## 1 Introduction
[23], who used PINNs in combination with a single relaxation time lattice Boltzmann method to solve inverse problems in fluid mechanics. They used PINNs to solve PDEs with unclear boundary conditions and initial conditions. [PERSON] et al. [24] solved the forward-backward problem in fluid dynamics by using PINNs in conjunction with the BGK equation. In addition, the performance of PINNs is extremely promising for applications in the engineering sciences. The stiff-PINN method developed by [PERSON] et al. [25] utilizes QSSA to enable PINNs to solve for stiffening chemical kinetics, which opens up the possibility of applying PINNs to a wide variety of reaction-diffusion systems involving stiffening kinetics. [PERSON] et al. [26] applied PINNs in a power system. [PERSON] et al. [27] proposed two generalized artificial intelligence frameworks for low-temperature plasma simulations, the coefficient-subnetwork (CS-PINN) physics-informed neural network and the Runge-Kutta physics-informed neural network (RK-PINN). PINNs are also prominent in coastal storm surge prediction [28] and geophysics [29], where they provide functions including state analysis, parameter estimation, dynamic analysis, macroscopic physical quantity computation, anomaly detection and localization, and data synthesis for real world problems by integrating specific physical information into state-of-the-art deep learning methods. Although PINNs have been widely used in solving PDEs, they still face many challenges, such as poor interpretability, difficult debugging of parameters, training difficulties, and unclear optimization strategies. Especially when dealing with higher-dimensional physical problems, PINNs consume a lot of time for training and debugging. For problems with nonunique solutions, traditional PINNs may not appear smooth enough in design. The hard-constraint physics-informed neural network (HPINN) was proposed by [PERSON] et al. [30] for solving topology optimization problems. [PERSON] et al. found that compared with traditional constrained optimization methods for PDEs based on the adjoint method and numerical PDEs solvers, HPINN is able to achieve similar optimization objectives and the resulting designs are smoother when dealing with problems with nonunique solutions. HPINN takes advantage of the recent advances in PINNs for solving PDEs without the need for large-scale datasets (generated by numerical PDEs solvers) for training and imposes hard constraints using penalization and augmented Lagrange methods. The training and debugging of HPINN we still extremely challenging. HPINN has advantages in terms of fast convergence and accuracy as well as solution smoothness. HPINN abandons the flexible boundary conditions and initial condition settings of traditional PINNs, making it extremely difficult to formulate an optimization strategy for HPINN. In order to improve the performance of HPINN and develop an optimization strategy, we propose a hard-constraint wide-body network PINN model (HWPINN). HWPINN introduces a wider neural network structure, which enhances the approximation ability of neural networks. By combining the highly constrained nature of HPINN, HWPINN further improves the accuracy of PINNs in solving PDEs while reducing the time and number of iterations required for training. This model provides a new optimization idea for optimizing HPINNs from the point of view of changing the network model, which offers the possibility of solving PDEs in positive problems with higher accuracy and speed. In this manuscript, we focus on three cases of PDEs: the 1D Allen-Cahn (AC) equation, the 1D Burgers equation, and the 2D wave equation. Among them, the 1D AC equation and the 1D Burgers equation are common PDEs in phase transition dynamics and computational fluid dynamics, and the code for their tensor-flow versions is provided in reference [22]. To compare the performance of HWPINN in different dimensions, the 2D wave equation is provided in this paper.