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Cheng Meng

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5 papers

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EAAI Journal 2026 Journal Article

Physics-informed deep learning for predictive risk perception in tunnel construction

Penghui Lin
Jilang Wang
Limao Zhang
Robert L.K. Tiong
Cheng Meng
Xin Zhao

Ensuring a safe and stable excavation process is essential in tunnel construction, particularly when using Earth Pressure Balance (EPB) Tunnel Boring Machines (TBMs). This study aims to enhance the prediction of soil chamber pressure (SCP), a key parameter for maintaining ground stability, by developing a physics-informed deep learning model. The proposed physics-informed deep neural Network (PDNN) embeds an ordinary differential equation (ODE) representing the pressure balance mechanism into the model's loss function, ensuring physical consistency. The PDNN model is evaluated against other advanced deep learning models using real-world TBM data. Results show that the PDNN achieves a high predictive accuracy, with the coefficient of determination ( R 2 ) values of 0. 97 and 0. 96 on training and testing data, respectively, while demonstrating strong generalization under small datasets and multi-step forecasting conditions. By incorporating physics-based constraints, the model improves both interpretability and reliability, as further validated through SHapley Additive explanation (SHAP) analysis. This work represents a novel and effective application of physics-informed machine learning in tunnel construction, bridging the gap between data-driven modeling and engineering domain knowledge to support proactive safety risk management.

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NeurIPS Conference 2025 Conference Paper

Gaussian Herding across Pens: An Optimal Transport Perspective on Global Gaussian Reduction for 3DGS

Tao Wang
Mengyu Li
Geduo Zeng
Cheng Meng
Qiong Zhang

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for radiance field rendering, but it typically requires millions of redundant Gaussian primitives, overwhelming memory and rendering budgets. Existing compaction approaches address this by pruning Gaussians based on heuristic importance scores, without global fidelity guarantee. To bridge this gap, we propose a novel optimal transport perspective that casts 3DGS compaction as global Gaussian mixture reduction. Specifically, we first minimize the composite transport divergence over a KD-tree partition to produce a compact geometric representation, and then decouple appearance from geometry by fine-tuning color and opacity attributes with far fewer Gaussian primitives. Experiments on benchmark datasets show that our method (i) yields negligible loss in rendering quality (PSNR, SSIM, LPIPS) compared to vanilla 3DGS with only 10\% Gaussians; and (ii) consistently outperforms state-of-the-art 3DGS compaction techniques. Notably, our method is applicable to any stage of vanilla or accelerated 3DGS pipelines, providing an efficient and agnostic pathway to lightweight neural rendering.

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JMLR Journal 2023 Journal Article

Importance Sparsification for Sinkhorn Algorithm

Mengyu Li
Jun Yu
Tao Li
Cheng Meng

Sinkhorn algorithm has been used pervasively to approximate the solution to optimal transport (OT) and unbalanced optimal transport (UOT) problems. However, its practical application is limited due to the high computational complexity. To alleviate the computational burden, we propose a novel importance sparsification method, called Spar-Sink, to efficiently approximate entropy-regularized OT and UOT solutions. Specifically, our method employs natural upper bounds for unknown optimal transport plans to establish effective sampling probabilities, and constructs a sparse kernel matrix to accelerate Sinkhorn iterations, reducing the computational cost of each iteration from $O(n^2)$ to $\widetilde{O}(n)$ for a sample of size $n$. Theoretically, we show the proposed estimators for the regularized OT and UOT problems are consistent under mild regularity conditions. Experiments on various synthetic data demonstrate Spar-Sink outperforms mainstream competitors in terms of both estimation error and speed. A real-world echocardiogram data analysis shows Spar-Sink can effectively estimate and visualize cardiac cycles, from which one can identify heart failure and arrhythmia. To evaluate the numerical accuracy of cardiac cycle prediction, we consider the task of predicting the end-systole time point using the end-diastole one. Results show Spar-Sink performs as well as the classical Sinkhorn algorithm, requiring significantly less computational time. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2023. ( edit, beta )

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NeurIPS Conference 2020 Conference Paper

Sufficient dimension reduction for classification using principal optimal transport direction

Cheng Meng
Jun Yu
Jingyi Zhang
Ping Ma
Wenxuan Zhong

Sufficient dimension reduction is used pervasively as a supervised dimension reduction approach. Most existing sufficient dimension reduction methods are developed for data with a continuous response and may have an unsatisfactory performance for the categorical response, especially for the binary-response. To address this issue, we propose a novel estimation method of sufficient dimension reduction subspace (SDR subspace) using optimal transport. The proposed method, named principal optimal transport direction (POTD), estimates the basis of the SDR subspace using the principal directions of the optimal transport coupling between the data respecting different response categories. The proposed method also reveals the relationship among three seemingly irrelevant topics, i. e. , sufficient dimension reduction, support vector machine, and optimal transport. We study the asymptotic properties of POTD and show that in the cases when the class labels contain no error, POTD estimates the SDR subspace exclusively. Empirical studies show POTD outperforms most of the state-of-the-art linear dimension reduction methods.

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NeurIPS Conference 2019 Conference Paper

Large-scale optimal transport map estimation using projection pursuit

Cheng Meng
Yuan Ke
Jingyi Zhang
Mengrui Zhang
Wenxuan Zhong
Ping Ma

This paper studies the estimation of large-scale optimal transport maps (OTM), which is a well known challenging problem owing to the curse of dimensionality. Existing literature approximates the large-scale OTM by a series of one-dimensional OTM problems through iterative random projection. Such methods, however, suffer from slow or none convergence in practice due to the nature of randomly selected projection directions. Instead, we propose an estimation method of large-scale OTM by combining the idea of projection pursuit regression and sufficient dimension reduction. The proposed method, named projection pursuit Monge map (PPMM), adaptively selects the most informative'' projection direction in each iteration. We theoretically show the proposed dimension reduction method can consistently estimate the most informative'' projection direction in each iteration. Furthermore, the PPMM algorithm weakly convergences to the target large-scale OTM in a reasonable number of steps. Empirically, PPMM is computationally easy and converges fast. We assess its finite sample performance through the applications of Wasserstein distance estimation and generative models.

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