Physics-informed acquisition weighting for stoichiometry-constrained Bayesian optimization of oxide thin-film growth

We present a physics-informed Bayesian optimization (PIBO) with a concise modification to its acquisition function to incorporate the physical prior knowledge. Specifically, this method multiplies the expected improvement (EI) by a weight encoding prior crystal growth physics. When applied to LaAlO3 molecular-beam epitaxy, the weighting function defines a flat stoichiometric window and penalizes off-window proposals, thereby steering the optimization toward physically plausible regions while maintaining controlled exploration. In a closed-loop optimization, relative to the bare EI, which often proposes off-stoichiometric conditions, the weighted EI constrains the search toward stoichiometric regions while retaining sufficient flexibility to explore neighboring conditions, eventually identifying an optimum slightly beyond the stoichiometric window. Within only 15 growth runs, the lattice constant of the grown LaAlO3 film converged to the bulk value, evidencing efficient and rapid optimization for the ideal stoichiometric growth. Because physics knowledge is incorporated solely through the weighting function, the approach requires only minimal modification to standard BO workflows and is readily applicable to other material systems, offering a general and practical route to AI-driven materials synthesis.

💡 Research Summary

In this work the authors introduce a physics‑informed Bayesian optimization (PIBO) framework that incorporates prior crystal‑growth knowledge directly into the acquisition function rather than the surrogate model. The key idea is to multiply the standard Expected Improvement (EI) acquisition by a deterministic weight w(δ) that encodes stoichiometric constraints for LaAlO₃ (LAO) molecular‑beam epitaxy (MBE). The weight is defined as a flat window of half‑width τ around the ideal La/Al supply ratio c = 1, with a Gaussian decay of width σ outside the window, plus a small ε term that guarantees a non‑zero probability of sampling off‑window points (an ε‑greedy style safeguard). This simple multiplicative modification steers the optimizer toward physically plausible regions while preserving enough exploration to tolerate experimental noise or model misspecification.

The authors apply the method to a three‑dimensional experimental space: (i) La/Al flux ratio δ, (ii) substrate temperature, and (iii) ozone‑nozzle‑to‑substrate distance. After seeding the Bayesian loop with five random growth runs, the weighted EI is maximized at each iteration to select the next experiment. For comparison, a conventional BO using bare EI is also run. The weighted EI consistently proposes points inside or near the stoichiometric window, whereas the bare EI frequently suggests highly off‑stoichiometric conditions that lead to phase failure (no LAO diffraction peaks) or large lattice‑constant deviations.

Within only 15 closed‑loop growth cycles, the lattice‑constant deviation Δc (difference between the measured c‑axis lattice constant and the bulk value) converges to zero, indicating that the film’s pseudocubic lattice constant matches that of bulk LAO. The optimal conditions identified are δ = 0.88, temperature = 892 °C, and nozzle‑distance = 5.5 mm—slightly outside the strict stoichiometric window, reflecting realistic calibration offsets and non‑unity sticking coefficients. X‑ray diffraction shows a ten‑fold increase in the LAO (002) peak intensity and the appearance of Laue fringes, confirming markedly improved crystallinity and surface smoothness. A homoepitaxial film grown under the same conditions on an LAO substrate exhibits no secondary phases, further validating the method’s ability to produce high‑quality single‑crystal oxide layers.

The paper also discusses extensions of the weighting scheme. For materials with asymmetric volatility (e.g., SrRuO₃ where RuO₂ is volatile), the weight can be made asymmetric by using different decay widths on the Ru‑rich and Ru‑poor sides. Moreover, temperature and oxygen‑partial‑pressure constraints could be incorporated using thermodynamic data such as free‑energy of formation or Ellingham diagrams, turning the weight into a multidimensional physics‑based prior.

Overall, the study demonstrates that a modest, mathematically transparent modification to the acquisition function can dramatically improve the efficiency and robustness of autonomous materials synthesis. By embedding domain knowledge as a weight, the optimizer avoids unphysical regions, reduces experimental failures, and converges to optimal growth parameters with far fewer iterations than conventional BO. The approach is readily transferable to other complex oxides, semiconductor epitaxy, and catalytic material discovery, offering a practical pathway toward AI‑driven, physics‑guided experimental automation.