Differentiable Physics for Sensor Placement in Full-Waveform Inversion

In full-waveform inversion (FWI), reconstruction quality depends strongly on sensor placement, yet informative sensor positions are generally unknown in advance. This challenge is particularly acute in physical settings, where the wave simulator used for inversion may differ from the observed system. We present a differentiable active-acquisition loop that alternates short blocks of FWI with continuous receiver-coordinate updates and reacquisition, allowing the geometry to adapt to the evolving reconstruction without requiring a predefined candidate set. We investigate two acquisition design objectives that do not require the true material model: waveform misfit differentiated through the unrolled FWI trajectory and stochastic Gauss--Newton illumination differentiated only through wave-solver sensitivities. In a two-dimensional synthetic acoustic example inspired by guided-wave non-destructive testing, both objectives improve reconstruction relative to a fixed receiver layout across ten paired repetitions. Under the same budget of 100 FWI updates, the waveform misfit and stochastic illumination objectives reduce mean model error by 9.4\% and 16.7\%, compared to the fixed layout. These synthetic results motivate future closed-loop experiments in which physical measurements replace simulated reacquisition.