Zheyu Jiang

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.

Jianxin Xie, Bing Yao, Zheyu Jiang

Soil moisture is a key hydrological parameter that has significant importance to human society and the environment. Accurate modeling and monitoring of soil moisture in crop fields, especially in the root zone (top 100 cm of soil), is essential for improving agricultural production and crop yield with the help of precision irrigation and farming tools. Realizing the full sensor data potential depends greatly on advanced analytical and predictive domain-aware models. In this work, we propose a physics-constrained deep learning (P-DL) framework to integrate physics-based principles on water transport and water sensing signals for effective reconstruction of the soil moisture dynamics. We adopt three different optimizers, namely Adam, RMSprop, and GD, to minimize the loss function of P-DL during the training process. In the illustrative case study, we demonstrate the empirical convergence of Adam optimizers outperforms the other optimization methods in both mini-batch and full-batch training.

Yinyi Lai, Jiaqi Shang, Zenghui Liu et al.

As terrestrial resources become increasingly depleted, the demand for deep-sea resource exploration has intensified. However, the extreme conditions in the deep-sea environment pose significant challenges for underwater operations, necessitating the development of robust detection robots. In this paper, we propose an advanced path planning methodology that integrates an improved A* algorithm with the Dynamic Window Approach (DWA). By optimizing the search direction of the traditional A* algorithm and introducing an enhanced evaluation function, our improved A* algorithm accelerates path searching and reduces computational load. Additionally, the path-smoothing process has been refined to improve continuity and smoothness, minimizing sharp turns. This method also integrates global path planning with local dynamic obstacle avoidance via DWA, improving the real-time response of underwater robots in dynamic environments. Simulation results demonstrate that our proposed method surpasses the traditional A* algorithm in terms of path smoothness, obstacle avoidance, and real-time performance. The robustness of this approach in complex environments with both static and dynamic obstacles highlights its potential in autonomous underwater vehicle (AUV) navigation and obstacle avoidance.