is drawn from the recent progressively balanced sampling (PBS) method in the computer vision domain. We first introduce online clustering based PBS, which balances the training sets based on pseudo-labels obtained from learned representations. We then develop the node centrality based PBS method to better preserve the intrinsic structure of graphs, which highlight the important nodes of the given graph. Besides, we theoretically consolidate our method by proving that the classifier learned by balanced sampling without labels on an imbalanced dataset can converge to the optimal balanced classifier with a linear rate. Extensive experiments on multiple imbalanced graph datasets and imbalance settings verify the effectiveness of our proposed framework, which significantly improves the performance of the recent state-of-the-art GCL methods. Further experimental ablations and analysis show that the ImGCL framework remarkably improves the representations of nodes in tail classes.

Ridgeless Regression with Random Features

Recent theoretical studies illustrated that kernel ridgeless regression can guarantee good generalization ability without an explicit regularization. In this paper, we investigate the statistical properties of ridgeless regression with random features and stochastic gradient descent. We explore the effect of factors in the stochastic gradient and random features, respectively. Specifically, random features error exhibits the double-descent curve. Motivated by the theoretical findings, we propose a tunable kernel algorithm that optimizes the spectral density of kernel during training. Our work bridges the interpolation theory and practical algorithm.

Sharper Utility Bounds for Differentially Private Models

In this paper, by introducing Generalized Bernstein condition, we propose the first $\mathcal{O}\big(\frac{\sqrt{p}}{n\epsilon}\big)$ high probability excess population risk bound for differentially private algorithms under the assumptions $G$-Lipschitz, $L$-smooth, and Polyak-{\L}ojasiewicz condition, based on gradient perturbation method. If we replace the properties $G$-Lipschitz and $L$-smooth by $\alpha$-H{\"o}lder smoothness (which can be used in non-smooth setting), the high probability bound comes to $\mathcal{O}\big(n^{-\frac{\alpha}{1+2\alpha}}\big)$ w.r.t $n$, which cannot achieve $\mathcal{O}\left(1/n\right)$ when $\alpha\in(0,1]$. To solve this problem, we propose a variant of gradient perturbation method, \textbf{max$\{1,g\}$-Normalized Gradient Perturbation} (m-NGP). We further show that by normalization, the high probability excess population risk bound under assumptions $\alpha$-H{\"o}lder smooth and Polyak-{\L}ojasiewicz condition can achieve $\mathcal{O}\big(\frac{\sqrt{p}}{n\epsilon}\big)$, which is the first $\mathcal{O}\left(1/n\right)$ high probability excess population risk bound w.r.t $n$ for differentially private algorithms under non-smooth conditions. Moreover, we evaluate the performance of the new proposed algorithm m-NGP, the experimental results show that m-NGP improves the performance of the differentially private model over real datasets. It demonstrates that m-NGP improves the utility bound and the accuracy of the DP model on real datasets simultaneously.

Stability and Generalization of Differentially Private Minimax Problems

In the field of machine learning, many problems can be formulated as the minimax problem, including reinforcement learning, generative adversarial networks, to just name a few. So the minimax problem has attracted a huge amount of attentions from researchers in recent decades. However, there is relatively little work on studying the privacy of the general minimax paradigm. In this paper, we focus on the privacy of the general minimax setting, combining differential privacy together with minimax optimization paradigm. Besides, via algorithmic stability theory, we theoretically analyze the high probability generalization performance of the differentially private minimax algorithm under the strongly-convex-strongly-concave condition. To the best of our knowledge, this is the first time to analyze the generalization performance of general minimax paradigm, taking differential privacy into account.

Model-free Reinforcement Learning for Content Caching at the Wireless Edge via Restless Bandits

An explosive growth in the number of on-demand content requests has imposed significant pressure on current wireless network infrastructure. To enhance the perceived user experience, and support latency-sensitive applications, edge computing has emerged as a promising computing paradigm. The performance of a wireless edge depends on contents that are cached. In this paper, we consider the problem of content caching at the wireless edge with unreliable channels to minimize average content request latency. We formulate this problem as a restless bandit problem, which is provably hard to solve. We begin by investigating a discounted counterpart, and prove that it admits an optimal policy of the threshold-type. We then show that the result also holds for the average latency problem. Using these structural results, we establish the indexability of the problem, and employ Whittle index policy to minimize average latency. Since system parameters such as content request rate are often unknown, we further develop a model-free reinforcement learning algorithm dubbed Q-Whittle learning that relies on our index policy. We also derive a bound on its finite-time convergence rate. Simulation results using real traces demonstrate that our proposed algorithms yield excellent empirical performance.

ASFD: Automatic and Scalable Face Detector

Along with current multi-scale based detectors, Feature Aggregation and Enhancement (FAE) modules have shown superior performance gains for cutting-edge object detection. However, these hand-crafted FAE modules show inconsistent improvements on face detection, which is mainly due to the significant distribution difference between its training and applying corpus, COCO vs. WIDER Face. To tackle this problem, we essentially analyse the effect of data distribution, and consequently propose to search an effective FAE architecture, termed AutoFAE by a differentiable architecture search, which outperforms all existing FAE modules in face detection with a considerable margin. Upon the found AutoFAE and existing backbones, a supernet is further built and trained, which automatically obtains a family of detectors under the different complexity constraints. Extensive experiments conducted on popular benchmarks, WIDER Face and FDDB, demonstrate the state-of-the-art performance-efficiency trade-off for the proposed automatic and scalable face detector (ASFD) family. In particular, our strong ASFD-D6 outperforms the best competitor with AP 96.7/96.2/92.1 on WIDER Face test, and the lightweight ASFD-D0 costs about 3.1 ms, more than 320 FPS, on the V100 GPU with VGA-resolution images.

Machine learning prediction for mean motion resonance behaviour -- The planar case

Most recently, machine learning has been used to study the dynamics of integrable Hamiltonian systems and the chaotic 3-body problem. In this work, we consider an intermediate case of regular motion in a non-integrable system: the behaviour of objects in the 2:3 mean motion resonance with Neptune. We show that, given initial data from a short 6250 yr numerical integration, the best-trained artificial neural network (ANN) can predict the trajectories of the 2:3 resonators over the subsequent 18750 yr evolution, covering a full libration cycle over the combined time period. By comparing our ANN's prediction of the resonant angle to the outcome of numerical integrations, the former can predict the resonant angle with an accuracy as small as of a few degrees only, while it has the advantage of considerably saving computational time. More specifically, the trained ANN can effectively measure the resonant amplitudes of the 2:3 resonators, and thus provides a fast approach that can identify the resonant candidates. This may be helpful in classifying a huge population of KBOs to be discovered in future surveys.

SCSNet: An Efficient Paradigm for Learning Simultaneously Image Colorization and Super-Resolution

In the practical application of restoring low-resolution gray-scale images, we generally need to run three separate processes of image colorization, super-resolution, and dows-sampling operation for the target device. However, this pipeline is redundant and inefficient for the independent processes, and some inner features could have been shared. Therefore, we present an efficient paradigm to perform {S}imultaneously Image {C}olorization and {S}uper-resolution (SCS) and propose an end-to-end SCSNet to achieve this goal. The proposed method consists of two parts: colorization branch for learning color information that employs the proposed plug-and-play \emph{Pyramid Valve Cross Attention} (PVCAttn) module to aggregate feature maps between source and reference images; and super-resolution branch for integrating color and texture information to predict target images, which uses the designed \emph{Continuous Pixel Mapping} (CPM) module to predict high-resolution images at continuous magnification. Furthermore, our SCSNet supports both automatic and referential modes that is more flexible for practical application. Abundant experiments demonstrate the superiority of our method for generating authentic images over state-of-the-art methods, e.g., averagely decreasing FID by 1.8$\downarrow$ and 5.1 $\downarrow$ compared with current best scores for automatic and referential modes, respectively, while owning fewer parameters (more than $\times$2$\downarrow$) and faster running speed (more than $\times$3$\uparrow$).

DeepScalper: A Risk-Aware Deep Reinforcement Learning Framework for Intraday Trading with Micro-level Market Embedding

Reinforcement learning (RL) techniques have shown great success in quantitative investment tasks, such as portfolio management and algorithmic trading. Especially, intraday trading is one of the most profitable and risky tasks because of the intraday behaviors of the financial market that reflect billions of rapidly fluctuating values. However, it is hard to apply existing RL methods to intraday trading due to the following three limitations: 1) overlooking micro-level market information (e.g., limit order book); 2) only focusing on local price fluctuation and failing to capture the overall trend of the whole trading day; 3) neglecting the impact of market risk. To tackle these limitations, we propose DeepScalper, a deep reinforcement learning framework for intraday trading. Specifically, we adopt an encoder-decoder architecture to learn robust market embedding incorporating both macro-level and micro-level market information. Moreover, a novel hindsight reward function is designed to provide the agent a long-term horizon for capturing the overall price trend. In addition, we propose a risk-aware auxiliary task by predicting future volatility, which helps the agent take market risk into consideration while maximizing profit. Finally, extensive experiments on two stock index futures and four treasury bond futures demonstrate that DeepScalper achieves significant improvement against many state-of-the-art approaches.