Dai Hai Nguyen

Dai Hai Nguyen, Duc Dung Nguyen, Atsuyoshi Nakamura et al.

We study multi-objective optimization over probability distributions in Wasserstein space. Recently, Nguyen et al. (2025) introduced Multiple Wasserstein Gradient Descent (MWGraD) algorithm, which exploits the geometric structure of Wasserstein space to jointly optimize multiple objectives. Building on this approach, we propose an accelerated variant, A-MWGraD, inspired by Nesterov's acceleration. We analyze the continuous-time dynamics and establish convergence to weakly Pareto optimal points in probability space. Our theoretical results show that A-MWGraD achieves a convergence rate of O(1/t^2) for geodesically convex objectives and O(e^{-\sqrtβt}) for $β$-strongly geodesically convex objectives, improving upon the O(1/t) rate of MWGraD in the geodesically convex setting. We further introduce a practical kernel-based discretization for A-MWGraD and demonstrate through numerical experiments that it consistently outperforms MWGraD in convergence speed and sampling efficiency on multi-target sampling tasks.

Dai Hai Nguyen, Koji Tsuda

Deep generative models have been shown powerful in generating novel molecules with desired chemical properties via their representations such as strings, trees or graphs. However, these models are limited in recommending synthetic routes for the generated molecules in practice. We propose a generative model to generate molecules via multi-step chemical reaction trees. Specifically, our model first propose a chemical reaction tree with predicted reaction templates and commercially available molecules (starting molecules), and then perform forward synthetic steps to obtain product molecules. Experiments show that our model can generate chemical reactions whose product molecules are with desired chemical properties. Also, the complete synthetic routes for these product molecules are provided.