The effectiveness of a wind turbine elastic support in reducing vibrations significantly impacts the unit’s lifespan. During the structural design process, it is necessary to consider the influence of structural design parameters on multiple performance indicators. While neural networks can fit the relationships between design parameters on multiple performance indicators, traditional modeling methods often isolate multiple tasks, hindering the learning on correlations between tasks and reducing efficiency. Moreover, acquiring training data through physical experiments is expensive and yields limited data, insufficient for effective model training. To address these challenges, this research introduces a data generation method using a digital twin model, simulating physical conditions to generate data at a lower cost. Building on this, a Multi-gate Mixture-of-Experts multi-task prediction model with Long Short-Term Memory (MMoE-LSTM) module is developed. LSTM enhances the model’s ability to extract nonlinear features from data, improving learning. Additionally, a dynamic weighting strategy, based on coefficient of variation weighting and ridge regression, is employed to automate loss weight adjustments and address imbalances in multi-task learning. The proposed model, validated on datasets created using the digital twin model, achieved over 95% predictive accuracy for multiple tasks, demonstrating that this method is effective.