According to psychologist D. Kahneman (2002 Nobel prize winner in economics for the work on decision making under uncertainty) there are two modes/systems of thinking. System 1 operates automatically and quickly, like deep learning empowered by automatic differentiation. System 2 allocates attention to the effortful mental activities, like building explainable heuristics in quantitative sciences.
In this talk we illustrate how applied mathematics is harnessing system 1 achievements of modern AI to build system 2 for quantitative sciences. Specifically, we discuss design, training and validation of the system 2 for
1) Lagrangian Large Eddy Simulations of Turbulent Flows
2) Physics Informed Machine Learning of Power Systems
3) Graphical and Agent Based Models of epidemiological bursts