Interpolation Method

Interpolation methods aim to estimate values at unobserved points based on known data, a crucial task across numerous scientific disciplines. Current research emphasizes developing efficient and accurate interpolation techniques, particularly focusing on neural network architectures like interpolating neural networks (INNs) and adaptations of existing methods for specific applications (e.g., manifold learning for indoor positioning, fractal interpolation for time series prediction). These advancements improve model accuracy, reduce computational costs, and enhance the reliability of scientific machine learning workflows, impacting fields ranging from computer-aided engineering to medical image analysis. The rigorous quantification of interpolation errors and the exploration of hybrid approaches combining interpolation with machine learning are also active research areas.