Incremental energy-based recurrent transformer-KAN for time series deformation simulation of soft tissue

In the field of virtual reality medicine, it is crucial to understand the mechanics of soft tissues. Data-driven neural network approaches offer significant computational efficiency and accuracy while naturally avoiding the non-convergence problem. However, these methods often ignore the time-series challenge and fail to address the problem of error accumulation during simulation. This study introduces a novel energy increment-based time series data-driven framework for simulating soft tissue deformation using the Transformer-KAN network. By utilizing the centroid displacement between consecutive frames instead of the displacement output of the previous frame, the proposed method reduces the prediction error of the recurrent network model. In addition, input preprocessing combined with a Gaussian diffusion distribution and corresponding loss constraints allows the network to predict deformation across the entire organ, not just in the vicinity of a collision point, thus improving the overall prediction accuracy. We compare three deep learning methods for time series simulation using four evaluation metrics, along with ablation experiments with data reduction modules and Gaussian energy constraints. The results show a strong correlation between the predictions of our method and the gold standard, confirming the effectiveness of our method in accurately modeling time series deformation.