5 papers
Relative entropy estimate and geometric ergodicity for implicit Langevin Monte Carlo
Lei Li, Jian-Guo Liu, Yuliang Wang
We study the implicit Langevin Monte Carlo (iLMC) method, which simulates the overdamped Langevin equation via an implicit iteration rule. In many applications, iLMC is favored ove…
Asymptotic uniform estimate of random batch method with replacement for the Cucker-Smale model
Shi Jin, Yuelin Wang, Yuliang Wang
The Random Batch Method (RBM) [S. Jin, L. Li and J.-G. Liu, Random Batch Methods (RBM) for interacting particle systems, J. Comput. Phys. 400 (2020) 108877] is not only an efficien…
On Random Batch Methods (RBM) for interacting particle systems driven by Lévy processes
Jian-Guo Liu, Yuliang Wang
In many real-world scenarios, the underlying random fluctuations are non-Gaussian, particularly in contexts where heavy-tailed data distributions arise. A typical example of such n…
Convergence of Random Batch Method with replacement for interacting particle systems
Zhenhao Cai, Jian-Guo Liu, Yuliang Wang
The Random Batch Method (RBM) proposed in [Jin et al. J Comput Phys, 2020] is an efficient algorithm for simulating interacting particle systems (IPS). In this paper, we investigat…
Topic-aware chatbot using Recurrent Neural Networks and Nonnegative Matrix Factorization
Yuchen Guo, Nicholas Hanoian, Zhexiao Lin +8
We propose a novel model for a topic-aware chatbot by combining the traditional Recurrent Neural Network (RNN) encoder-decoder model with a topic attention layer based on Nonnegati…