Minghua Chen

Minghua Chen, Weihua Deng, Yujiang Wu

In this paper, we discuss the time-space Caputo-Riesz fractional diffusion equation with variable coefficients on a finite domain. The finite difference schemes for this equation are provided. We theoretically prove and numerically verify that the implicit finite difference scheme is unconditionally stable (the explicit scheme is conditionally stable with the stability condition $\frac{τ^γ}{(Δx)^α}+\frac{τ^γ}{(Δy)^β} <C$) and 2nd order convergent in space direction, and $(2-γ)$-th order convergent in time direction, where $γ\in(0,1]$.

Jinlong Tu, Lian Lu, Minghua Chen et al.

The critical need for clean and economical sources of energy is transforming data centers that are primarily energy consumers to also energy producers. We focus on minimizing the operating costs of next-generation data centers that can jointly optimize the energy supply from on-site generators and the power grid, and the energy demand from servers as well as power conditioning and cooling systems. We formulate the cost minimization problem and present an offline optimal algorithm. For "on-grid" data centers that use only the grid, we devise a deterministic online algorithm that achieves the best possible competitive ratio of $2-α_{s}$, where $α_{s}$ is a normalized look-ahead window size. For "hybrid" data centers that have on-site power generation in addition to the grid, we develop an online algorithm that achieves a competitive ratio of at most \textmd{\normalsize {\small $\frac{P_{\max} (2-α_{s})}{c_{o}+c_{m}/L} [1+2\frac{P_{\max}-c_{o}}{P_{\max}(1+α_{g})}]$}}, where $α_{s}$ and $α_{g}$ are normalized look-ahead window sizes, $P_{\max}$ is the maximum grid power price, and $L$, $c_{o}$, and $c_{m}$ are parameters of an on-site generator. Using extensive workload traces from Akamai with the corresponding grid power prices, we simulate our offline and online algorithms in a realistic setting. Our offline (resp., online) algorithm achieves a cost reduction of 25.8% (resp., 20.7%) for a hybrid data center and 12.3% (resp., 7.3%) for an on-grid data center. The cost reductions are quite significant and make a strong case for a joint optimization of energy supply and energy demand in a data center. A hybrid data center provides about 13% additional cost reduction over an on-grid data center representing the additional cost benefits that on-site power generation provides over using the grid alone.

Xiang Pan, Wanjun Huang, Minghua Chen et al.

The existence of multiple load-solution mappings of non-convex AC-OPF problems poses a fundamental challenge to deep neural network (DNN) schemes. As the training dataset may contain a mixture of data points corresponding to different load-solution mappings, the DNN can fail to learn a legitimate mapping and generate inferior solutions. We propose DeepOPF-AL as an augmented-learning approach to tackle this issue. The idea is to train a DNN to learn a unique mapping from an augmented input, i.e., (load, initial point), to the solution generated by an iterative OPF solver with the load and initial point as intake. We then apply the learned augmented mapping to solve AC-OPF problems much faster than conventional solvers. Simulation results over IEEE test cases show that DeepOPF-AL achieves noticeably better optimality and similar feasibility and speedup performance, as compared to a recent DNN scheme, with the same DNN size yet elevated training complexity.

Minghua Chen, Yantao Wang, Xiao Cheng et al.

We propose a locally one dimensional (LOD) finite difference method for multidimensional Riesz fractional diffusion equation with variable coefficients on a finite domain. The numerical method is second-order convergent in both space and time directions, and its unconditional stability is strictly proved. Comparing with the popular first-order finite difference method for fractional operator, the form of obtained matrix algebraic equation is changed from $(I-A)u^{k+1}=u^k+b^{k+1}$ to $(I-{\widetilde A})u^{k+1}=(I+{\widetilde B})u^k+{\tilde b}^{k+1/2}$; the three matrices $A$, ${\widetilde A}$ and ${\widetilde B}$ are all Toeplitz-like, i.e., they have completely same structure and the computational count for matrix vector multiplication is $\mathcal{O}(N {log} N)$; and the computational costs for solving the two matrix algebraic equations are almost the same. The LOD-multigrid method is used to solve the resulting matrix algebraic equation, and the computational count is $\mathcal{O}(N {log} N)$ and the required storage is $\mathcal{O}(N)$, where $N$ is the number of grid points. Finally, the extensive numerical experiments are performed to show the powerfulness of the second-order scheme and the LOD-multigrid method.

Weihua Deng, Minghua Chen

This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional diffusion equation. The second order finite difference scheme is used to discretize the space fractional derivative and the Crank-Nicolson procedure to the time derivative. We theoretically prove and numerically verify that the presented numerical methods are unconditionally stable and second order convergent in both space and time directions. In particular, for the Riesz fractional diffusion equation, the idea of reducing the splitting error is used to further improve the algorithm, and the unconditional stability and convergency are also strictly proved and numerically verified for the improved scheme.

Tsun Ho Aaron Cheung, Min Zhou, Minghua Chen

Deep learning approaches for the Alternating Current-Optimal Power Flow (AC-OPF) problem are under active research in recent years. A common shortcoming in this area of research is the lack of a dataset that includes both a realistic power network topology and the corresponding realistic loads. To address this issue, we construct an AC-OPF formulation-ready dataset called TAS-97 that contains realistic network information and realistic bus loads from Tasmania's electricity network. We found that the realistic loads in Tasmania are correlated between buses and they show signs of an underlying multivariate normal distribution. Feasibility-optimized end-to-end deep neural network models are trained and tested on the constructed dataset. Trained on samples with bus loads generated from a fitted multivariate normal distribution, our learning-based AC-OPF solver achieves 0.13% cost optimality gap, 99.73% feasibility rate, and 38.62 times of speedup on realistic testing samples when compared to PYPOWER.

Jinda Xu, Yuhao Song, Daming Wang et al.

In an era overwhelmed by vast amounts of data, the effective curation of web-crawl datasets is essential for optimizing model performance. This paper tackles the challenges associated with the unstructured and heterogeneous nature of such datasets. Traditional heuristic curation methods often inadequately capture complex features, resulting in biases and the exclusion of relevant data. We introduce an advanced, learning-driven approach, Ensemble Curation Of DAta ThroUgh Multimodal Operators (EcoDatum), incorporating a novel quality-guided deduplication method to ensure balanced feature distributions. EcoDatum strategically integrates various unimodal and multimodal data curation operators within a weak supervision ensemble framework, utilizing automated optimization to score each data point effectively. EcoDatum, which significantly improves the data curation quality and efficiency, outperforms existing state-of-the-art (SOTA) techniques, ranked 1st on the DataComp leaderboard, with an average performance score of 0.182 across 38 diverse evaluation datasets. This represents a 28% improvement over the DataComp baseline method, demonstrating its effectiveness in improving dataset curation and model training efficiency.

Tianyu Zhao, Xiang Pan, Minghua Chen et al.

Ensuring solution feasibility is a key challenge in developing Deep Neural Network (DNN) schemes for solving constrained optimization problems, due to inherent DNN prediction errors. In this paper, we propose a ``preventive learning'' framework to guarantee DNN solution feasibility for problems with convex constraints and general objective functions without post-processing, upon satisfying a mild condition on constraint calibration. Without loss of generality, we focus on problems with only inequality constraints. We systematically calibrate inequality constraints used in DNN training, thereby anticipating prediction errors and ensuring the resulting solutions remain feasible. We characterize the calibration magnitudes and the DNN size sufficient for ensuring universal feasibility. We propose a new Adversarial-Sample Aware training algorithm to improve DNN's optimality performance without sacrificing feasibility guarantee. Overall, the framework provides two DNNs. The first one from characterizing the sufficient DNN size can guarantee universal feasibility while the other from the proposed training algorithm further improves optimality and maintains DNN's universal feasibility simultaneously. We apply the framework to develop DeepOPF+ for solving essential DC optimal power flow problems in grid operation. Simulation results over IEEE test cases show that it outperforms existing strong DNN baselines in ensuring 100% feasibility and attaining consistent optimality loss ($<$0.19%) and speedup (up to $\times$228) in both light-load and heavy-load regimes, as compared to a state-of-the-art solver. We also apply our framework to a non-convex problem and show its performance advantage over existing schemes.

Wanjun Huang, Xiang Pan, Minghua Chen et al.

AC optimal power flow (AC-OPF) problems need to be solved more frequently in the future to maintain stable and economic power system operation. To tackle this challenge, a deep neural network-based voltage-constrained approach (DeepOPF-V) is proposed to solve AC-OPF problems with high computational efficiency. Its unique design predicts voltages of all buses and then uses them to reconstruct the remaining variables without solving non-linear AC power flow equations. A fast post-processing process is developed to enforce the box constraints. The effectiveness of DeepOPF-V is validated by simulations on IEEE 118/300-bus systems and a 2000-bus test system. Compared with existing studies, DeepOPF-V achieves decent computation speedup up to four orders of magnitude and comparable performance in optimality gap and preserving the feasibility of the solution.

Xiang Pan, Minghua Chen, Tianyu Zhao et al.

High percentage penetrations of renewable energy generations introduce significant uncertainty into power systems. It requires grid operators to solve alternative current optimal power flow (AC-OPF) problems more frequently for economical and reliable operation in both transmission and distribution grids. In this paper, we develop a Deep Neural Network (DNN) approach, called DeepOPF, for solving AC-OPF problems in a fraction of the time used by conventional solvers. A key difficulty for applying machine learning techniques for solving AC-OPF problems lies in ensuring that the obtained solutions respect the equality and inequality physical and operational constraints. Generalized the 2-stage procedure in [1], [2], DeepOPF first trains a DNN model to predict a set of independent operating variables and then directly compute the remaining dependable ones by solving power flow equations. Such an approach not only preserves the power-flow balance equality constraints but also reduces the number of variables to predict by the DNN, cutting down the number of neurons and training data needed. DeepOPF then employs a penalty approach with a zero-order gradient estimation technique in the training process to preserve the remaining inequality constraints. As another contribution, we drive a condition for tuning the size of the DNN according to the desired approximation accuracy, which measures the DNN generalization capability. It provides theoretical justification for using DNN to solve the AC-OPF problem. Simulation results of IEEE 30/118/300-bus and a synthetic 2000-bus test cases show that DeepOPF speeds up the computing time by up to two orders of magnitude as compared to a state-of-the-art solver, at the expense of $<$0.1% cost difference.

Xiang Pan, Tianyu Zhao, Minghua Chen et al.

We develop DeepOPF as a Deep Neural Network (DNN) approach for solving security-constrained direct current optimal power flow (SC-DCOPF) problems, which are critical for reliable and cost-effective power system operation.DeepOPF is inspired by the observation that solving SC-DCOPF problems for a given power network is equivalent to depicting a high-dimensional mapping from the load inputs to the generation and phase angle outputs. We first train a DNN to learn the mapping and predict the generations from the load inputs. We then directly reconstruct the phase angles from the generations and loads by using the power flow equations. Such a predict-and-reconstruct approach reduces the dimension of the mapping to learn, subsequently cutting down the size of the DNN and the amount of training data needed. We further derive a condition for tuning the size of the DNN according to the desired approximation accuracy of the load-generation mapping. We develop a post-processing procedure based on $\ell_1$-projection to ensure the feasibility of the obtained solution, which can be of independent interest. Simulation results for IEEE test cases show that DeepOPF generates feasible solutions with less than 0.2% optimality loss, while speeding up the computation time by up to two orders of magnitude as compared to a state-of-the-art solver.

Yubin Zang, Minghua Chen, Sigang Yang et al.

In this paper, a novel architecture of electro-optical neural networks based on the time-stretch method is proposed and numerically simulated. By stretching time-domain ultrashort pulses, multiplications of large scale weight matrices and vectors can be implemented on light and multiple-layer of feedforward neural network operations can be easily implemented with fiber loops. Via simulation, the performance of a three-layer electro-optical neural network is tested by the handwriting digit recognition task and the accuracy reaches 88% under considerable noise.

Ge Ma, Zhi Wang, Miao Zhang et al.

Today's Internet has witnessed an increase in the popularity of mobile video streaming, which is expected to exceed 3/4 of the global mobile data traffic by 2019. To satisfy the considerable amount of mobile video requests, video service providers have been pushing their content delivery infrastructure to edge networks--from regional CDN servers to peer CDN servers (e.g., smartrouters in users' homes)--to cache content and serve users with storage and network resources nearby. Among the edge network content caching paradigms, Wi-Fi access point caching and cellular base station caching have become two mainstream solutions. Thus, understanding the effectiveness and performance of these solutions for large-scale mobile video delivery is important. However, the characteristics and request patterns of mobile video streaming are unclear in practical wireless network. In this paper, we use real-world datasets containing 50 million trace items of nearly 2 million users viewing more than 0.3 million unique videos using mobile devices in a metropolis in China over 2 weeks, not only to understand the request patterns and user behaviors in mobile video streaming, but also to evaluate the effectiveness of Wi-Fi and cellular-based edge content caching solutions. To understand performance of edge content caching for mobile video streaming, we first present temporal and spatial video request patterns, and we analyze their impacts on caching performance using frequency-domain and entropy analysis approaches. We then study the behaviors of mobile video users, including their mobility and geographical migration behaviors. Using trace-driven experiments, we compare strategies for edge content caching including LRU and LFU, in terms of supporting mobile video requests. Moreover, we design an efficient caching strategy based on the measurement insights and experimentally evaluate its performance.

Qiang Guo, Hongwei Chen, Yuxi Wang et al.

Single-pixel cameras based on the concepts of compressed sensing (CS) leverage the inherent structure of images to retrieve them with far fewer measurements and operate efficiently over a significantly broader spectral range than conventional silicon-based cameras. Recently, photonic time-stretch (PTS) technique facilitates the emergence of high-speed single-pixel cameras. A significant breakthrough in imaging speed of single-pixel cameras enables observation of fast dynamic phenomena. However, according to CS theory, image reconstruction is an iterative process that consumes enormous amounts of computational time and cannot be performed in real time. To address this challenge, we propose a novel single-pixel imaging technique that can produce high-quality images through rapid acquisition of their effective spatial Fourier spectrum. We employ phase-shifting sinusoidal structured illumination instead of random illumination for spectrum acquisition and apply inverse Fourier transform to the obtained spectrum for image restoration. We evaluate the performance of our prototype system by recognizing quick response (QR) codes and flow cytometric screening of cells. A frame rate of 625 kHz and a compression ratio of 10% are experimentally demonstrated in accordance with the recognition rate of the QR code. An imaging flow cytometer enabling high-content screening with an unprecedented throughput of 100,000 cells/s is also demonstrated. For real-time imaging applications, the proposed single-pixel microscope can significantly reduce the time required for image reconstruction by two orders of magnitude, which can be widely applied in industrial quality control and label-free biomedical imaging.