Holon Templates Language Add-Plug Ins SYSTEMS SIMULATION Initiate … Integrate SYSTEMS CORRELATION Find … to Match SYSTEMS OPTIMIZATION Find … to Maxim
{"Image DocumentName": "Metaphoric (Non-Algorithmic) Template Modeling", "Image ImageDescription": "Optimal Design & Control Application. Visible Source Code. This optimal design and control application is a simple but sophisticated mathematical example involving all three solver classes. It is an optimization problem containing a two-point boundary value simulation. The inner boundary value simulation must find the initial condition of a coupled set of differential equations to match a terminal point boundary condition. This is an iterative inverse problem, and so is the outer optimization problem. Thus we have nested inverse problems, in which the inner one solves a set of simultaneous differential equations. Both perform automatic differentiation of its respective model to compute the gradient and higher derivatives of the function being searched for the solution condition. This involves the recursive nesting of the two differentiation coordinate systems. As the inner solution is found by iteratively searching its coordinates until the solution condition is matched, its differential results must be transformed for use by the outer optimization solver in its search for the optimum condition. This requires an iterative differential geometry coordinate system transformation, which is part of the search-engine harness. (non-algorithmic) Find A in TWOPT. to Minimize OBJ. OPTDES. Find Y. in TRAJ. to Match Y. 1. TWOPT. Integrate DIFF. TRAJ. DIFF. X = f(A,X,Y,Z) Y = f(A,X,Y,Z) Z = f(A,X,Y,Z) Optimization. Solver. TWOPT. Find Y. in TRAJ. to Match Y. 1. TRAJ. Integrate DIFF. DIFF. X = f(A,X,Y,Z) Y = f(A,X,Y,Z) Z = f(A,X,Y,Z) AD Arithmetic. \uf0d1A. AD Arithmetic. \uf0d1Y0. DIFF. X = f(A,X,Y,Z) Y = f(A,X,Y,Z) Z = f(A,X,Y,Z) TRAJ. Integrate DIFF. Simulation. Solver. Correlation. Solver. Differential Coordinate System Inheritance. Holistic: Simultaneous Equations.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}