Bayesian Co-Navigation of a Computational Physical Model and AFM Experiment to Autonomously Survey a Combinatorial Materials Library (2512.08084v1)

Published 8 Dec 2025 in cond-mat.mtrl-sci

Abstract: Building autonomous experiment workflows requires transcending beyond the data-driven surrogate models to incorporate and dynamically refine physical theory during exploration. Here we demonstrate the first fully automated experimental realization of Bayesian co-navigation - a framework in which an autonomous agent simultaneously runs a physical experiment and a computationally expensive physical model. Using an automated AFM platform coupled to a kinetic Monte Carlo (kMC) model of thin-film growth, the system infers a set of effective bond energies for the (CrTaWV)x-Mo(1-x) pseudo-binary combinatorial library, progressively adjusting the kMC parameters to decrease the epistemic disparity between simulation and experiment. This real-time theoretical refinement enables the kMC model to capture the behavior of the specific materials system and reveals the mechanistic role of hetero-bonding in governing surface diffusion. Together, these results establish co-navigation as a general strategy for tightly integrating physical models with autonomous experimental platforms to produce interpretable and continually self-correcting theoretical modelling of complex materials systems.

Summary

The paper demonstrates that the Bayesian co-navigation algorithm dynamically couples a kinetic Monte Carlo physical model with an AFM experiment to enable autonomous exploration of combinatorial thin-film libraries.
It employs active learning and Bayesian optimization to drastically reduce the number of AFM scans while ensuring real-time calibration and mechanistic interpretability.
The framework reveals critical material insights, including energetically favorable hetero-bond ordering and U-shaped roughness profiles that highlight composition-dependent surface evolution.

Introduction

The paper "Bayesian Co-Navigation of a Computational Physical Model and AFM Experiment to Autonomously Survey a Combinatorial Materials Library" (2512.08084) introduces a fully automated experimental framework wherein a Bayesian co-navigation algorithm tightly couples a kinetic Monte Carlo (kMC) physical model and an atomic force microscopy (AFM) platform. The system autonomously explores combinatorial thin-film libraries, dynamically calibrating the theoretical model in real time as experiments proceed. This marks a substantive departure from traditional Bayesian optimization (BO) paradigms, which typically rely on static or offline parameter calibration and surrogate-driven approaches. The core contribution lies in algorithmically intertwining experiment and theory, facilitating rapid discovery, interpretability, and mechanism elucidation in materials science.

Background: Autonomous Experimentation and Existing Limitations

Contemporary autonomous materials discovery platforms exploit high-throughput instrumentation conjoined with BO and ML surrogates to efficiently traverse multidimensional synthesis and characterization spaces. However, mainstream BO implementations—often using Gaussian Process (GP) surrogate models—either ignore or treat physical models as fixed priors. Recent works have augmented BO with LLMs to improve acquisition strategies and incorporate priors, but all fundamentally decouple expensive physical models and experiment within the optimization loop (2512.08084, Ramos et al., 2023, Huang, 7 Aug 2025).

Multi-fidelity and multitask BO strategies provide adaptive allocation of sampling budgets between varying information sources, but do not address settings where both theory and experiment are expensive and non-stationary. Moreover, direct use of low-fidelity surrogates introduces significant epistemic uncertainty, limiting mechanistic interpretability and accuracy for complex materials systems.

The co-navigation architecture operationalizes a multi-loop active learning protocol, integrating:

A theoretical (simulation) loop with a kMC model, where the most salient parameters (effective A-A, B-B, and A-B bond energies) serve as hyperparameters subject to iterative inference.
An experimental loop using AFM for acquisition of compositional surface roughness data across a (CrTaWV)x-Mo(1-x) pseudo-binary thin-film library.
An outer theory-update loop (T-loop) that:
1. Quantifies model-observation mismatch (using MSE over predicted versus measured roughness),
2. Employs BO to refine model hyperparameters,
3. Ensures the theoretical and experimental surrogates are continuously aligned.

This approach enables adaptive, composition-resolved exploration, avoiding inefficient grid-based characterization while guaranteeing that both theory and experiment co-evolve. Crucially, the framework calibrates the digital twin (kMC model) online, rather than relying on offline iterative or batchwise model adjustments.

Experimental and Simulation Strategies

Physical System

The combinatorial library is synthesized by co-sputtering from a CrTaWV alloy and Mo targets; the system exhibits a quasi-linear composition gradient and a strong, non-monotonic evolution of surface roughness. AFM scans establish the ground-truth with 100 compositional points, revealing a U-shaped roughness profile with a maximum near $x \approx 0.7$ .

Theoretical Model

The kMC model is constructed as a two-dimensional lattice system where surface diffusion and morphology are governed by tractional kinetic rates parameterized by effective broken-bond energies ( $E_{AA}$ , $E_{BB}$ , $E_{AB}$ ) and step-edge effects. Each kMC simulation deposits $10^4$ atoms, with the simulation output empirically rescaled to match AFM-measured roughness values.

Autonomous Execution

Initial model parameters are randomized; exploration commences with five initial experimental and theoretical points. The system proceeds with a 10:1 simulation-to-experiment ratio, leveraging uncertainty-driven acquisition (LCB) and a memory-tail mechanism to prevent overfitting to obsolete parameter regimes. The implementation achieves efficient convergence within 201 iterations, compared to over 16 hours for exhaustive experimental characterization.

Results and Analysis

Model Convergence and Bond Energy Inference

The co-navigation process yields theoretical roughness profiles converging toward the experimentally observed shape, notably reproducing the U-shaped roughness-composition curve and the position of its maximum. Early-stage large parametric excursions give way to a stable regime where the inferred bond energies satisfy the robust ordering $E_{AB} > E_{AA}, E_{BB}$ .

This pattern, where hetero-bonds (A-B, CrTaWV–Mo) are energetically more favorable than homo-bonds, directly identifies composition-dependent limitation of adatom surface diffusion (manifested as a roughness maximum at intermediate compositions). The system thus transitions from broad hyperparameter exploration (marked by elevated MSE) to exploitation and fine-tuning, with the algorithmic T-loop driving theory-experiment alignment.

Efficiency and Data Economy

The co-navigation framework substantially reduces the number of required AFM scans (a 10-fold reduction relative to theory queries and drastic reduction relative to brute-force mapping) while maintaining direct interpretability and retaining mechanistic accuracy. The memory-tail protocol for the theoretical surrogate model avoids non-stationarity induced by evolving kMC parameters, ensuring statistical robustness in surrogate-driven BO.

Implications for Model Generalizability and Autonomous Discovery

The direct coupling of theoretical model calibration to ongoing experimental exploration enables not only efficient coverage of combinatorial materials spaces but also physical mechanism elucidation. The theoretical surrogate receives continuous correction from real observations, inherently producing a sample-efficient, physically valid digital twin.

Broader Implications and Future Perspectives

The Bayesian co-navigation protocol sets a new methodological baseline for autonomous experimentation in domains where both model and experiment are expensive and mechanistic interpretability is required. The approach transcends surrogate-driven paradigms and establishes dynamic theory-experiment co-evolution as a central principle for automated materials discovery.

Practical implications include:

Rapid digital twin realization: The framework can be generalized across a wide variety of systems featuring expensive, high-fidelity models and experimental throughput constraints.
Mechanistic insight extraction: Direct inference of key physical parameters during autonomous experiments fosters a deeper understanding of complex phenomena, bridging the simulation-experiment gap.
Scalable, interpretable autonomy: The architecture is extensible to richer physical models, complex design spaces, and even further integration with AI-based prior design (including LLMs for acquisition functions and priors).

Future research may incorporate more complex multi-scale models, on-the-fly surrogate acceleration for heavier computations, and integration with closed-loop generative design systems. Extension to domains like catalysis, battery design, and functional thin films with nontrivial order-disorder transitions is a natural direction.

Conclusion

The demonstrated Bayesian co-navigation of an AFM experiment and a kinetic Monte Carlo physical model effectively combines real-time theoretical model calibration with autonomous, sample-efficient experimental exploration. The framework yields both accurate material-specific predictions and direct mechanistic insight into composition-dependent surface evolution within a combinatorial library. The process establishes co-navigation as a scalable, interpretable, and generalizable strategy for the synthesis of self-correcting digital twins in complex materials systems, with significant ramifications for the future of autonomous experimentation and AI-driven scientific discovery.