CASCADE v3.1GlobalMOO + pymoo

CASCADE v3.1

Calculus-Adaptive Scale-Calibrated Derivative Engine

5-step pipeline using GlobalMOO for k-discovery and edge-finding, pymoo for interior optimization

The 5-Step CASCADE Pipeline

CASCADE transforms any physics problem into a form where MOO can explore regions near singularities that classical optimization cannot reach.

1. Find k
2. Transform
3. Find Edges
4. Search
5. Convert

Pipeline Steps

Implementation: simulations/utils/cascade.py,meta_calculus/moo_integration.py

1

Find Optimal k (GlobalMOO)

Use GlobalMOO to discover which calculus variant (k-value) is optimal for your problem's singularity structure. The k-lookup table provides starting points.

Method: NSGA-II MOO
Output: Optimal k, w, p
Example: k=-1 for 1/r
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2

Convert Problem to NNC Format

Transform the problem bounds into NNC space using k from Step 1. Frame finding the solution as a multi-objective optimization.

x_nnc = alpha_k(x_physics)// Forward transform
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3

Find Edges (GlobalMOO)

Use GlobalMOO to discover the edges of the simulation space - the boundaries of what's achievable. This is GlobalMOO's unique capability.

Objectives: Distance to singularity, scheme disagreement
Output: [lower_bound, upper_bound] edges
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4

Interior Search (pymoo NSGA-II)

Use the defined edges to help a specialized model search for the particular MOO answer within the bounded region.

Bounds: Constrained by Step 3 edges
Output: Pareto front in NNC space
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5

Convert Back to Regular Math

Transform the NNC solutions back to classical physics coordinates for interpretation.

x_physics = alpha_k^(-1)(y_nnc)// Inverse transform

Interactive Visualization

Implementation Files

Core CASCADE

simulations/utils/cascade.pymeta_calculus/moo_integration.py

Documentation

docs/THREE-MOO-CASCADE-METHODOLOGY.mdsimulations/CASCADE_QUICK_REFERENCE.md