Continuous Dynamic Modeling via Neural ODEs for Popularity Trajectory Prediction

TL;DR

This work addresses predicting the full, continuous popularity trajectory of information cascades by modeling diffusion dynamics with neural ODEs. NODEPT combines a dynamic and temporal state–aware encoder with a memory-augmented, attention-based ODE generator and a decoder to output $\hat{P_c^t}$ for arbitrary future times. Training uses a variational objective (ELBO) augmented with an increment loss to encourage realistic trajectory growth, and experiments on three real-world datasets show superior trajectory and single-point predictions versus strong baselines. The approach offers practical benefits for understanding diffusion dynamics, change rates, and growth patterns, enabling flexible, long-horizon predictions and informed decision-making in marketing, moderation, and information monitoring.

Abstract

Popularity prediction for information cascades has significant applications across various domains, including opinion monitoring and advertising recommendations. While most existing methods consider this as a discrete problem, popularity actually evolves continuously, exhibiting rich dynamic properties such as change rates and growth patterns. In this paper, we argue that popularity trajectory prediction is more practical, as it aims to forecast the entire trajectory of how popularity unfolds over arbitrary future time. This approach offers insights into both instantaneous popularity and the underlying dynamic properties. However, traditional methods for popularity trajectory prediction primarily rely on specific diffusion mechanism assumptions, which may not align well with real-world dynamics and compromise their performance. To address these limitations, we propose NODEPT, a novel approach based on neural ordinary differential equations (ODEs) for popularity trajectory prediction. NODEPT models the continuous dynamics of the underlying diffusion system using neural ODEs. We first employ an encoder to initialize the latent state representations of information cascades, consisting of two representation learning modules that capture the co-evolution structural characteristics and temporal patterns of cascades from different perspectives. More importantly, we then introduce an ODE-based generative module that learns the dynamics of the diffusion system in the latent space. Finally, a decoder transforms the latent state into the prediction of the future popularity trajectory. Our experimental results on three real-world datasets demonstrate the superiority and rationality of the proposed NODEPT method.

Figures (4)

• Figure 1: Popularity trajectories of different information cascades.
• Figure 2: Framework of our proposed NODEPT.
• Figure 3: Effect of $\lambda_1$ and memory module size on all datasets.
• Figure 4: Trajectories of information cascade popularity.