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Abstract In scientific machine learning (SciML), a key challenge is learning unknown, evolving physical processes and making predictions across spatio-temporal scales. For example, in real-world manufacturing problems like additive manufacturing, users adjust known machine settings while unknown environmental parameters simultaneously fluctuate. To make reliable predictions, it is desired for a model to not only capture long-range spatio-temporal interactions from data but also adapt to new and unknown environments; traditional machine learning models excel at the first task but often lack physical interpretability and struggle to generalize under varying environmental conditions. To tackle these challenges, we propose the attention-based spatio-temporal neural operator (ASNO), a novel architecture that combines separable attention mechanisms for spatial and temporal interactions and adapts to unseen physical parameters. Inspired by the backward differentiation formula, ASNO learns a transformer for temporal prediction and extrapolation and an attention-based neural operator for handling varying external loads, enhancing interpretability by isolating historical state contributions and external forces, enabling the discovery of underlying physical laws and generalizability to unseen physical environments. Empirical results on SciML benchmarks demonstrate that ASNO outperforms existing models, establishing its potential for engineering applications, physics discovery, and interpretable machine learning. 

A comprehensive constitutive theory is developed for the diaphragm. The theory can describe the mechanical properties of the diaphragm muscle in its passive and active states in a unified manner. It also describes the mechanical properties of the diaphragm under mechanical loads in arbitrary directions. The theoretical model involves seven material constants that represent the nonlinear elastic moduli and activation strains of the diaphragm muscle. The values of these material constants are determined by using in vitro experimental data, including that from shear loading experiments which are documented in this work for the first time. 

Abstract Predictive maintenance in truck fleet management is essential to reduce downtime and maintenance costs, yet traditional approaches often rely on static, rule-based schedules that fail to capture real-time operational variability. In this paper, we propose a robust digital twin (DT) framework for predictive maintenance specifically designed for tire predictive maintenance that integrates real-time tire health data, dynamic decision-making, and adaptive model updates to optimize tire resource allocation and enhance system health. Our framework is unique in its ability to incorporate uncertainty-aware dynamic programming, drift detection, and adaptive surrogate model updates within the digital twin. Specifically, we develop an uncertainty-aware dynamic linear programming (U-DLP) approach to optimize tire placement and servicing schedules based on continuously updated tire health data through surrogate model. To ensure DT reliability, we employ the maximum concept discrepancy (MCD) method to detect drift by identifying discrepancies between predicted and actual tire performance, thereby flagging data for necessary tire health model updates. Subsequently, we introduce an uncertainty-aware low-rank adaptation (U-LORA) method to efficiently update the tire health model by dynamically refining the surrogate model based on measured uncertainty. Simulation results indicate that our framework extends tire lifespan by nearly 50% compared to conventional methods, requiring fewer tires to achieve the same operational mileage, while also reducing tire waste and maintenance costs. This integrated digital twin framework offers a reliable and efficient solution for tire predictive maintenance, enhancing fleet sustainability and operational efficiency. 

In many operations management problems, we need to make decisions sequentially to minimize the cost, satisfying certain constraints. One modeling approach to such problems is the constrained Markov decision process (CMDP). In this work, we develop a data-driven primal-dual algorithm to solve CMDPs. Our approach alternatively applies regularized policy iteration to improve the policy and subgradient ascent to maintain the constraints. Under mild regularity conditions, we show that the algorithm converges at rate [Formula: see text], where T is the number of iterations, for both the discounted and long-run average cost formulations. Our algorithm can be easily combined with advanced deep learning techniques to deal with complex large-scale problems with the additional benefit of straightforward convergence analysis. When the CMDP has a weakly coupled structure, our approach can further reduce the computational complexity through an embedded decomposition. We apply the algorithm to two operations management problems: multiclass queue scheduling and multiproduct inventory management. Numerical experiments demonstrate that our algorithm, when combined with appropriate value function approximations, generates policies that achieve superior performance compared with state-of-the-art heuristics. This paper was accepted by Baris Ata, stochastic models and simulation. Funding: Y. Chen was supported by the Hong Kong Research Grants Council, Early Career Scheme Fund [Grant 26508924], and partially supported by a grant from the National Natural Science Foundation of China [Grant 72495125]. J. Dong was supported by the National Science Foundation [Grant 1944209]. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.03736 . 

Mantle slabs imaged by seismic tomography provide complementary subsurface information that could improve global plate reconstructions because they are indications of ancient tectonic plates. Linking mantle slabs to the surface plates requires approaches that follow geodynamic principles in a highly vigorous mantle. Here, we propose a new workflow that couples a slab unfolding approach and a mantle circulation model (MCM) through which tomotectonic reconstructions can be performed, evaluated and improved in a closed-loop experiment. We publish the most recent version of our unfolded-slab constrained, geodynamically self-consistent plate reconstruction, Tomopac2, in which comprehensive intra-oceanic subductions within the Pacific-Panthalassa realms are implemented. These intra-oceanic subductions are crucial for understanding the evolution of the mantle and surface tectonics in the central Pacific, western North America and East Asia since the Mesozoic. Our model also incorporates subduction along western South America. Our closed-loop experiment allows us to reinterpret published tomotectonic reconstructions based on the vertical sinking slabs hypothesis. We conclude that highly vigorous mantle flow that allows lateral slab transport up to 4000 km and non-constant sinking rates that deviate by up to $10\hspace{0.17em}\mathrm{mm}\hspace{0.17em}{\mathrm{yr}}^{-1}$locally within an approximately $1000$ km area must be accounted for in tomotectonic reconstructions.