Geometry adaptive waveformer for cardio-vascular modeling

Modeling cardiovascular anatomies poses a significant challenge due to their complex, irregular structures and inherent pathological conditions. Numerical simulations, while accurate, are often computationally expensive, limiting their practicality in clinical settings. Traditional machine learning methods, on the other hand, often struggle with some major hurdles, including high dimensionality of the inputs, inability to effectively work with irregular grids, and preserving the time dependencies of responses in dynamic problems. In response to these challenges, this paper proposes geometry adaptive waveformer, a novel neural operator to predict blood flow dynamics in the cardiovascular system. The framework is primarily composed of three components: a geometry encoder, a geometry decoder, and a waveformer. The encoder transforms input defined on the irregular domain to a regular domain using a graph operator-based network and signed distance functions. The waveformer operates on the transformed field on the irregular grid. Finally, the decoder reverses this process, transforming the output from the regular grid back to the physical space. We evaluate the efficacy of the approach on different sets of cardiovascular data. The results obtained illustrate the effectiveness of the proposed model in accurately predicting blood flow dynamics in the cardiovascular system, establishing the proposed approach as a computationally efficient and clinically feasible alternative to traditional methods.