Keep the Result That Changes the Question
A failed check can narrow a useful question. Two published numerical studies show why the original failure must remain visible.
Topic
Computation & code
Numerical methods, simulation and reproducible computation.
Start with an article
Filter writing on this topic →How Many Equilibria Did the Optimizer Miss?
A folding-energy study separates minima from saddles, global energy ordering from metastability, and branch discovery from proof, asking when an optimizer's attractive shape map leaves something important out.
Can a Mesh Preserve the Event?
A matched-work experiment asks whether uniform, residual, or goal-oriented finite-element meshes best preserve a growing-domain modal-transition time. In this first smoke test, uniform wins.
From Simulation to Certificate
A frozen two-compartment positive-system benchmark separates finite spectral checks from verified all-parameter decay bounds and shows a benchmark-specific cost of restricting the quadratic certificate to be diagonal.
One Integrator Across the Fast-Slow Boundary
A frozen Michaelis-Menten audit separates exact conservation, positivity, and a fixed-step asymptotic limit from accuracy, stiffness failures, and solver-superiority claims.
Random Stress Tests Are Not Certificates
A deterministic interval benchmark shows exactly what a worst-case certificate contains, and why fixed random, Latin-hypercube, and local-search results remain incumbents.
Follow a reading path
All paths →City models: from forecasts to decisions
Start with a classroom timetable, then examine missing traffic states, numerical event errors and the limits of model reduction.
First: When the Timetable Lies to the Ventilation System
Go a little deeper
Project overviews
2026
American Put Free-Boundary Audit
A reproducible obstacle-PDE study resolves the American put exercise boundary and audits price, Greeks, convergence, and complementarity across three numerical methods.
2026
Differential Adhesion Cell-Sorting Audit
A reproducible cellular Potts study separates neighbour sorting from engulfment and tests adhesion, motility, initial conditions, energetics, and cell-shape plausibility.
2026
How Many Equilibria Did the Optimizer Miss?
A controlled folding-energy study audits the difference between finding the lowest known energy, recovering every stable family, and tracing unstable equilibrium branches.
2026
Can a Mesh Preserve the Event?
A matched-work Phase-1 experiment finds that a uniform mesh preserves a growing-domain modal-transition time better than one-shot residual and DWR meshes at 36 elements.
2026
From Simulation to Certificate
A frozen synthetic two-compartment benchmark separates finite spectral checks from verified all-parameter decay certificates and measures a benchmark-specific diagonal restriction gap.
2026
One Integrator Across the Fast-Slow Boundary
A frozen Michaelis-Menten property audit verifies conservation, non-negativity and the fixed-step slow limit while preserving the null result that its AP update does not beat backward Euler on error.