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

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. $\text{F}$iber-$\text{I}$nformed $\text{D}$ifferentiable $\text{E}$xperimental Design ($\text{FIDE}$) 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 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 help or harm withheld downstream predictions depending on baseline reliability, can be used prospectively from aggregate predictions, and remains computationally usable for a $32$-dimensional configuration law.