ModelScript Algorithms Catalog

ModelScript is powered by a comprehensive foundation of peer-reviewed mathematical, compiler, and formal verification algorithms. Rather than relying on opaque external black boxes, ModelScript implements these algorithms natively in WebAssembly and TypeScript, with inline citations, architectural rationales, and explicit tracking of upstream inputs and downstream consumers.

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Computational Map

The algorithms catalog spans seven core domains across the compilation, simulation, and verification pipelines:

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Algorithm Directory

Category	Primary Algorithms	Implementation Package
Structural DAE	Pantelides Algorithm, Tarjan BLT, Cellier-Elmqvist Tearing	@modelscript/runtime
Acausal Balancing	Acausal Potential Equalization, Kirchhoff Flows, Stream Mixing	@modelscript/modelica
Autodiff & Relaxations	Dual Numbers, AdTape, CPR Graph Coloring, McCormick, Affine, Hybrid Adjoint Saltation Matrices, Aitken Dynamic $\mathrm{\Delta }$-Relaxation	@modelscript/runtime & @modelscript/simulate
Numerical Solvers	Tsit5, Rodas-4P, TR-BDF2, SDE, BVP	@modelscript/simulate
Optimization	L-BFGS-B, CMA-ES, Differential Evolution, PSO, NSGA-II	@modelscript/simulate
SMT & Verification	Nelson-Oppen, CDCL SAT, Craig Interpolation, HC4, STL, Zonotopes	@modelscript/runtime/formal
Model Checking & Safety	Spacer CHC PDR, IC3 Engine, Stochastic Barrier Certificates, WebGPU OWL 2 RL Reasoner, ISO 26262 / DO-178C Back-to-Back Equivalence	@modelscript/runtime/formal & @modelscript/runtime/gpu
Abstract Interpretation	WTO Fixpoint, TVPI, Octagon DBM, Array Segments, DDE Method-of-Steps Flowpipes, Hamilton-Jacobi-Isaacs (HJI) Level-Set Reachability	@modelscript/runtime/formal & @modelscript/runtime/analysis
Graph Rewriting	Triple Graph Grammars, CPA, WCOJ, E-Graphs, GSS, Salsa	@modelscript/dsl
Linear Memory Structures	Roaring Bitmaps, Front-Coded Dictionary, Paged B+ Tree	@modelscript/runtime
Scientific & Digital Twins	Sparse Cholesky, Sparse LU, Householder QR, Gröbner, POD, Buckingham Pi, Arena MHE, Joint-State UKF & MCMC Calibration, Page-Hinkley / CUSUM Drift, RUL Prognostics	@modelscript/runtime & @modelscript/simulate
SDP, BVP, Continuum & CAD	Primal-Dual SDP, Multiple Shooting BVP, CSG, WebGPU D3Q19 LBM CFD, Tet4/Tet10 Corotational FEA, STEP B-Rep Mesher, Swept-Volume Clearance, GD&T Stack-Up, CAD Parameter Inversion, ECAD Gerber / Router / DRC	@modelscript/runtime, @modelscript/simulate & @modelscript/cad
Diagram Layout & Diffing	Tamassia TSM, Port ILP Solver, Dogleg Channel Router, Fault Tree / Sequence / Swimlane Layouts, PSCAD SLD Routing, Semantic Visual Diffing, CRDT Collaborative Presence	@modelscript/diagram