With society entering the Internet era, the volume and speed of data and information have been increasing. Predicting the popularity of information cascades can help with high-value information delivery and public opinion monitoring on the internet platforms. The current state-of-the-art models for predicting information popularity utilize deep learning methods such as graph convolution networks (GCNs) and recurrent neural networks (RNNs) to capture early cascades and temporal features to predict their popularity increments. However, these previous methods mainly focus on the micro features of information cascades, neglecting their general macroscopic patterns. Furthermore, they also lack consideration of the impact of information heterogeneity on spread popularity. To overcome these limitations, we propose a physics-informed neural network with adaptive clustering learning mechanism, PIACN, for predicting the popularity of information cascades. Our proposed model not only models the macroscopic patterns of information dissemination through physics-informed approach for the first time but also considers the influence of information heterogeneity through an adaptive clustering learning mechanism. Extensive experimental results on three real-world datasets demonstrate that our model significantly outperforms other state-of-the-art methods in predicting information popularity.