在本論文中，我們基於含有奇異擾動參數的非線性擴散方程，建構了神經網路模型以預測方程的解。我們從簡單的線性方程出發，逐步擴展到邊界項含有未知解的隱式方程，我們以物理訊息神經網路進行模型的訓練並且我們將結果與精確解做對比。我們發現以切比雪夫點來當訓練點求解方程效率較佳。最後，我們將這一方法延伸到求解無法得知精確解的非線性方程。

In this paper, we construct a neural network model to solve the singularly perturbed nonlinear diffusion equation. We started from solving linear equations and gradually extended our methodology to consider problems with implicit boundary conditions, namely, the boundary condition contains the unknown solution. We solve the problem using physics-informed neural network. We found that using Chebyshev nodes as the training points improves the efficiency of the training significantly. Finally, we extend this approach to solve nonlinear equations for which exact solutions are not known.

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