In multi-channel paid user acquisition, early and accurate prediction of user retention at the channel level is crucial for optimizing budget allocation. User retention curves display a pronounced temporal pattern: an initial period of high churn transitions into long-term stability. This pattern is further characterized by regular fluctuations attributable to seasonality and exhibits high serial autocorrelation. These intrinsic properties make such curves highly suitable for analysis within a time-series forecasting framework. However, forecasting user retention ratio for large-scale short-video platform faces three major challenges: significant heterogeneity across channels, pronounced global trend of decay followed by saturation, and short look-back windows. To address these challenges, we propose PPDL, a novel forecasting framework that integrates physical priors with deep learning. We first introduce a trend-residual decomposition component. The trend is modeled using the Weibull distribution, whose parameters are learned via a Multilayer Perceptron (MLP). Secondly, for the residual component, we design an auxiliary embedding module on top of a deep learning backbone to maintain the channel identity awareness. Finally, to enhance the model's sensitivity to trends, we design a Multiscale Trend-penalized loss function. The proposed approach PPDL is validated through comprehensive experiments on industrial-scale datasets, covering three applications with an average of 30+ channels each. Experimental results show that PPDL achieves improvements across different backbones and significantly outperforms existing online solutions.

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