Empirical Interpolation Method

The Empirical Interpolation Method (EIM) is a dimensionality reduction technique used to efficiently approximate high-dimensional functions, particularly those arising from parameterized partial differential equations or large datasets. Current research focuses on extending EIM's capabilities, including integrating it with neural networks (e.g., Neural EIM) to handle nonlinear problems and adapting it for tensor data (e.g., t-DEIM) to preserve multi-dimensional correlations. These advancements improve the efficiency of reduced-order modeling, accelerating computations in various applications like fluid dynamics and image analysis while maintaining accuracy, thereby impacting fields requiring computationally intensive simulations and data processing.