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

Autonomous experimentation has transformed microscopy and materials discovery by enabling closed-loop optimization including imaging and spectroscopy tuning, strucutre property relationship discovery, and exploration of combinatorial libraries. However, most current workflows remain limited to selecting measurements within fixed objective or hypothesis spaces, rather than generating new physical models from experimental data. Here, we introduce an open hypothesis-learning framework that combines symbolic regression with large-language-model-based physical evaluation and implement it for autonomous scanning probe microscopy. Symbolic regression generates candidate analytical relationships directly from sparse measurements, while the language-model evaluator ranks these candidates according to physical plausibility, scaling behavior, and consistency with known mechanisms. We demonstrate the approach on autonomous piezoresponse force microscopy measurements of ferroelectric domain switching in a PZT thin film. Starting from five seed measurements, the workflow evolves from physically incomplete candidate expressions toward interpretable voltage-time growth laws consistent with kinetic domain-wall motion. This work extends autonomous microscopy from closed-loop optimization toward open hypothesis discovery, where candidate physical laws emerge from the experiment itself rather than being specified in advance. More broadly, the framework establishes a route for integrating symbolic regression, physical reasoning, and adaptive experimentation into hierarchical autonomous scientific workflows.

Autonomous agents choose actions using scores that may not reflect experimental success. We developed OPERA, an operator-residual framework for optical experiments. It represents experimental actions as optical operators and evaluates their outcomes using physically interpretable residuals. Operators specify executable changes to measurement, control or reconstruction, while residuals report departures from specified physical conditions. The agent uses both to select, combine or generate operators, and physical performance is evaluated independently against a withheld reference. Across three optical tasks, score-only feedback produced score increases without physical improvement in 23.6--39.0% of decisions, compared with 0.9--1.9% for operator-residual feedback. Operator-residual feedback increased the probability of reaching and maintaining task targets and reduced experimental budgets. Protocols selected in digital twins were transferred to three optical instruments, and repeated experiments showed a lower projection budget in structured-light reconstruction. Together, operators and residuals guide autonomous decisions using measurable physical evidence.

Here, we explore the problem of error propagation mitigation in modular digital twins as a sequential decision process. Building on a companion study that used a Hidden Markov Model (HMM) to infer latent error regimes from surrogate-physics residuals, we develop a Markov Decision Process (MDP) in which the inferred regimes serve as states, corrective interventions serve as actions, and a scalar reward that takes into consideration the cost-benefit tradeoff between system fidelity and maintenance expense. The baseline transition matrix is extracted from the HMM-learned parameters. We then extend the formulation to a Partially Observable MDP (POMDP) that accounts for the imperfect nature of regime classification by maintaining a belief distribution updated via Bayesian filtering, with the HMM confusion matrix serving as the observation model. Both formulations are solved via dynamic programming and validated through Gillespie stochastic simulation. We then benchmark two model-free reinforcement learning algorithms, Q-learning and REINFORCE, to assess whether effective policies can be learned without explicit model knowledge. A systematic comparison of different intervention policies demonstrates that the MDP policy achieves the highest cumulative reward and fraction of time in nominal operation, while the POMDP recovers approximately 95% of MDP performance under realistic observation noise. Sensitivity analyses across observation quality, repair probability, and discount factor confirm the robustness of these conclusions, and the major gaps in the policy hierarchy are statistically significant at $p < 0.001$. The gap between MDP and POMDP performance quantifies the value of information providing a principled criterion for investing in improved classification accuracy.