🏵️The Math of Stochasticity plus AI Expansion

Stochasticity addresses randomness in systems using mathematical tools like SDEs and SPDEs. It relies on functional analysis and probability theory to quantify uncertainty. Modern approaches incorporate deep learning, such as PINNs and FNOs, for solving complex PDEs. Numerical methods like Monte Carlo simulations bridge theory and application, aiding in fields like fluid dynamics and statistical mechanics. Stochasticity provides a framework for understanding and predicting behavior in uncertain systems.