Unveiling advection-dominated interactions: Efficacy of neural networks in natural systems modelling

Studying the interactions between advection and dispersion in natural systems, especially in cases where advection predominates, are important because it is necessary to accurately model physical phenomena in domains like hydrology, atmospheric science, environmental engineering, etc. Conventional analytical and numerical methods often have drawbacks, such as high computational costs and challenges in accurately modeling complex behaviors. Improved simulation and a deeper understanding of these interactions are made possible by neural networks' capacity to learn from big datasets and simulate complex relationships. To demonstrate that deep neural networks effectively capture scenarios within physical processes where advection plays a dominant role, the effectiveness of applying deep neural networks to a third-order dispersive partial differential equation incorporating advection and dispersion terms has been investigated in this study.