Numerical Stability

Numerical stability in computational methods, particularly within machine learning and scientific computing, focuses on ensuring reliable and accurate results despite inherent limitations of finite-precision arithmetic and potential instabilities in algorithms. Current research emphasizes improving the stability of neural networks (including convolutional and physics-informed networks), optimization algorithms (like Adam), and numerical schemes for solving differential equations, often through techniques like differentiable regularization, error correction, and careful hyperparameter tuning. Addressing numerical instability is crucial for the reliability and trustworthiness of machine learning models and simulations across diverse scientific and engineering applications, impacting everything from medical diagnosis to climate modeling.