Difficulty aware temporal transformer optimized by multi objective particle swarm optimization for sports score trend forecasting

Historical score trend forecasting is important for sports analytics, but existing methods often treat schedule-related variables as ordinary features and lack explicit modeling of match difficulty. To address this issue, this paper proposes a difficulty-aware temporal forecasting framework, termed DAT-IPSO, for historical score trend prediction and schedule-difficulty attribution. A composite schedule-difficulty coefficient is constructed from opponent strength, home–away difficulty, schedule density, rest pressure, and recent-form difficulty. This coefficient is incorporated into a temporal Transformer through difficulty embedding and normalized difficulty-guided self-attention to condition temporal dependency modeling on varying schedule contexts. Meanwhile, an improved particle swarm optimization strategy with scalarized multi-criteria validation fitness is introduced to jointly configure model hyperparameters, difficulty-factor weights, and loss-function weights. Experimental results show that DAT-IPSO outperforms representative statistical, machine-learning, recurrent neural-network, and standard Transformer baselines in prediction accuracy and trend consistency. Difficulty-weight stability, factor-removal sensitivity, and test-wide attention analysis indicate that opponent strength, schedule density, and rest pressure provide relatively strong predictive contributions to the forecasting model. These results demonstrate that the proposed framework improves score trend forecasting while providing model-level schedule-difficulty attribution without implying causal effects.