Non Euclidean Domain

Non-Euclidean domains, encompassing data structures like graphs and irregular geometries, pose significant challenges for traditional machine learning methods designed for Euclidean spaces. Current research focuses on developing novel neural network architectures, such as physics-informed neural networks (PINNs) and neural operators, to effectively process and analyze data within these complex domains, often incorporating techniques like spectral embeddings and geometry encoders to capture relevant features. These advancements are crucial for tackling real-world problems in diverse fields, including engineering design, healthcare (e.g., analyzing biological networks), and scientific simulations where data inherently resides in non-Euclidean spaces.