Zeyuan Song

Ziwei Huang, Zeyuan Song, Paola Sebastiani et al.

RSNet is an open-source R package that provides a resampling-based framework for robust and interpretable network inference, designed to address the limited-sample-size challenges common in high-dimensional data. It supports both the estimation of partial correlation networks modeled as Gaussian networks and conditional Gaussian Bayesian networks for mixed data types that combine continuous and discrete variables. The framework incorporates multiple resampling strategies, including bootstrap, subsampling, and cluster-based approaches, to accommodate both independent and correlated observations. To enhance interpretability, RSNet integrates graphlet-based topology analysis that captures higher-order connectivity and edge sign information, enabling single-node and subnetwork-level insights. Notably, RSNet is the first R package to efficiently construct signed graphlet degree vector matrices (GDVMs) in near-constant time for sparse networks, providing scalable analysis of higher-order network structure. Collectively, RSNet offers a versatile tool for statistically reliable and interpretable network inference in high-dimensional data.

Zeyuan Song, Zheyu Jiang

The spatiotemporal water flow dynamics in unsaturated soils can generally be modeled by the Richards equation. To overcome the computational challenges associated with solving this highly nonlinear partial differential equation (PDE), we present a novel solution algorithm, which we name as the MP-FVM (Message Passing-Finite Volume Method), to holistically integrate adaptive fixed-point iteration scheme, encoder-decoder neural network architecture, Sobolev training, and message passing mechanism in a finite volume discretization framework. We thoroughly discuss the need and benefits of introducing these components to achieve synergistic improvements in accuracy and stability of the solution. We also show that our MP-FVM algorithm can accurately solve the mixed-form $n$-dimensional Richards equation with guaranteed convergence under reasonable assumptions. Through several illustrative examples, we demonstrate that our MP-FVM algorithm not only achieves superior accuracy, but also better preserves the underlying physical laws and mass conservation of the Richards equation compared to state-of-the-art solution algorithms and the commercial HYDRUS solver.