Zhiyuan Wang

Sanket Jantre, Deepak Akhare, Zhiyuan Wang et al.

Partial differential equations (PDEs) underpin the modeling of many natural and engineered systems. It can be convenient to express such models as neural PDEs rather than using traditional numerical PDE solvers by replacing part or all of the PDE's governing equations with a neural network representation. Neural PDEs are often easier to differentiate, linearize, reduce, or use for uncertainty quantification than the original numerical solver. They are usually trained on solution trajectories obtained by long-horizon rollout of the PDE solver. Here we propose a more sample-efficient data-augmentation strategy for generating neural PDE training data from a computer model by space-filling sampling of local "stencil" states. This approach removes a large degree of spatiotemporal redundancy present in trajectory data and oversamples states that may be rarely visited but help the neural PDE generalize across the state space. We demonstrate that accurate neural PDE stencil operators can be learned from synthetic training data generated by the computational equivalent of 10 timesteps' worth of numerical simulation. Accuracy is further improved if we assume access to a single full-trajectory simulation from the computer model, which is typically available in practice. Across several PDE systems, we show that our data-augmented stencil data yield better trained neural stencil operators, with clear performance gains compared with naively sampled stencil data from simulation trajectories. Finally, with only 10 solver steps' worth of augmented stencil data, our approach outperforms traditional ML emulators trained on thousands of trajectories in long-horizon rollout accuracy and stability.

Shengcai Liu, Hui Ou-yang, Zhiyuan Wang et al.

Learning the structure of Bayesian networks (BNs) from data is challenging, especially for datasets involving a large number of variables. The recently proposed divide-and-conquer (D\&D) strategies present a promising approach for learning large BNs. However, they still face a main issue of unstable learning accuracy across subproblems. In this work, we introduce the idea of employing structure learning ensemble (SLE), which combines multiple BN structure learning algorithms, to consistently achieve high learning accuracy. We further propose an automatic approach called Auto-SLE for learning near-optimal SLEs, addressing the challenge of manually designing high-quality SLEs. The learned SLE is then integrated into a D\&D method. Extensive experiments firmly show the superiority of our method over D\&D methods with single BN structure learning algorithm in learning large BNs, achieving accuracy improvement usually by 30\%$\sim$225\% on datasets involving 10,000 variables. Furthermore, our method generalizes well to datasets with many more (e.g., 30000) variables and different network characteristics than those present in the training data for learning the SLE. These results indicate the significant potential of employing (automatic learning of) SLEs for scalable BN structure learning.

Yimin Fan, Zhiyuan Wang, Yuanpeng Lin et al.

Real time traffic navigation is an important capability in smart transportation technologies, which has been extensively studied these years. Due to the vast development of edge devices, collecting real time traffic data is no longer a problem. However, real traffic navigation is still considered to be a particularly challenging problem because of the time-varying patterns of the traffic flow and unpredictable accidents/congestion. To give accurate and reliable navigation results, predicting the future traffic flow(speed,congestion,volume,etc) in a fast and accurate way is of great importance. In this paper, we adopt the ideas of ensemble learning and develop a two-stage machine learning model to give accurate navigation results. We model the traffic flow as a time series and apply XGBoost algorithm to get accurate predictions on future traffic conditions(1st stage). We then apply the Top K Dijkstra algorithm to find a set of shortest paths from the give start point to the destination as the candidates of the output optimal path. With the prediction results in the 1st stage, we find one optimal path from the candidates as the output of the navigation algorithm. We show that our navigation algorithm can be greatly improved via EOPF(Enhanced Optimal Path Finding), which is based on neural network(2nd stage). We show that our method can be over 7% better than the method without EOPF in many situations, which indicates the effectiveness of our model.

Jianzhe Lin, Qi Wang, Rabab Ward et al.

Previous transfer learning methods based on deep network assume the knowledge should be transferred between the same hidden layers of the source domain and the target domains. This assumption doesn't always hold true, especially when the data from the two domains are heterogeneous with different resolutions. In such case, the most suitable numbers of layers for the source domain data and the target domain data would differ. As a result, the high level knowledge from the source domain would be transferred to the wrong layer of target domain. Based on this observation, "where to transfer" proposed in this paper should be a novel research frontier. We propose a new mathematic model named DT-LET to solve this heterogeneous transfer learning problem. In order to select the best matching of layers to transfer knowledge, we define specific loss function to estimate the corresponding relationship between high-level features of data in the source domain and the target domain. To verify this proposed cross-layer model, experiments for two cross-domain recognition/classification tasks are conducted, and the achieved superior results demonstrate the necessity of layer correspondence searching.