Xun Huan

Joseph Cohen, Xun Huan, Jun Ni

In the era of industrial big data, prognostics and health management is essential to improve the prediction of future failures to minimize inventory, maintenance, and human costs. Used for the 2021 PHM Data Challenge, the new Commercial Modular Aero-Propulsion System Simulation dataset from NASA is an open-source benchmark containing simulated turbofan engine units flown under realistic flight conditions. Deep learning approaches implemented previously for this application attempt to predict the remaining useful life of the engine units, but have not utilized labeled failure mode information, impeding practical usage and explainability. To address these limitations, a new prognostics approach is formulated with a customized loss function to simultaneously predict the current health state, the eventual failing component(s), and the remaining useful life. The proposed method incorporates principal component analysis to orthogonalize statistical time-domain features, which are inputs into supervised regressors such as random forests, extreme random forests, XGBoost, and artificial neural networks. The highest performing algorithm, ANN-Flux, achieves AUROC and AUPR scores exceeding 0.95 for each classification. In addition, ANN-Flux reduces the remaining useful life RMSE by 38% for the same test split of the dataset compared to past work, with significantly less computational cost.

Zhiyi Chen, Harshal Maske, Huanyi Shui et al.

The modeling of multistage manufacturing systems (MMSs) has attracted increased attention from both academia and industry. Recent advancements in deep learning methods provide an opportunity to accomplish this task with reduced cost and expertise. This study introduces a stochastic deep Koopman (SDK) framework to model the complex behavior of MMSs. Specifically, we present a novel application of Koopman operators to propagate critical quality information extracted by variational autoencoders. Through this framework, we can effectively capture the general nonlinear evolution of product quality using a transferred linear representation, thus enhancing the interpretability of the data-driven model. To evaluate the performance of the SDK framework, we carried out a comparative study on an open-source dataset. The main findings of this paper are as follows. Our results indicate that SDK surpasses other popular data-driven models in accuracy when predicting stagewise product quality within the MMS. Furthermore, the unique linear propagation property in the stochastic latent space of SDK enables traceability for quality evolution throughout the process, thereby facilitating the design of root cause analysis schemes. Notably, the proposed framework requires minimal knowledge of the underlying physics of production lines. It serves as a virtual metrology tool that can be applied to various MMSs, contributing to the ultimate goal of Zero Defect Manufacturing.

Jay Lee, Hanqi Su, Marco Macchi et al.

The evolution of artificial intelligence (AI) and machine learning (ML) is reshaping smart manufacturing by providing new capabilities for efficiency, adaptability, and autonomy across industrial value chains. However, the deployment of AI and ML in industrial settings still faces critical challenges, including the complexity of industrial big data, effective data management, integration with heterogeneous sensing and control systems, and the demand for trustworthy, explainable, and reliable operation in high-stakes industrial environments. In this roadmap, we present a comprehensive perspective on the foundations, applications, and emerging directions of AI and ML in smart manufacturing. It is structured in three parts. The first highlights the foundations and trends that frame the evolution of AI in smart manufacturing. The second focuses on key topics where AI is already enabling advances, including industrial big data analytics, advanced sensing and perception, autonomous systems, additive and laser-based manufacturing, digital twins, robotics, supply chain and logistics optimization, and sustainable manufacturing. The third section explores non-traditional ML approaches that are opening new frontiers, such as physics-informed AI, generative AI, semantic AI, advanced digital twins, explainable AI, RAMS, data-centric metrology, LLMs, and foundation models for highly connected and complex manufacturing systems. By identifying both opportunities and remaining barriers across these areas, this roadmap outlines the advances needed in methods, integration strategies, and industrial adoption. We hope this roadmap will serve as a guide for researchers, engineers, and practitioners to accelerate innovation, align academic and industrial priorities, and ensure that AI-driven smart manufacturing delivers reliable, sustainable, and scalable impact for the future of manufacturing ecosystems.

Wanggang Shen, Jiayuan Dong, Xun Huan

We present variational sequential optimal experimental design (vsOED), a novel method for optimally designing a finite sequence of experiments within a Bayesian framework with information-theoretic criteria. vsOED employs a one-point reward formulation with variational posterior approximations, providing a provable lower bound to the expected information gain. Numerical methods are developed following an actor-critic reinforcement learning approach, including derivation and estimation of variational and policy gradients to optimize the design policy, and posterior approximation using Gaussian mixture models and normalizing flows. vsOED accommodates nuisance parameters, implicit likelihoods, and multiple candidate models, while supporting flexible design criteria that can target designs for model discrimination, parameter inference, goal-oriented prediction, and their weighted combinations. We demonstrate vsOED across various engineering and science applications, illustrating its superior sample efficiency compared to existing sequential experimental design algorithms.

Chengyang Huang, Siddhartha Srivastava, Kenneth K. Y. Ho et al.

Inverse reinforcement learning (IRL) is a powerful paradigm for uncovering the incentive structure that drives agent behavior, by inferring an unknown reward function from observed trajectories within a Markov decision process (MDP). However, most existing IRL methods require access to the transition function, either prescribed or estimated \textit{a priori}, which poses significant challenges when the underlying dynamics are unknown, unobservable, or not easily sampled. We propose Fokker--Planck inverse reinforcement learning (FP-IRL), a novel physics-constrained IRL framework tailored for systems governed by Fokker--Planck (FP) dynamics. FP-IRL simultaneously infers both the reward and transition functions directly from trajectory data, without requiring access to sampled transitions. Our method leverages a conjectured equivalence between MDPs and the FP equation, linking reward maximization in MDPs with free energy minimization in FP dynamics. This connection enables inference of the potential function using our inference approach of variational system identification, from which the full set of MDP components -- reward, transition, and policy -- can be recovered using analytic expressions. We demonstrate the effectiveness of FP-IRL through experiments on synthetic benchmarks and a modified version of the Mountain Car problem. Our results show that FP-IRL achieves accurate recovery of agent incentives while preserving computational efficiency and physical interpretability.

Joseph Cohen, Xun Huan, Jun Ni

Data-driven artificial intelligence models require explainability in intelligent manufacturing to streamline adoption and trust in modern industry. However, recently developed explainable artificial intelligence (XAI) techniques that estimate feature contributions on a model-agnostic level such as SHapley Additive exPlanations (SHAP) have not yet been evaluated for semi-supervised fault diagnosis and prognosis problems characterized by class imbalance and weakly labeled datasets. This paper explores the potential of utilizing Shapley values for a new clustering framework compatible with semi-supervised learning problems, loosening the strict supervision requirement of current XAI techniques. This broad methodology is validated on two case studies: a heatmap image dataset obtained from a semiconductor manufacturing process featuring class imbalance, and a benchmark dataset utilized in the 2021 Prognostics and Health Management (PHM) Data Challenge. Semi-supervised clustering based on Shapley values significantly improves upon clustering quality compared to the fully unsupervised case, deriving information-dense and meaningful clusters that relate to underlying fault diagnosis model predictions. These clusters can also be characterized by high-precision decision rules in terms of original feature values, as demonstrated in the second case study. The rules, limited to 1-2 terms utilizing original feature scales, describe 12 out of the 16 derived equipment failure clusters with precision exceeding 0.85, showcasing the promising utility of the explainable clustering framework for intelligent manufacturing applications.

Xun Huan, Jayanth Jagalur, Youssef Marzouk

Questions of `how best to acquire data' are essential to modeling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavor can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parameterized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.

Aniket Jivani, Cosmin Safta, Beckett Y. Zhou et al.

We present a bifidelity Karhunen-Loève expansion (KLE) surrogate model for field-valued quantities of interest (QoIs) under uncertain inputs. The approach combines the spectral efficiency of the KLE with polynomial chaos expansions (PCEs) to preserve an explicit mapping between input uncertainties and output fields. By coupling inexpensive low-fidelity (LF) simulations that capture dominant response trends with a limited number of high-fidelity (HF) simulations that correct for systematic bias, the proposed method enables accurate and computationally affordable surrogate construction. To further improve surrogate accuracy, we form an active learning strategy that adaptively selects new HF evaluations based on the surrogate's generalization error, estimated via cross-validation and modeled using Gaussian process regression. New HF samples are then acquired by maximizing an expected improvement criterion, targeting regions of high surrogate error. The resulting BF-KLE-AL framework is demonstrated on three examples of increasing complexity: a one-dimensional analytical benchmark, a two-dimensional convection-diffusion system, and a three-dimensional turbulent round jet simulation based on Reynolds-averaged Navier--Stokes (RANS) and enhanced delayed detached-eddy simulations (EDDES). Across these cases, the method achieves consistent improvements in predictive accuracy and sample efficiency relative to single-fidelity and random-sampling approaches.

Zhiyi Chen, Harshal Maske, Devesh Upadhyay et al.

This paper presents a modeling-control synthesis to address the quality control challenges in multistage manufacturing systems (MMSs). A new feedforward control scheme is developed to minimize the quality variations caused by process disturbances in MMSs. Notably, the control framework leverages a stochastic deep Koopman (SDK) model to capture the quality propagation mechanism in the MMSs, highlighted by its ability to transform the nonlinear propagation dynamics into a linear one. Two roll-to-roll case studies are presented to validate the proposed method and demonstrate its effectiveness. The overall method is suitable for nonlinear MMSs and does not require extensive expert knowledge.

Xubo Gu, Xun Huan, Yao Ren et al.

Monitoring battery health is essential for ensuring safe and efficient operation. However, there is an inherent trade-off between assessment speed and diagnostic depth-specifically, between rapid overall health estimation and precise identification of internal degradation states. Capturing detailed internal battery information efficiently remains a major challenge, yet such insights are key to understanding the various degradation mechanisms. To address this, we develop a parameterized physics-informed neural network (P-PINNSPM) over the key aging-related parameter space for a single particle model. The model can accurately predict internal battery variables across the parameter space and identifies internal parameters in about 30 seconds-achieving a 47x speedup over the finite volume method-while maintaining high accuracy. These parameters improve the battery state-of-health (SOH) estimation accuracy by at least 60.61%, compared to models without parameter incorporation. Moreover, they enable extrapolation to unseen SOH levels and support robust estimation across diverse charging profiles and operating conditions. Our results demonstrate the strong potential of physics-informed machine learning to advance real-time, data-efficient, and physics-aware battery management systems.

Nan Feng, Xun Huan

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior distribution of model parameters, and then propagating posterior samples through the predictive model via Monte Carlo simulation. This sequential workflow can be computationally demanding, particularly for high-fidelity models such as those governed by partial differential equations. We propose a variational Bayesian framework that directly targets the posterior-predictive distribution and jointly learns variational approximations of both the posterior and the corresponding predictive distribution. The formulation introduces a variational upper bound on the Kullback--Leibler divergence together with moment-based regularization terms. The variational distributions are trained in an amortized manner, shifting computational effort to an offline stage and enabling efficient online inference. Numerical experiments ranging from analytical benchmarks to a finite-element solid mechanics problem demonstrate that the proposed method achieves more accurate predictive distributions than conventional two-stage variational inference, while substantially reducing the cost of online predictive inference.

Jiayuan Dong, Christian Jacobsen, Mehdi Khalloufi et al.

Bayesian optimal experimental design (OED) seeks experiments that maximize the expected information gain (EIG) in model parameters. Directly estimating the EIG using nested Monte Carlo is computationally expensive and requires an explicit likelihood. Variational OED (vOED), in contrast, estimates a lower bound of the EIG without likelihood evaluations by approximating the posterior distributions with variational forms, and then tightens the bound by optimizing its variational parameters. We introduce the use of normalizing flows (NFs) for representing variational distributions in vOED; we call this approach vOED-NFs. Specifically, we adopt NFs with a conditional invertible neural network architecture built from compositions of coupling layers, and enhanced with a summary network for data dimension reduction. We present Monte Carlo estimators to the lower bound along with gradient expressions to enable a gradient-based simultaneous optimization of the variational parameters and the design variables. The vOED-NFs algorithm is then validated in two benchmark problems, and demonstrated on a partial differential equation-governed application of cathodic electrophoretic deposition and an implicit likelihood case with stochastic modeling of aphid population. The findings suggest that a composition of 4--5 coupling layers is able to achieve lower EIG estimation bias, under a fixed budget of forward model runs, compared to previous approaches. The resulting NFs produce approximate posteriors that agree well with the true posteriors, able to capture non-Gaussian and multi-modal features effectively.

Shijie Zhong, Wanggang Shen, Tommie Catanach et al.

Optimal experimental design (OED) provides a systematic approach to quantify and maximize the value of experimental data. Under a Bayesian approach, conventional OED maximizes the expected information gain (EIG) on model parameters. However, we are often interested in not the parameters themselves, but predictive quantities of interest (QoIs) that depend on the parameters in a nonlinear manner. We present a computational framework of predictive goal-oriented OED (GO-OED) suitable for nonlinear observation and prediction models, which seeks the experimental design providing the greatest EIG on the QoIs. In particular, we propose a nested Monte Carlo estimator for the QoI EIG, featuring Markov chain Monte Carlo for posterior sampling and kernel density estimation for evaluating the posterior-predictive density and its Kullback-Leibler divergence from the prior-predictive. The GO-OED design is then found by maximizing the EIG over the design space using Bayesian optimization. We demonstrate the effectiveness of the overall nonlinear GO-OED method, and illustrate its differences versus conventional non-GO-OED, through various test problems and an application of sensor placement for source inversion in a convection-diffusion field.

Jeremiah Hauth, Cosmin Safta, Xun Huan et al.

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural network models have proved to be adept at modeling processes with spatial-temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial-temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance.Projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.

Zheyu Zhang, Jiayuan Dong, Jie Liu et al.

We present GO-CBED, a goal-oriented Bayesian framework for sequential causal experimental design. Unlike conventional approaches that select interventions aimed at inferring the full causal model, GO-CBED directly maximizes the expected information gain (EIG) on user-specified causal quantities of interest, enabling more targeted and efficient experimentation. The framework is both non-myopic, optimizing over entire intervention sequences, and goal-oriented, targeting only model aspects relevant to the causal query. To address the intractability of exact EIG computation, we introduce a variational lower bound estimator, optimized jointly through a transformer-based policy network and normalizing flow-based variational posteriors. The resulting policy enables real-time decision-making via an amortized network. We demonstrate that GO-CBED consistently outperforms existing baselines across various causal reasoning and discovery tasks-including synthetic structural causal models and semi-synthetic gene regulatory networks-particularly in settings with limited experimental budgets and complex causal mechanisms. Our results highlight the benefits of aligning experimental design objectives with specific research goals and of forward-looking sequential planning.

Christian Jacobsen, Jiayuan Dong, Mehdi Khalloufi et al.

We introduce a comprehensive data-driven framework aimed at enhancing the modeling of physical systems, employing inference techniques and machine learning enhancements. As a demonstrative application, we pursue the modeling of cathodic electrophoretic deposition (EPD), commonly known as e-coating. Our approach illustrates a systematic procedure for enhancing physical models by identifying their limitations through inference on experimental data and introducing adaptable model enhancements to address these shortcomings. We begin by tackling the issue of model parameter identifiability, which reveals aspects of the model that require improvement. To address generalizability , we introduce modifications which also enhance identifiability. However, these modifications do not fully capture essential experimental behaviors. To overcome this limitation, we incorporate interpretable yet flexible augmentations into the baseline model. These augmentations are parameterized by simple fully-connected neural networks (FNNs), and we leverage machine learning tools, particularly Neural Ordinary Differential Equations (Neural ODEs), to learn these augmentations. Our simulations demonstrate that the machine learning-augmented model more accurately captures observed behaviors and improves predictive accuracy. Nevertheless, we contend that while the model updates offer superior performance and capture the relevant physics, we can reduce off-line computational costs by eliminating certain dynamics without compromising accuracy or interpretability in downstream predictions of quantities of interest, particularly film thickness predictions. The entire process outlined here provides a structured approach to leverage data-driven methods. Firstly, it helps us comprehend the root causes of model inaccuracies, and secondly, it offers a principled method for enhancing model performance.

Venkat Nemani, Luca Biggio, Xun Huan et al.

On top of machine learning models, uncertainty quantification (UQ) functions as an essential layer of safety assurance that could lead to more principled decision making by enabling sound risk assessment and management. The safety and reliability improvement of ML models empowered by UQ has the potential to significantly facilitate the broad adoption of ML solutions in high-stakes decision settings, such as healthcare, manufacturing, and aviation, to name a few. In this tutorial, we aim to provide a holistic lens on emerging UQ methods for ML models with a particular focus on neural networks and the applications of these UQ methods in tackling engineering design as well as prognostics and health management problems. Toward this goal, we start with a comprehensive classification of uncertainty types, sources, and causes pertaining to UQ of ML models. Next, we provide a tutorial-style description of several state-of-the-art UQ methods: Gaussian process regression, Bayesian neural network, neural network ensemble, and deterministic UQ methods focusing on spectral-normalized neural Gaussian process. Established upon the mathematical formulations, we subsequently examine the soundness of these UQ methods quantitatively and qualitatively (by a toy regression example) to examine their strengths and shortcomings from different dimensions. Then, we review quantitative metrics commonly used to assess the quality of predictive uncertainty in classification and regression problems. Afterward, we discuss the increasingly important role of UQ of ML models in solving challenging problems in engineering design and health prognostics. Two case studies with source codes available on GitHub are used to demonstrate these UQ methods and compare their performance in the life prediction of lithium-ion batteries at the early stage and the remaining useful life prediction of turbofan engines.

Wanggang Shen, Xun Huan

We present a mathematical framework and computational methods to optimally design a finite number of sequential experiments. We formulate this sequential optimal experimental design (sOED) problem as a finite-horizon partially observable Markov decision process (POMDP) in a Bayesian setting and with information-theoretic utilities. It is built to accommodate continuous random variables, general non-Gaussian posteriors, and expensive nonlinear forward models. sOED then seeks an optimal design policy that incorporates elements of both feedback and lookahead, generalizing the suboptimal batch and greedy designs. We solve for the sOED policy numerically via policy gradient (PG) methods from reinforcement learning, and derive and prove the PG expression for sOED. Adopting an actor-critic approach, we parameterize the policy and value functions using deep neural networks and improve them using gradient estimates produced from simulated episodes of designs and observations. The overall PG-sOED method is validated on a linear-Gaussian benchmark, and its advantages over batch and greedy designs are demonstrated through a contaminant source inversion problem in a convection-diffusion field.

Maria Han Veiga, Xi Meng, Oleg Y. Gnedin et al.

We describe a novel end-to-end approach using Machine Learning to reconstruct the power spectrum of cosmological density perturbations at high redshift from observed quasar spectra. State-of-the-art cosmological simulations of structure formation are used to generate a large synthetic dataset of line-of-sight absorption spectra paired with 1-dimensional fluid quantities along the same line-of-sight, such as the total density of matter and the density of neutral atomic hydrogen. With this dataset, we build a series of data-driven models to predict the power spectrum of total matter density. We are able to produce models which yield reconstruction to accuracy of about 1% for wavelengths $k \leq 2 h Mpc^{-1}$, while the error increases at larger $k$. We show the size of data sample required to reach a particular error rate, giving a sense of how much data is necessary to reach a desired accuracy. This work provides a foundation for developing methods to analyse very large upcoming datasets with the next-generation observational facilities.

Panagiotis Tsilifis, Xun Huan, Cosmin Safta et al.

Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorithms, resulting in a reduced polynomial chaos approximation with optimal sparsity. The developed adaptation algorithm consists of a two-step optimization procedure that computes the optimal coefficients and the input projection matrix of a low dimensional chaos expansion with respect to an optimally rotated basis. We demonstrate the attractive features of our algorithm through several numerical examples including the application on Large-Eddy Simulation (LES) calculations of turbulent combustion in a HIFiRE scramjet engine.

Xun Huan, Youssef M. Marzouk

The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new strategies for the optimal design of sequential experiments. First, we rigorously formulate the general sequential optimal experimental design (sOED) problem as a dynamic program. Batch and greedy designs are shown to result from special cases of this formulation. We then focus on sOED for parameter inference, adopting a Bayesian formulation with an information theoretic design objective. To make the problem tractable, we develop new numerical approaches for nonlinear design with continuous parameter, design, and observation spaces. We approximate the optimal policy by using backward induction with regression to construct and refine value function approximations in the dynamic program. The proposed algorithm iteratively generates trajectories via exploration and exploitation to improve approximation accuracy in frequently visited regions of the state space. Numerical results are verified against analytical solutions in a linear-Gaussian setting. Advantages over batch and greedy design are then demonstrated on a nonlinear source inversion problem where we seek an optimal policy for sequential sensing.