Jianguo Wu

Duo Wang, Xinming Wang, Chao Wang et al.

Multi-output Gaussian process (MGP) models have attracted significant attention for their flexibility and uncertainty-quantification capabilities, and have been widely adopted in multi-source transfer learning scenarios due to their ability to capture inter-task correlations. However, they still face several challenges in transfer learning. First, the input spaces of the source and target domains are often heterogeneous, which makes direct knowledge transfer difficult. Second, potential prior knowledge and physical information are typically ignored during heterogeneous transfer, hampering the utilization of domain-specific insights and leading to unstable mappings. Third, inappropriate information sharing among target and sources can easily lead to negative transfer. Traditional models fail to address these issues in a unified way. To overcome these limitations, this paper proposes a Double-Regularized Heterogeneous Gaussian Process framework (R^2-HGP). Specifically, a trainable prior probability mapping model is first proposed to align the heterogeneous input domains. The resulting aligned inputs are treated as latent variables, upon which a multi-source transfer GP model is constructed and the entire structure is integrated into a novel conditional variational autoencoder (CVAE) based framework. Physical insights is further incorporated as a regularization term to ensure that the alignment results adhere to known physical knowledge. Next, within the multi-source transfer GP model, a sparsity penalty is imposed on the transfer coefficients, enabling the model to adaptively select the most informative source outputs and suppress negative transfer. Extensive simulations and real-world engineering case studies validate the effectiveness of our R^2-HGP, demonstrating consistent superiority over state-of-the-art benchmarks across diverse evaluation metrics.

Xinming Wang, Simon Mak, John Miller et al.

A critical bottleneck for scientific progress is the costly nature of computer simulations for complex systems. Surrogate models provide an appealing solution: such models are trained on simulator evaluations, then used to emulate and quantify uncertainty on the expensive simulator at unexplored inputs. In many applications, one often has available data on related systems. For example, in designing a new jet turbine, there may be existing studies on turbines with similar configurations. A key question is how information from such ``source'' systems can be transferred for effective surrogate training on the ``target'' system of interest. We thus propose a new LOcal transfer Learning Gaussian Process (LOL-GP) model, which leverages a carefully-designed Gaussian process to transfer such information for surrogate modeling. The key novelty of the LOL-GP is a latent regularization model, which identifies regions where transfer should be performed and regions where it should be avoided. Such a ``local transfer'' property is present in many scientific systems: at certain parameters, systems may behave similarly and thus transfer is beneficial; at other parameters, they may behave differently and thus transfer is detrimental. By accounting for local transfer, the LOL-GP can temper the risk of ``negative transfer'', i.e., the risk of worsening predictive performance from information transfer. We derive a Gibbs sampling algorithm for efficient posterior predictive sampling on the LOL-GP, for both the multi-source and multi-fidelity transfer settings. We then show, via a suite of numerical experiments and an application for jet turbine design, the improved surrogate performance of the LOL-GP over existing methods.

Cheolhei Lee, Xing Wang, Jianguo Wu et al.

Active learning is a subfield of machine learning that is devised for design and modeling of systems with highly expensive sampling costs. Industrial and engineering systems are generally subject to physics constraints that may induce fatal failures when they are violated, while such constraints are frequently underestimated in active learning. In this paper, we develop a novel active learning method that avoids failures considering implicit physics constraints that govern the system. The proposed approach is driven by two tasks: the safe variance reduction explores the safe region to reduce the variance of the target model, and the safe region expansion aims to extend the explorable region exploiting the probabilistic model of constraints. The global acquisition function is devised to judiciously optimize acquisition functions of two tasks, and its theoretical properties are provided. The proposed method is applied to the composite fuselage assembly process with consideration of material failure using the Tsai-wu criterion, and it is able to achieve zero-failure without the knowledge of explicit failure regions.

Cheolhei Lee, Kaiwen Wang, Jianguo Wu et al.

Active learning is a subfield of machine learning that focuses on improving the data collection efficiency of expensive-to-evaluate systems. Especially, active learning integrated surrogate modeling has shown remarkable performance in computationally demanding engineering systems. However, the existence of heterogeneity in underlying systems may adversely affect the performance of active learning. In order to improve the learning efficiency under this regime, we propose the partitioned active learning that seeks the most informative design points for partitioned Gaussian process modeling of heterogeneous systems. The proposed active learning consists of two systematic subsequent steps: the global searching scheme accelerates the exploration of active learning by investigating the most uncertain design space, and the local searching exploits the circumscribed information induced by the local GP. We also propose Cholesky update driven numerical remedies for our active learning to address the computational complexity challenge. The proposed method is applied to numerical simulations and two real-world case studies about (i) the cost-efficient automatic fuselage shape control in aerospace manufacturing; and (ii) the optimal design of tribocorrosion-resistant alloys in materials science. The results show that our approach outperforms benchmark methods with respect to prediction accuracy and computational efficiency.

Cheolhei Lee, Jianguo Wu, Wenjia Wang et al.

Developing machine learning enabled smart manufacturing is promising for composite structures assembly process. To improve production quality and efficiency of the assembly process, accurate predictive analysis on dimensional deviations and residual stress of the composite structures is required. The novel composite structures assembly involves two challenges: (i) the highly nonlinear and anisotropic properties of composite materials; and (ii) inevitable uncertainty in the assembly process. To overcome those problems, we propose a neural network Gaussian process model considering input uncertainty for composite structures assembly. Deep architecture of our model allows us to approximate a complex process better, and consideration of input uncertainty enables robust modeling with complete incorporation of the process uncertainty. Based on simulation and case study, the NNGPIU can outperform other benchmark methods when the response function is nonsmooth and nonlinear. Although we use composite structure assembly as an example, the proposed methodology can be applicable to other engineering systems with intrinsic uncertainties.