Physics makes the difference: Bayesian optimization and active learning via augmented Gaussian process

Both experimental and computational methods for the exploration of structure, functionality, and properties of materials often necessitate the search across broad parameter spaces to discover optimal experimental conditions and regions of interest in the image space or parameter space of computational models. The direct grid search of the parameter space tends to be extremely time-consuming, leading to the development of strategies balancing exploration of unknown parameter spaces and exploitation towards required performance metrics. However, classical Bayesian optimization strategies based on the Gaussian process (GP) do not readily allow for the incorporation of the known physical behaviors or past knowledge. Here we explore a hybrid optimization/exploration algorithm created by augmenting the standard GP with a structured probabilistic model of the expected system’s behavior. This approach balances the flexibility of the non-parametric GP approach with a rigid structure of physical knowledge encoded into the parametric model. The fully Bayesian treatment of the latter allows additional control over the optimization via the selection of priors for the model parameters. The method is demonstrated for a noisy version of the classical objective function used to evaluate optimization algorithms and further extended to physical lattice models. This methodology is expected to be universally suitable for injecting prior knowledge in the form of physical models and past data in the Bayesian optimization framework.

Structural performance assessment considering both observed and latent environmental and operational conditions: A Gaussian process and probability principal component analysis method

Structural faults like damage and degradations will cause changes in structure response data. Performance assessment can be conducted by investigating such changes. In real implementations however, structural responses are affected by environmental and operational variations (EOVs) as well. Such variation should be well captured by the assessment model when detecting structural changes. It should be noted that not all EOVs can be measured by the monitoring system. When both observed and latent EOVs have significant effects on the monitored structural responses, these two effects should be considered properly. Furthermore, uncertainties can be significant for the monitoring data since loads and EOVs cannot be directly controlled under working conditions. To address these problems, this work proposes a performance assessment method considering both observed and latent EOVs. A Gaussian process is used to model the functional behaviour between structural response and observed EOVs whilst principal component analysis is used to eliminate the effect of latent EOVs. These two methods are combined using a Bayesian formulation and the effect of both observed and latent EOVs are modelled. The associated model parameters are inferred through probability density functions to account for the uncertainties. A synthetic data example is presented to validate the proposed method. It is also applied to the monitoring data of a long-span cable-stayed bridge with different damage scenarios considered, illustrating its capability of real implementations in structural health monitoring.

Winter Wheat Nitrogen Estimation Based on Ground-Level and UAV-Mounted Sensors

A better understanding of wheat nitrogen status is important for improving N fertilizer management in precision farming. In this study, four different sensors were evaluated for their ability to estimate winter wheat nitrogen. A Gaussian process regression (GPR) method with the sequential backward feature removal (SBBR) routine was used to identify the best combinations of vegetation indices (VIs) sensitive to wheat N indicators for different sensors. Wheat leaf N concentration (LNC), plant N concentration (PNC), and the nutrition index (NNI) were estimated by the VIs through parametric regression (PR), multivariable linear regression (MLR), and Gaussian process regression (GPR). The study results reveal that the optical fluorescence sensor provides more accurate estimates of winter wheat N status at a low-canopy coverage condition. The Dualex Nitrogen Balance Index (NBI) is the best leaf-level indicator for wheat LNC, PNC and NNI at the early wheat growth stage. At the early growth stage, Multiplex indices are the best canopy-level indicators for LNC, PNC, and NNI. At the late growth stage, ASD VIs provide accurate estimates for wheat N indicators. This study also reveals that the GPR with SBBR analysis method provides more accurate estimates of winter wheat LNC, PNC, and NNI, with the best VI combinations for these sensors across the different winter wheat growth stages, compared with the MLR and PR methods.