In the fields of physics and engineering, it is crucial to understand phase transition dynamics. This field involves fundamental partial differential equations (PDEs) such as the Allen–Cahn, Burgers, and two-dimensional (2D) wave equations. In alloys, the evolution of the phase transition interface is described by the Allen–Cahn equation. Vibrational and wave phenomena during phase transitions are modeled using the Burgers and 2D wave equations. The combination of these equations gives comprehensive information about the dynamic behavior during a phase transition. Numerical modeling methods such as finite difference method (FDM), finite volume method (FVM) and finite element method (FEM) are often applied to solve phase transition problems that involve many partial differential equations (PDEs). However, physical problems can lead to computational complexity, increasing computational costs dramatically. Physics-informed neural networks (PINNs), as new neural network algorithms, can integrate physical law constraints with neural network algorithms to solve partial differential equations (PDEs), providing a new way to solve PDEs in addition to the traditional numerical modeling methods. In this paper, a hard-constraint wide-body PINN (HWPINN) model based on PINN is proposed. This model improves the effectiveness of the approximation by adding a wide-body structure to the approximation neural network part of the PINN architecture. A hard constraint is used in the physically driven part instead of the traditional practice of PINN constituting a residual network with boundary or initial conditions. The high accuracy of HWPINN for solving PDEs is verified through numerical experiments. One-dimensional (1D) Allen–Cahn, one-dimensional Burgers, and two-dimensional wave equation cases are set up for numerical experiments. The properties of the HWPINN model are inferred from the experimental data. The solution predicted by the model is compared with the FDM solution for evaluating the experimental error in the numerical experiments. HWPINN shows great potential for solving the PDE forward problem and provides a new approach for solving PDEs.

As a new seawater standard, the International Thermodynamic Equation of Seawater-2010 (TEOS-10) has made it possible to accurately calculate salinity changes caused by small changes in the relative proportions of inorganic dissolved constituents in the open ocean and thus to accurately calculate the thermodynamic properties of seawater. However, offshore and semi-enclosed seas are subject to the dual influence of geo-biochemical processes and terrestrial inputs, and the spatial and temporal variations in the relative composition of their seawater are more complex, resulting in very few studies of salinity change due to changes in the relative composition in these regions, and the applicability of the TEOS-10 in these seas needs to be further evaluated. The Bohai Sea is a typical semi-enclosed sea that has accumulated a large amount of physical oceanography and marine chemistry measurements, making it an ideal area to study the effects of changes in the relative composition of seawater on salinity. Based on repeated measurements of Section B in the Bohai Sea from 1985 to 2020, complemented by quasi-synchronous large-scale measurements of the Bohai Sea from 2006 to 2007, this study found that [HCO3−] and [Ca2+] ions anomalies dominate the relative composition anomalies of dissolved substances in this sea relative to the Standard Sea Water (SSW). These additional components could increase the absolute salinity SA by up to 0.1 g·kg^-1 and the practical salinity SP by 0~0.04 according to the TEOS-10 algorithm and the mathematical model Pa08. Based on the specific environmental characteristics of the Bohai Sea, the sources, spatial and temporal variations, and influencing factors of the relative compositional anomalies are analyzed, and the empirical formulas of the absolute salinity anomaly δSA and practical salinity anomaly δSP for the Bohai Sea are further fitted, with the uncertainty of 0.007~0.021 g·kg^-1 for δSA and 0.003~0.008 for δSP. The above results can not only improve the accuracy of the thermodynamic properties of the Bohai Seawater, but also provide the compatibility level of the long-term salinity changes in the Bohai Sea and its adjacent waters.

This study addresses how to maintain oceanic mixing along potential density surface in ocean data assimilation (ODA). It is well known that the oceanic mixing across the potential density surface is much weaker than that along the potential density surface. However, traditional ODA schemes allow the mixing across the potential density surface and thus may result in extra assimilation errors. Here, a new ODA scheme that uses potential density gradient information of the model background to rescale observational adjustment is designed to improve the quality of assimilation. The new scheme has been tested using a regional ocean model within a multiscale 3-dimensional variational framework. Results show that the new scheme effectively prevents the excessive unphysical projection of observational information in the direction across potential density surface and thus improves assimilation quality greatly. Forecast experiments also show that the new scheme significantly improves the model forecast skills through providing more dynamically consistent initial conditions