Search for: All records

Abstract A simple and efficient Bayesian machine learning (BML) training algorithm, which exploits only a 20‐year short observational time series and an approximate prior model, is developed to predict the Niño 3 sea surface temperature (SST) index. The BML forecast significantly outperforms model‐based ensemble predictions and standard machine learning forecasts. Even with a simple feedforward neural network (NN), the BML forecast is skillful for 9.5 months. Remarkably, the BML forecast overcomes the spring predictability barrier to a large extent: the forecast starting from spring remains skillful for nearly 10 months. The BML algorithm can also effectively utilize multiscale features: the BML forecast of SST using SST, thermocline, and windburst improves on the BML forecast using just SST by at least 2 months. Finally, the BML algorithm also reduces the forecast uncertainty of NNs and is robust to input perturbations. 

Abstract This paper develops manifold learning techniques for the numerical solution of PDE-constrained Bayesian inverse problems on manifolds with boundaries. We introduce graphical Matérn-type Gaussian field priors that enable flexible modeling near the boundaries, representing boundary values by superposition of harmonic functions with appropriate Dirichlet boundary conditions. We also investigate the graph-based approximation of forward models from PDE parameters to observed quantities. In the construction of graph-based prior and forward models, we leverage the ghost point diffusion map algorithm to approximate second-order elliptic operators with classical boundary conditions. Numerical results validate our graph-based approach and demonstrate the need to design prior covariance models that account for boundary conditions.