Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the components of deep learning. A large class of physical problems in materials science and mechanics involve moving boundaries, where interface flux balance conditions are to be satisfied while solving DEs. Examples of such systems include free surface flows, shock propagation, solidification of pure and alloy systems etc. While recent research works have explored applicability of PINNs for an uncoupled system (such as solidification of pure system), the present work reports a PINN-based approach to solve coupled systems involving multiple governing parameters (energy and species, along with multiple interface balance equations). This methodology employs an architecture consisting of a separate network for each variable with a separate treatment of each phase, a training strategy which alternates between temporal learning and adaptive loss weighting, and a scheme which progressively reduces the optimisation space. While solving the benchmark problem of binary alloy solidification, it is distinctly successful at capturing the complex composition profile, which has a characteristic discontinuity at the interface and the resulting predictions align well with the analytical solutions. The procedure can be generalised for solving other transient multiphysics problems especially in the low-data regime and in cases where measurements can reveal new physics.

本研究解决了耦合移动边界偏微分方程（PDEs）的复杂物理问题，填补了现有应用的空白。提出了一种基于PINN的方法，通过引入多个变量的独立网络架构和交替学习策略，成功捕捉了合金固化中的复杂组成特征及其界面不连续性，这一方法在低数据环境中展现出广泛的适用性和潜在影响。

基于物理信息神经网络（PINN）的方法论用于耦合移动边界偏微分方程