Coherent elastic strain is an important but often neglected contribution to phase-separation thermodynamics in alloy systems where decomposed phases have appreciable lattice mismatch. We develop a thermodynamic framework that incorporates coherent elastic compatibility directly into phase-diagram calculations alongside conventional CALPHAD chemical free energies. Applied to the BCC Nb-V system, the framework shows that coherent elasticity substantially suppresses phase separation, narrows the miscibility gap, and lowers the critical temperature toward experimentally observed values. Beyond these quantitative effects, the coherent constraint qualitatively alters the interpretation of phase equilibria: the equilibrium decomposition compositions become functions of both temperature and overall alloy composition, so the two-phase boundary no longer represents unique coexistence compositions. These results establish coherent elasticity as a key thermodynamic factor in lattice-mismatched systems and provide a general framework for coherent phase-diagram modeling.

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.

Phase diagrams are fundamental for understanding phase stability and guiding the synthesis of new materials. However, constructing high-dimensional phase diagrams through exhaustive CALPHAD (CALculation of PHAse Diagrams) computations remains costly. We introduce a Bayesian Active Learning for Phase Diagram Discovery (BALPI) framework that efficiently identifies phase stability regions by adaptively sampling the thermodynamic space using uncertainty-aware acquisition strategies. BALPI integrates Gaussian Process Classifiers and Regressors within two complementary formulations-classification and level-set estimation-and introduces non-myopic Bayesian acquisition functions, including the Soft Mean Objective Cost of Uncertainty (SMOCU) and an extended straddle (e-straddle) criterion. Using CALPHAD-based phase stability predictions as the ground-truth oracle, BALPI achieves accurate reconstruction of phase boundaries with significantly fewer queries than conventional label propagation and label spreading baselines. Results on SiO2-Al2O3-MgO and Ni-Ti-Hf-Cu systems demonstrate that BALPI captures disconnected phase regions and achieves consistent reductions in Bayesian error and computational cost. More importantly, this work establishes BALPI as a general framework for uncertainty-guided phase diagram discovery and highlights the potential of Bayesian active learning to accelerate computational thermodynamics and materials design, through the efficient exploration of the phase stability landscape at much lower costs relative to competing strategies.

This review develops a four-level metallurgy-informed Bayesian optimization framework for alloy discovery, validated through closed-loop experimental campaigns.

Closed-loop materials discovery iterates between proposing candidate structures and evaluating their properties, and property evaluation dominates the cost. In the generative variant, a learned prior proposes candidate crystals and a property oracle scores them; we ask whether a cheap probabilistic surrogate can triage the generator's output, and what such a surrogate must do well. Across three architecturally distinct pretrained diffusion priors (MatterGen, CrystalFlow, ADiT) and two targets (room-temperature heat capacity and bulk modulus), we insert a Gaussian process acquisition gate between structure generation and the oracle in an RL-steered generative workflow. The gate matches or exceeds ungated fine-tuning of the generative model while capping oracle calls at a fixed per-cycle budget. Budget-matched ablations isolate the mechanism. At an identical four-call budget, ranking-based selection outperforms arbitrary selection, confirming that the gain comes from the surrogate's choice; the gate comes within ∼9% of exhaustive oracle spending at roughly one-fifth of the calls. A density-functional-theory check of the bulk-modulus discoveries confirms the learned oracle to within 2.5% on average and the surrogate's ranking of the generated structures at Spearman ρ= 0.94. A cross-factorial benchmark of surrogate performance spanning mechanical, electronic, and vibrational properties identifies pretrained ORB embeddings with a Gaussian process as the most reliable combination, which we adopt as the building blocks of the proposed workflow. The complete pipeline is released as open-source software.

Refractory complex concentrated alloys (RCCAs), composed of multiple principal refractory elements, are promising candidates for high-temperature structural applications due to their exceptional thermal stability and high melting points. However, their mechanical performance is often compromised by interstitial impurities-particularly oxygen, nitrogen, and carbon-which segregate to grain boundaries and promote embrittlement. In this study, we investigate the solubility and thermodynamic behavior of oxygen interstitials in a model Nb45Ti25Hf15Ta15 RCCA system. We synthesized (Nb45Ti25Hf15Ta15)100-xOx alloys with varying oxygen contents (x=0-5 at.%) via plasma arc melting and characterized their phase evolution and microstructure using XRD, SEM, and TEM. Complementary computational modeling was performed using machine-learning interatomic potentials (MLIPs) integrated with Monte Carlo simulations to probe oxygen interactions at the atomic scale. Our results reveal an effective solubility limit for oxygen between 0.8 and 1.0 at.%, beyond which HfO2 formation is energetically favorable. This combined experimental-computational framework provides a predictive approach for managing interstitial behavior in RCCAs, enabling improved alloy design strategies for enhanced mechanical performance.

The acceleration of materials discovery requires digital platforms that go beyond data repositories to embed learning, optimization, and decision-making directly into research workflows. We introduce DataScribe, an AI-native, cloud-based materials discovery platform that unifies heterogeneous experimental and computational data through ontology-backed ingestion and machine-actionable knowledge graphs. The platform integrates FAIR-compliant metadata capture, schema and unit harmonization, uncertainty-aware surrogate modeling, and native multi-objective multi-fidelity Bayesian optimization, enabling closed-loop propose-measure-learn workflows across experimental and computational pipelines. DataScribe functions as an application-layer intelligence stack, coupling data governance, optimization, and explainability rather than treating them as downstream add-ons. We validate the platform through case studies in electrochemical materials and high-entropy alloys, demonstrating end-to-end data fusion, real-time optimization, and reproducible exploration of multi-objective trade spaces. By embedding optimization engines, machine learning, and unified access to public and private scientific data directly within the data infrastructure, and by supporting open, free use for academic and non-profit researchers, DataScribe functions as a general-purpose application-layer backbone for laboratories of any scale, including self-driving laboratories and geographically distributed materials acceleration platforms, with built-in support for performance, sustainability, and supply-chain-aware objectives.

Whereas compositionally graded alloys (CGAs) are often proposed for use in structural components where the combination of alloys within a single part can substantially improve performance, this work proposes and demonstrates the rapid design, synthesis, and characterization of CGAs for the purpose of alloy space exploration. To illustrate this, a composition gradient in the CoCrFeNi alloy space was planned between the maximum and minimum stacking fault energy (SFE) predicted by an existing state-of-the-art machine learning model. One of the goals of this study was to investigate the applicability of this model across a large range of output values and compositions. The compositional gradient path was designed to be monotonic in the SFE and to avoid regions that did not meet constraints predicted via CALculation of PHase Diagrams (CALPHAD). Compositions were selected to produce a linear gradient in SFE and were built using laser directed energy deposition (L-DED) with elemental powders. The resulting gradient was characterized for microstructure and mechanical properties, including hardness, elastic modulus, and strain rate sensitivity. More broadly, the results of this investigation demonstrate the ability of the methods employed to expose blind spots in alloy models and gain knowledge about alloy design spaces in a high-throughput manner.

Seemingly identical Bulk Metallic Glasses (BMG) often exhibit strikingly different mechanical properties despite having the same composition and fictive temperature. A postulated mechanism underlying these differences is the presence of "defects" and density variations. Motivated by this perspective, we introduce physically realistic and quantitatively controllable density fluctuations in molecular dynamics simulations to systematically examine their role in shear band formation under applied stress. We find that the critical shear strain is strongly dependent on the magnitude and size of the fluctuations, revealing a nonlinear activation behavior associated with localized rejuvenation. This finding also elucidates why, historically, critical shear stresses obtained in simulations have differed so much from those found experimentally, as typical simulations setups might favor unrealistically uniform geometries.

Identifying regions of design space subject to spinodal decomposition is a critical component of alloy design in high-dimensional composition spaces. In cases where designers are seeking to exploit spinodal microstructures to tailor alloy properties, prediction of microstructure evolution and morphology is also needed. In this work, we present a Machine Learning Interatomic Potential (MLIP)-trained, CALPHAD-based, open-source workflow for high-throughput microstructure stability analysis and visualization. In this workflow, coherent strain contributions are captured via high-throughput MLIP elastic constant calculations. To predict microstructure morphology for compositions of interest, MLIP-generated thermodynamic models are fed into an elasto-chemical phase field simulation. Both stability analyses and phase-field simulations utilize analytically-derived Gibbs energy Hessians to improve computational efficiency and accuracy over finite difference approximations. We demonstrate this workflow by investigating microstructure stability in the Hf-Nb-Ti-V quaternary system.

Three-dimensional concrete 3D printing (3DCP) faces persistent challenges in achieving consistent geometric quality and reproducible printability across varying process conditions, limiting its large-scale industrial adoption. This study presents a data-driven framework that integrates experimental characterization with machine learning-based prediction to evaluate and optimize geometric quality in 3DCP. Functional geometries (cubes, overhangs, and bridges) were fabricated using a robotic printing system at controlled nozzle speeds (75–150 mm/s) and flow rates (478–593 cm3/s), resulting in 46 cubes, 21 overhangs, and 66 bridges. High-resolution imaging enabled quantitative extraction of geometric indicators, including layer height variation, angle deviation, and bridge span stability, which were consolidated into a weighted geometric quality metric. Two predictive models were developed: the first estimated geometric deviations from process parameters, while the second inversely predicted optimal process parameters for a desired material response. Among several algorithms, CatBoost and DecisionTree regressors exhibited the strongest performance, with the best model achieving an R2 of 0.74 and a mean absolute error of 1.5 mm. The derived printability map identified optimal operational regions (100–115 mm/s, 470–490 cm3/s) corresponding to stable, high-quality prints. This integrated experimental–computational approach establishes a quantitative foundation for real-time process optimization, adaptive control, and quality assurance in additive construction.

Many materials design attributes that are central to adoption, such as aesthetics, perceived quality, or user-specific preferences, are difficult to quantify directly, making preference feedback a practical proxy for optimization. Here we present a preference-driven Bayesian optimization framework and demonstrate it using ring color as a concrete case study. This case study simulates a scenario in which a jeweler synthesizes a ring with a given chemistry and presents it to a stakeholder, who expresses a preference relative to an incumbent ring color. Our approach, preferential Bayesian optimization (PBO), learns a latent utility function over alloy composition space, with perceived color obtained via a Thermo-Calc optical forward model. Using preference feedback, the framework iteratively proposes new alloy chemistries predicted to better align with user aesthetic preferences. After a limited number of proposed alloys and their associated colors, the user selects the most desirable option, guiding the search toward optimal aesthetic outcomes. We then evaluate the cost of the proposed alloys and identify a cost-aesthetic Pareto front, enabling informed trade-offs between affordability and visual appeal. The proposed framework is readily applicable to materials design problems in which subjective or hard-to-measure attributes play a dominant role in decision-making.

The accelerating pace and expanding scope of materials discovery demand optimization frameworks that efficiently navigate vast design spaces with complex response surfaces while judiciously allocating limited evaluation resources. We present a cost-aware, batch Bayesian optimization scheme powered by deep Gaussian process (DGP) surrogates and a heterotopic querying strategy. Our DGP surrogate, formed by stacking GP layers, models complex hierarchical relationships among high-dimensional compositional features and captures correlations across multiple target properties, propagating uncertainty through successive layers. We integrate evaluation cost into an upper-confidence-bound acquisition extension, which, together with heterotopic querying, proposes small batches of candidates in parallel, balancing exploration of under-characterized regions with exploitation of high-mean, low-variance predictions across correlated properties. Applied to refractory high-entropy alloys for high-temperature applications, our framework converges to optimal formulations in fewer iterations with cost-aware queries than conventional GP-based BO, highlighting the value of deep, uncertainty-aware, cost-sensitive strategies in materials campaigns.

CALPHAD model parameter optimization is inherently challenging due to non-smooth objective functions, high-dimensional parameter spaces, and the need for uncertainty quantification (UQ). Traditional weighted nonlinear least squares approaches are computationally efficient but local, whereas black-box global optimizers and ensemble Markov Chain Monte Carlo (MCMC) methods provide broader exploration at substantial computational cost. The objective of this work is to combine the global exploration capability of gradient-informed Hamiltonian Monte Carlo-specifically the No-U-Turn Sampler (NUTS)-with local deterministic refinement using BFGS to efficiently optimize multicomponent CALPHAD models with minimal manual intervention. Analytic gradients are computed via the Jansson derivative framework. The methodology is demonstrated on the Cr-Fe binary system and extended to the Cr-Fe-Ni ternary system with 32 degrees of freedom. For Cr-Fe, NUTS achieves comparable or superior optimality relative to ensemble MCMC while requiring over an order-of-magnitude fewer likelihood evaluations. Parameter uncertainties are quantified through NUTS sampling and propagated to thermodynamic observables using local expansion, demonstrating a novel modular approach that combines binary and ternary parameter subsets without requiring global relaxation. These results establish gradient-informed exploration as a scalable strategy for multicomponent CALPHAD optimization and provide a practical route towards efficient higher-order database development with quantified uncertainty.

Bayesian Optimization with multi-objective acquisition functions such as q-Expected Hypervolume Improvement (qEHVI) requires efficient candidate optimization to maximize acquisition function values. Traditional approaches rely on continuous optimization methods like Sequential Least Squares Programming (SLSQP) for candidate selection. However, these gradient-based methods can become trapped in local optima, particularly in complex or high-dimensional objective landscapes. This paper presents a simulated annealing-based approach for candidate optimization in batch acquisition functions as an alternative to conventional continuous optimization methods. We evaluate our simulated annealing approach against SLSQP across four benchmark multi-objective optimization problems: ZDT1 (30D, 2 objectives), DTLZ2 (7D, 3 objectives), Kursawe (3D, 2 objectives), and Latent-Aware (4D, 2 objectives). Our results demonstrate that simulated annealing consistently achieves superior hypervolume performance compared to SLSQP in most test functions. The improvement is particularly pronounced for DTLZ2 and Latent-Aware problems, where simulated annealing reaches significantly higher hypervolume values and maintains better convergence characteristics. The histogram analysis of objective space coverage further reveals that simulated annealing explores more diverse and optimal regions of the Pareto front. These findings suggest that metaheuristic optimization approaches like simulated annealing can provide more robust and effective candidate optimization for multi-objective Bayesian optimization, offering a promising alternative to traditional gradient-based methods for batch acquisition function optimization.

Additive manufacturing offers the opportunity to move beyond the traditional material-per-function paradigm by embedding multiple, spatially distributed behaviors within a single material structure. In this study, functionally graded (FG) Nickel-Titanium (NiTi) shape memory alloys (SMAs) were fabricated using laser powder bed fusion (LPBF) by deliberate spatial modulation of process parameters to locally control Ni content and, consequently, the martensitic transformation behavior, starting with a single feedstock powder. Quantitative Wavelength-dispersive spectroscopy (WDS) maps reveal systematic Ni variations across adjacent scan fields, while differential scanning calorimetry (DSC) confirms corresponding transformation temperatures spanning a similar to 150 degrees C window within the same build. Thermo-mechanical characterization under constant-stress thermal cycling and isothermal loading (both tension and compression) revealed: (i) stepwise, multi-zone actuation in a single part, with discrete strain increments up to total strain of 6% (most pronounced in tension), (ii) coexisting superelasticity (SE) and shape memory effect (SME) in different regions of one component, enabling simultaneous load-adaptive and thermally driven responses, and (iii) a clear dependence of functional performance on part dimensions and build sequence, which influence Ni loss through thermal history (heat accumulation, remelting, and exposure time) beyond volumetric energy density alone. The graded interfaces remain well bonded and free of macroscopic discontinuities, supporting reliable strain transfer across zones. These results establish LPBF-fabricated FG NiTi as a platform for spatially graded transformation landscapes, multi-stage actuation, and combined SE and SME in a single as-printed part, offering a fabrication route toward integrated, multifunctional SMA structures for soft robotics, adaptive mechanisms, aerospace/space structures, and biomedical devices.