Adaptive sensing beyond non-adaptive information limits: End-to-end co-design of geometry, policy, and inference

Inverse design has transformed vast physical parameter spaces into a substrate for emergent functionality, raising the tantalizing prospect of relocating intelligence from the digital domain into the physical world itself. Nowhere is this prospect more consequential than in sensing, where the analog-to-digital interface imposes a fundamental bottleneck: information not captured by the hardware is irrevocably lost to any downstream algorithm. Existing approaches improve information capture through either sensor hardware optimization or adaptive measurement strategies operating on fixed hardware, but rarely both in concert. A principled migration of intelligence from digital to physical demands their joint optimization: the sensing geometry must be co-designed with a policy that determines what to measure next. We formulate this co-design as joint dynamic programming (joint-DP), a unified optimization over sensor geometry and a Bellman-optimal adaptive measurement policy. The outer hardware gradient is obtained through differentiable dynamic programming with a sharp Bellman maximum. A hierarchy of relaxations extends the framework from small discrete POMDPs to freeform photonic topologies with more than $10^5$ design pixels.