Capstone sequence · 3 projects
Projects, Applications & Research Pathways
Synthesize everything from Levels 0–3 into open-ended projects that combine classical analysis, numerical methods, and agent-based scientific computing.
Each project requires 5–7 hours and produces a complete deliverable: code, report, plots, and metrics.
Capstone Projects
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4.1 — Agent-Based Simulation of Physical Systems
Build an agent that simulates a multi-body gravitational system, adaptively selecting time steps and integration methods to maintain accuracy and stability.
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4.2 — Neural Solver vs Classical Solver Benchmark
Implement both a classical RK4/finite-difference solver and a neural ODE/PINN solver for the same problem, then benchmark accuracy, speed, and generalization.
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4.3 — Scientific Machine Learning for Real Data
Apply SINDy or PINN methods to a real-world dataset (epidemiological, climate, or mechanical vibration data) to discover or validate governing equations.