Posteriori Error

A posteriori error estimation focuses on determining the accuracy of approximations, particularly in complex systems like those modeled by partial differential equations (PDEs). Current research emphasizes developing efficient methods for calculating these errors, often integrating them directly into model training processes using neural networks (e.g., convolutional neural networks, physics-informed neural networks) and Bayesian optimization techniques. This work is crucial for improving the reliability and efficiency of numerical simulations across diverse fields, from uncertainty quantification in structural dynamics to advanced machine learning applications involving PDEs. The resulting certified error bounds enhance the trustworthiness of model predictions and guide adaptive refinement strategies for optimal resource allocation.