AI BriefingTwindex generates replayable certificates to prove parameter identifiability in ODEs and PDEs
·2026.11.10 02:50
Key point
Twindex generates JSON certificates that verify if distinct parameter values, such as R0 = 2.5 and R0 = 20, fit data equally well under bounded noise assumptions.
Details
- Twindex identifies "twins" where different parameter sets fit data equally well, providing exact proofs that no estimator can recover the parameter better than +/- half the gap under stated bounded-noise assumptions.
- A real-data example using the 1978 boarding-school flu outbreak (BMJ) showed SIR models with R0 = 2.5 and R0 = 20 both fit 5 days of counts, with Twindex identifying the specific next-day count that would separate them.
- The tool supports ODE models with polynomials, division, exp, sin, and cos, as well as 1-D/2-D elliptic and heat-equation PDEs, and allows numerical audits of any Python simulator.
- Proofs are replayable via a standard-library Python checker using rational arithmetic (no floats), with a browser demo running locally via Pyodide at ~0.2 s per proof.
- Limitations include bounded noise assumptions, conditional proofs based on stated model and noise bounds, and difficulty scaling beyond a few parameters.
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