Treffer: Parallelization of the Koopman Operator Based on CUDA and Its Application in Multidimensional Flight Trajectory Prediction.

This paper introduces a parallelized approach to reconstruct Koopman computational graphs from the perspective of parallel computing to address the computational efficiency bottleneck in approximating Koopman operators within high-dimensional spaces. We propose the KPA (Koopman Parallel Accelerator), a parallelized algorithm that restructures the Koopman computational workflow to transform sequential time-step computations into parallel tasks. KPA leverages GPU parallelism to improve execution efficiency without compromising model accuracy. To validate the algorithm's effectiveness, we apply KPA to a flight trajectory prediction scenario based on the Koopman operator. Within the CUDA kernel implementation of KPA, several optimization techniques—such as shared memory, tiling, double buffering, and data prefetching—are employed. We compare our implementation against two baselines: the original Koopman neural operator for trajectory prediction implemented in TensorFlow (TF-baseline) and its XLA-compiled variant (TF-XLA). The experimental results demonstrate that KPA achieves a 2.47× speed up over TF-baseline and a 1.09× improvement over TF-XLA when predicting a 1422-dimensional flight trajectory. Additionally, an ablation study on block size and the number of streaming multiprocessors (SMs) reveals that the best performance is obtained with the block size of 16 × 16 and SM = 8. The results demonstrate that KPA can significantly accelerate Koopman operator computations, making it suitable for high-dimensional, large-scale, or real-time applications. [ABSTRACT FROM AUTHOR]

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