Yifan Chen

Shantanu Shahane, Sheide Chammas, Deniz A. Bezgin et al. · gatech

Conventional WENO3 methods are known to be highly dissipative at lower resolutions, introducing significant errors in the pre-asymptotic regime. In this paper, we employ a rational neural network to accurately estimate the local smoothness of the solution, dynamically adapting the stencil weights based on local solution features. As rational neural networks can represent fast transitions between smooth and sharp regimes, this approach achieves a granular reconstruction with significantly reduced dissipation, improving the accuracy of the simulation. The network is trained offline on a carefully chosen dataset of analytical functions, bypassing the need for differentiable solvers. We also propose a robust model selection criterion based on estimates of the interpolation's convergence order on a set of test functions, which correlates better with the model performance in downstream tasks. We demonstrate the effectiveness of our approach on several one-, two-, and three-dimensional fluid flow problems: our scheme generalizes across grid resolutions while handling smooth and discontinuous solutions. In most cases, our rational network-based scheme achieves higher accuracy than conventional WENO3 with the same stencil size, and in a few of them, it achieves accuracy comparable to WENO5, which uses a larger stencil.

Anudhyan Boral, Zhong Yi Wan, Leonardo Zepeda-Núñez et al.

We introduce a data-driven learning framework that assimilates two powerful ideas: ideal large eddy simulation (LES) from turbulence closure modeling and neural stochastic differential equations (SDE) for stochastic modeling. The ideal LES models the LES flow by treating each full-order trajectory as a random realization of the underlying dynamics, as such, the effect of small-scales is marginalized to obtain the deterministic evolution of the LES state. However, ideal LES is analytically intractable. In our work, we use a latent neural SDE to model the evolution of the stochastic process and an encoder-decoder pair for transforming between the latent space and the desired ideal flow field. This stands in sharp contrast to other types of neural parameterization of closure models where each trajectory is treated as a deterministic realization of the dynamics. We show the effectiveness of our approach (niLES - neural ideal LES) on a challenging chaotic dynamical system: Kolmogorov flow at a Reynolds number of 20,000. Compared to competing methods, our method can handle non-uniform geometries using unstructured meshes seamlessly. In particular, niLES leads to trajectories with more accurate statistics and enhances stability, particularly for long-horizon rollouts.

Yuanxing Liu, Wei-Nan Zhang, Yifan Chen et al.

E-commerce pre-sales dialogue aims to understand and elicit user needs and preferences for the items they are seeking so as to provide appropriate recommendations. Conversational recommender systems (CRSs) learn user representation and provide accurate recommendations based on dialogue context, but rely on external knowledge. Large language models (LLMs) generate responses that mimic pre-sales dialogues after fine-tuning, but lack domain-specific knowledge for accurate recommendations. Intuitively, the strengths of LLM and CRS in E-commerce pre-sales dialogues are complementary, yet no previous work has explored this. This paper investigates the effectiveness of combining LLM and CRS in E-commerce pre-sales dialogues, proposing two collaboration methods: CRS assisting LLM and LLM assisting CRS. We conduct extensive experiments on a real-world dataset of Ecommerce pre-sales dialogues. We analyze the impact of two collaborative approaches with two CRSs and two LLMs on four tasks of Ecommerce pre-sales dialogue. We find that collaborations between CRS and LLM can be very effective in some cases.

Huan Zhang, Yifan Chen, Eric Vanden-Eijnden et al.

Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial differential equations over time. This work shows that sequential-in-time training methods can be understood broadly as either optimize-then-discretize (OtD) or discretize-then-optimize (DtO) schemes, which are well known concepts in numerical analysis. The unifying perspective leads to novel stability and a posteriori error analysis results that provide insights into theoretical and numerical aspects that are inherent to either OtD or DtO schemes such as the tangent space collapse phenomenon, which is a form of over-fitting. Additionally, the unified perspective facilitates establishing connections between variants of sequential-in-time training methods, which is demonstrated by identifying natural gradient descent methods on energy functionals as OtD schemes applied to the corresponding gradient flows.

Sebastien M. R. Arnold, Pierre L'Ecuyer, Liyu Chen et al.

Reinforcement learning constantly deals with hard integrals, for example when computing expectations in policy evaluation and policy iteration. These integrals are rarely analytically solvable and typically estimated with the Monte Carlo method, which induces high variance in policy values and gradients. In this work, we propose to replace Monte Carlo samples with low-discrepancy point sets. We combine policy gradient methods with Randomized Quasi-Monte Carlo, yielding variance-reduced formulations of policy gradient and actor-critic algorithms. These formulations are effective for policy evaluation and policy improvement, as they outperform state-of-the-art algorithms on standardized continuous control benchmarks. Our empirical analyses validate the intuition that replacing Monte Carlo with Quasi-Monte Carlo yields significantly more accurate gradient estimates.

Yang Fang, Xiang Zhao, Yifan Chen et al.

In network representation learning we learn how to represent heterogeneous information networks in a low-dimensional space so as to facilitate effective search, classification, and prediction solutions. Previous network representation learning methods typically require sufficient task-specific labeled data to address domain-specific problems. The trained model usually cannot be transferred to out-of-domain datasets. We propose a self-supervised pre-training and fine-tuning framework, PF-HIN, to capture the features of a heterogeneous information network. Unlike traditional network representation learning models that have to train the entire model all over again for every downstream task and dataset, PF-HIN only needs to fine-tune the model and a small number of extra task-specific parameters, thus improving model efficiency and effectiveness. During pre-training, we first transform the neighborhood of a given node into a sequence. PF-HIN is pre-trained based on two self-supervised tasks, masked node modeling and adjacent node prediction. We adopt deep bi-directional transformer encoders to train the model, and leverage factorized embedding parameterization and cross-layer parameter sharing to reduce the parameters. In the fine-tuning stage, we choose four benchmark downstream tasks, i.e., link prediction, similarity search, node classification, and node clustering. PF-HIN consistently and significantly outperforms state-of-the-art alternatives on each of these tasks, on four datasets.