Raymundo Arróyave

Danial Khatamsaz, Vahid Attari, Raymundo Arroyave et al.

Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine model output uncertainties based on the uncertainty in its input variables. The most common and simplest approach to propagate the uncertainty from a model inputs to its outputs is by feeding a large number of samples to the model, known as Monte Carlo (MC) simulation which requires exhaustive sampling from the input variable distributions. However, MC simulations are impractical when models are computationally expensive. In this work, we investigate the hypothesis that while all samples are useful on average, some samples must be more useful than others. Thus, reordering MC samples and propagating more useful samples can lead to enhanced convergence in statistics of interest earlier and thus, reducing the computational burden of UP process. Here, we introduce a methodology to adaptively reorder MC samples and show how it results in reduction of computational expense of UP processes.

Mrinalini Mulukutla, Robert Robinson, Danial Khatamsaz et al.

Materials design is a critical driver of innovation, yet overlooking the technological, economic, and environmental risks inherent in materials and their supply chains can lead to unsustainable and risk-prone solutions. To address this, we present a novel risk-aware design approach that integrates Supply-Chain Aware Design Strategies into the materials development process. This approach leverages existing language models and text analysis to develop a specialized model for predicting materials feedstock supply risk indices. To efficiently navigate the multi-objective, multi-constraint design space, we employ Batch Bayesian Optimization (BBO), enabling the identification of Pareto-optimal high entropy alloys (HEAs) that balance performance objectives with minimized supply risk. A case study using the MoNbTiVW system demonstrates the efficacy of our approach in four scenarios, highlighting the significant impact of incorporating supply risk into the design process. By optimizing for both performance and supply risk, we ensure that the developed alloys are not only high-performing but also sustainable and economically viable. This integrated approach represents a critical step towards a future where materials discovery and design seamlessly consider sustainability, supply chain dynamics, and comprehensive life cycle analysis.

Siya Zhu, Raymundo Arróyave, Doğuhan Sarıtürk

Accurate phase diagram prediction is crucial for understanding alloy thermodynamics and advancing materials design. While traditional CALPHAD methods are robust, they are resource-intensive and limited by experimentally assessed data. This work explores the use of machine learning interatomic potentials (MLIPs) such as M3GNet, CHGNet, MACE, SevenNet, and ORB to significantly accelerate phase diagram calculations by using the Alloy Theoretic Automated Toolkit (ATAT) to map calculations of the energies and free energies of atomistic systems to CALPHAD-compatible thermodynamic descriptions. Using case studies including Cr-Mo, Cu-Au, and Pt-W, we demonstrate that MLIPs, particularly ORB, achieve computational speedups exceeding three orders of magnitude compared to DFT while maintaining phase stability predictions within acceptable accuracy. Extending this approach to liquid phases and ternary systems like Cr-Mo-V highlights its versatility for high-entropy alloys and complex chemical spaces. This work demonstrates that MLIPs, integrated with tools like ATAT within a CALPHAD framework, provide an efficient and accurate framework for high-throughput thermodynamic modeling, enabling rapid exploration of novel alloy systems. While many challenges remain to be addressed, the accuracy of some of these MLIPs (ORB in particular) are on the verge of paving the way toward high-throughput generation of CALPHAD thermodynamic descriptions of multi-component, multi-phase alloy systems.

Keqiang Yan, Xiner Li, Hongyi Ling et al.

We consider the problem of crystal materials generation using language models (LMs). A key step is to convert 3D crystal structures into 1D sequences to be processed by LMs. Prior studies used the crystallographic information framework (CIF) file stream, which fails to ensure SE(3) and periodic invariance and may not lead to unique sequence representations for a given crystal structure. Here, we propose a novel method, known as Mat2Seq, to tackle this challenge. Mat2Seq converts 3D crystal structures into 1D sequences and ensures that different mathematical descriptions of the same crystal are represented in a single unique sequence, thereby provably achieving SE(3) and periodic invariance. Experimental results show that, with language models, Mat2Seq achieves promising performance in crystal structure generation as compared with prior methods.

Lianhao Zhou, Hongyi Ling, Keqiang Yan et al.

We aim at designing language agents with greater autonomy for crystal materials discovery. While most of existing studies restrict the agents to perform specific tasks within predefined workflows, we aim to automate workflow planning given high-level goals and scientist intuition. To this end, we propose Materials Agent unifying Planning, Physics, and Scientists, known as MAPPS. MAPPS consists of a Workflow Planner, a Tool Code Generator, and a Scientific Mediator. The Workflow Planner uses large language models (LLMs) to generate structured and multi-step workflows. The Tool Code Generator synthesizes executable Python code for various tasks, including invoking a force field foundation model that encodes physics. The Scientific Mediator coordinates communications, facilitates scientist feedback, and ensures robustness through error reflection and recovery. By unifying planning, physics, and scientists, MAPPS enables flexible and reliable materials discovery with greater autonomy, achieving a five-fold improvement in stability, uniqueness, and novelty rates compared with prior generative models when evaluated on the MP-20 data. We provide extensive experiments across diverse tasks to show that MAPPS is a promising framework for autonomous materials discovery.

Christofer Hardcastle, Ryan O Mullan, Raymundo Arroyave et al.

Alloy design can be framed as a constraint-satisfaction problem. Building on previous methodologies, we propose equipping Gaussian Process Classifiers (GPCs) with physics-informed prior mean functions to model the boundaries of feasible design spaces. Through three case studies, we highlight the utility of informative priors for handling constraints on continuous and categorical properties. (1) Phase Stability: By incorporating CALPHAD predictions as priors for solid-solution phase stability, we enhance model validation using a publicly available XRD dataset. (2) Phase Stability Prediction Refinement: We demonstrate an in silico active learning approach to efficiently correct phase diagrams. (3) Continuous Property Thresholds: By embedding priors into continuous property models, we accelerate the discovery of alloys meeting specific property thresholds via active learning. In each case, integrating physics-based insights into the classification framework substantially improved model performance, demonstrating an efficient strategy for constraint-aware alloy design.

Ming Zhong, Dehao Liu, Raymundo Arroyave et al.

This paper proposes a semi-supervised methodology for training physics-informed machine learning methods. This includes self-training of physics-informed neural networks and physics-informed Gaussian processes in isolation, and the integration of the two via co-training. We demonstrate via extensive numerical experiments how these methods can ameliorate the issue of propagating information forward in time, which is a common failure mode of physics-informed machine learning.

Sk Md Ahnaf Akif Alvi, Mrinalini Mulukutla, Nicolas Flores et al.

Surrogate modeling techniques have become indispensable in accelerating the discovery and optimization of high-entropy alloys(HEAs), especially when integrating computational predictions with sparse experimental observations. This study systematically evaluates the fitting performance of four prominent surrogate models conventional Gaussian Processes(cGP), Deep Gaussian Processes(DGP), encoder-decoder neural networks for multi-output regression and XGBoost applied to a hybrid dataset of experimental and computational properties in the AlCoCrCuFeMnNiV HEA system. We specifically assess their capabilities in predicting correlated material properties, including yield strength, hardness, modulus, ultimate tensile strength, elongation, and average hardness under dynamic and quasi-static conditions, alongside auxiliary computational properties. The comparison highlights the strengths of hierarchical and deep modeling approaches in handling heteroscedastic, heterotopic, and incomplete data commonly encountered in materials informatics. Our findings illustrate that DGP infused with machine learning-based prior outperform other surrogates by effectively capturing inter-property correlations and input-dependent uncertainty. This enhanced predictive accuracy positions advanced surrogate models as powerful tools for robust and data-efficient materials design.

Danial Khatamsaz, Joseph Wagner, Brent Vela et al.

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.

Levi McClenny, Mulugeta Haile, Vahid Attari et al.

In many real-world applications of deep learning, estimation of a target may rely on various types of input data modes, such as audio-video, image-text, etc. This task can be further complicated by a lack of sufficient data. Here we propose a Deep Multimodal Transfer-Learned Regressor (DMTL-R) for multimodal learning of image and feature data in a deep regression architecture effective at predicting target parameters in data-poor domains. Our model is capable of fine-tuning a given set of pre-trained CNN weights on a small amount of training image data, while simultaneously conditioning on feature information from a complimentary data mode during network training, yielding more accurate single-target or multi-target regression than can be achieved using the images or the features alone. We present results using phase-field simulation microstructure images with an accompanying set of physical features, using pre-trained weights from various well-known CNN architectures, which demonstrate the efficacy of the proposed multimodal approach.

Guang Zhao, Raymundo Arroyave, Xiaoning Qian

In multi-objective Bayesian optimization and surrogate-based evolutionary algorithms, Expected HyperVolume Improvement (EHVI) is widely used as the acquisition function to guide the search approaching the Pareto front. This paper focuses on the exact calculation of EHVI given a nondominated set, for which the existing exact algorithms are complex and can be inefficient for problems with more than three objectives. Integrating with different decomposition algorithms, we propose a new method for calculating the integral in each decomposed high-dimensional box in constant time. We develop three new exact EHVI calculation algorithms based on three region decomposition methods. The first grid-based algorithm has a complexity of $O(m\cdot n^m)$ with $n$ denoting the size of the nondominated set and $m$ the number of objectives. The Walking Fish Group (WFG)-based algorithm has a worst-case complexity of $O(m\cdot 2^n)$ but has a better average performance. These two can be applied for problems with any $m$. The third CLM-based algorithm is only for $m=3$ and asymptotically optimal with complexity $Θ(n\log{n})$. Performance comparison results show that all our three algorithms are at least twice faster than the state-of-the-art algorithms with the same decomposition methods. When $m>3$, our WFG-based algorithm can be over $10^2$ faster than the corresponding existing algorithms. Our algorithm is demonstrated in an example involving efficient multi-objective material design with Bayesian optimization.