Run-to-run (R2R) control is widely used in advanced manufacturing. Conventional R2R control methods often assume that system disturbances exhibit linear structures or low-rank approximations in high-dimensional data, such as images or videos. While these assumptions facilitate implementation, they limit the effectiveness of R2R control in managing sophisticated manufacturing processes with intricate nonlinear disturbances. To address these challenges, we propose a novel nonlinear spatio-temporal R2R control framework that estimates system disturbances using a diffusion model and applies control actions to compensate for them. The proposed approach integrates an offline modeling phase to capture disturbance dynamics and an online control phase that dynamically adjusts control actions to minimize deviations from the target system response. Unlike conventional deterministic control strategies, the proposed method explicitly quantifies uncertainty, enabling more robust and informed decision-making. The effectiveness of this method is validated through simulation studies and a case study, demonstrating its adaptability in complex, high-dimensional environments.
Accurate parameter estimation for ordinary differential equation (ODE) models is essential for understanding complex dynamical systems, particularly in epidemiological applications. This task is challenging in the presence of nonlinear dynamics and partial observability, where only indirect and noisy measurements of the system are available. In this article, we study parameter inference for ODE models, motivated by COVID-19 case counts in the United States during the Omicron wave. We adopt a high-dimensional compartmental model, capturing epidemiological heterogeneity where observations correspond to aggregated daily confirmed cases. We propose a regularized physics-informed neural network (PINN) framework that jointly estimates system trajectories and unknown model parameters. Unlike standard PINN approaches, which typically rely on heuristic choices of the regularization weight, we introduce a principled selection of this parameter via cross-validation to balance data fidelity and ODE constraints. This approach is conceptually related to generalized smoothing methods, but leverages neural networks for flexible trajectory representation. We establish theoretical guarantees for the proposed estimator, including convergence rates for the neural network approximation and consistency of the learned trajectories. Through simulation studies, we demonstrate that the proposed method achieves performance comparable to, and in some cases improves upon, existing approaches. The application of COVID-19 data further illustrates its effectiveness in capturing complex epidemic dynamics and providing accurate forecasts.
Split-plot designs are widely used when some factors are difficult to change, enabling the implementation of larger experiments. When nonregular fractional factorial treatment structures are used, some effect contrasts can be partially confounded with whole plots, rather than being either orthogonal or fully confounded. This is particularly so for some choices of the number of subplot units per whole plot. Our article proposes clear split-plot designs constructed via a parallel flats structure. We show that these designs divide the factorial effects into two orthogonal subspaces, simplifying model selection. Our proposed class of split-plot parallel flats designs are flexible in run sizes, are straightforward to construct, and enjoy additional benefits versus other nonregular and algorithmically-generated split-plot designs that lack this structure.
