Towards Autonomous Experimentation: Bayesian Optimization over Problem Formulation Space for Accelerated Alloy Development

TL;DR

The paper tackles the challenge of fixed problem formulations in autonomous materials discovery by proposing Bayesian optimization over a problem formulation space, enabling a system to identify the most valuable problem to solve as new data arrive. It formalizes this space with a P_K construction and uses a Normal Boundary Intersection framework to connect problem formulations to a multi-attribute utility via Gaussian process surrogates, complemented by AI-assisted discovery that filters infeasible problems. A demonstrative in silico study on Mo-Nb-Ti-V-W alloys demonstrates that the framework converges to a sweet spot that satisfies key thresholds for ductility, strength, density, and solidification range, illustrating potential reductions in discovery time and resources. The work lays groundwork for future integration of human feedback to dynamically adapt preferences in real-world experiments and to balance stakeholder viewpoints through composite utilities, advancing autonomous design in high-entropy and refractory alloy development.

Abstract

Accelerated discovery in materials science demands autonomous systems capable of dynamically formulating and solving design problems. In this work, we introduce a novel framework that leverages Bayesian optimization over a problem formulation space to identify optimal design formulations in line with decision-maker preferences. By mapping various design scenarios to a multi attribute utility function, our approach enables the system to balance conflicting objectives such as ductility, yield strength, density, and solidification range without requiring an exact problem definition at the outset. We demonstrate the efficacy of our method through an in silico case study on a Mo-Nb-Ti-V-W alloy system targeted for gas turbine engine blade applications. The framework converges on a sweet spot that satisfies critical performance thresholds, illustrating that integrating problem formulation discovery into the autonomous design loop can significantly streamline the experimental process. Future work will incorporate human feedback to further enhance the adaptability of the system in real-world experimental settings.

Figures (8)

• Figure 1: Schematic of a real development campaign to identify refractory alloys for ultra-high temperature applications up to 2000 $^{\circ}$C---see Ref. acemi2024multi for more details. Rather than a fixed optimization problem, the development effort turned into a highly dynamic process where the alloy design problem formulation changed at each batch (BT): BT1–4 differ by the addition of constraints and changes in the selection policy, informed by experimental results. BT5 is the first batch to use machine learning for “closing the experimental loop” via Bayesian optimization. W: Tungsten Constraint. ST: Solidus temperature constraint. BCC: phase stability constraint. YS: Yield strength constraint. B/G: Pugh ratio ductility constraint. CP: Cauchy pressure ductility constraint. VEC: Valence electron concentration ductility constraint. CSC: Hot cracking susceptibility coefficient constraint. BAL: Balling resistance constraint. Reproduced with permission from acemi2024multi.
• Figure 2: Illustration of the normal boundary intersection method for discovering the optimal Pareto front. The method begins by initializing subproblems over the Convex Hull of Individual Minima (CHIM) and then sequentially solving them by searching along a quasi-normal vector directed toward the origin. The solution corresponding to the farthest point from the CHIM is identified as part of the Pareto front.
• Figure 3: Step-by-step representation of our proposed framework. After completing the initialization steps, the Bayesian design loop explores the problem formulation space to discover the optimal problem whose solution maximizes a utility value function.
• Figure 4: Comparison of optimum utility versus the average achieved utility from 30 simulations. Best and worst simulation results are also shown to illustrate variation.
• Figure 5: Utility value functions constructed to capture the decision-maker's preferences for different QoIs. Green stars indicate the optimum properties that maximize the multi-attribute utility function.