FIDE: Fiber-Informed Differentiable Experimental Design for Reference-Relative Law Dynamics

Pietro Zanotta, Ján Drgoňa

Aggregate measurements generally leave an evolving population law underdetermined, so different measurement systems can be equally adequate for a scientific task while constraining different aspects of the law. We study how to resolve this residual design freedom in baseline-preserving settings, where an existing dynamical model remains the working baseline outside quantities explicitly valued by the task. \textbf{F}iber-\textbf{I}nformed \textbf{D}ifferentiable \textbf{E}xperimental Design (\textbf{FIDE}) completes each candidate's aggregate constraints by information projection relative to a common frozen reference, then ranks scientifically adequate designs by the dynamical revision required to realize the resulting completed paths. The resulting \emph{Full action} is the minimum mean-squared velocity correction needed to realize a completed path; equivalently, its square root is the sharp reference-relative expectation-rate discrepancy over a gradient-normalized Sobolev class. This defines a conditional minimum-revision principle for baseline-preserving design rather than a generic truth-recovery objective. Experiments show that this preference changes sensor selection, can…