From Closed-Loop Optimization to Open Decision Making: Coupled Digital Twins for Predictive and Autonomous Microscopy

Automated experimentation is moving from closed-loop optimization toward open decision-making, where human or AI planners must forecast the consequences of candidate actions before executing them. Such forecasts require a model of both sides of the experiment: how the sample is likely to respond and what the instrument is likely to detect. We therefore introduce a coupled digital-twin framework that separates these roles and then links them. In this framework, the sample twin encodes material state inferred from prior knowledge and measurements till the moment. The instrument twin captures signal formation, feedback dynamics, and operating constraints based on prior knowledge. When coupled, the two twins estimate expected outcomes, uncertainty, and risk for candidate microscope operations. For amplitude-modulation scanning probe microscopy, we realize this framework with a physics-informed encoder of force-distance curves, a deterministic scanner model of cantilever and feedback dynamics, and sparse learned residual corrections. The encoder first recovers scanner-driving descriptors with sub-nanometer accuracy. The calibrated scanner then reproduces typical traces within a few nanometers and identifies operating-point noise amplification as the main source of mismatch. Supplementary phase analysis localizes residual error to the phase channel, which clarifies where added physics is needed. Together, these results establish coupled sample and instrument twins as a practical foundation for predictive microscope operation and autonomous experimental planning.