## söndag 11 november 2018

### Turbulence Riddle Solved by AI as Automated Computational Mathematical Modeling ACMM

 The (super)human intellect of Euler (1707-83) formulated Euler's equation for fluid flow.
The information society is based on computational mathematical modeling with Automated Computational Mathematical Modeling ACMM now emerging as a form of Artificial Intelligence AI.

The FEniCS Project is software for ACMM in a setting of (partial) differential equations (mathematical models of physical systems) offering automation of discretisation and computational solution.

Unicorn/FEniCS is a unified solver for solid and fluid dynamics, which offers a solution to the major unsolved problem of mathematical modeling of turbulent fluid flow in the form of an automated turbulence model as the product of best possible computational solution of Euler's equations for fluid flow.

This is presented by Johan Jansson in edX courses on High Performance Finite Element Modeling Part I and Part II. Take the courses and see yourself! This is a high-light of the educational program DigiMat carrying from basic school to university bringing ACMM to the people!

The turbulence model is the result of AI in the form of a computational procedure for finding a best possible solution to a set of partial differential equations formed by the Human Intelligence HI of Euler as the sharpest mind of the scientific revolution. Here HI sets the goal and ACMM is the factual process to reach the goal.

The solution of the riddle of turbulence thus comes out from a combination of HI and AI in a setting where HI showed to be too weak to give an answer, as witnessed by

Werner Heisenberg:
• When I meet God, I’m going to ask him two questions: why relativity? And why turbulence? I really believe he’ll have an answer for the first.
Horace Lamb:
• I am an old man now, and when I die and go to heaven, there are two matters on which I hope for enlightenment. One is quantum electrodynamics and the other is the turbulent motion of fluids. About the former, I am really rather optimistic.
 Turbulent flow (video) around a jumbojet in landing as best possible solution of Euler's equations.
We here view AI as an extension of HI and not (merely) as a replacement as in self-driving cars,
recalling that after all driving a car does not need much intelligence. But predicting turbulent flow does and requires both HI and AI.

Notice that AI is beyond full understanding of HI since AI is a self-learning system and not a system taught by HI. In particular the automatic turbulence model offered by ACMM is beyond full understanding by HI as a the result of a self-learning adaptive computational procedure, generating the turbulent viscosity which showed to be evasive for HI alone.

Notice further that once turbulent fluid motion can be simulated by ACMM, computational fluid environments can be set up for testing of airplane designs, training of pilots or self-learning of flying vehicles as a combined vehicle-environment application of AI.