Sampling behavioral model parameters for ensemble-based sensitivity analysis using Gaussian process emulation and active subspaces

Abstract

Ensemble-based uncertainty quantification and global sensitivity analysis of environmental models requires generating large ensembles of parameter-sets. This can already be difficult when analyzing moderately complex models based on partial differential equations because many parameter combinations cause an implausible model behavior even though the individual parameters are within plausible ranges. In this work, we apply Gaussian Process Emulators (GPE) as surrogate models in a sampling scheme. In an active-training phase of the surrogate model, we target the behavioral boundary of the parameter space before sampling this behavioral part of the parameter space more evenly by passive sampling. Active learning increases the subsequent sampling efficiency, but its additional costs pay off only for a sufficiently large sample size. We exemplify our idea with a catchment-scale subsurface flow model with uncertain material properties, boundary conditions, and geometric descriptors of the geological structure. We then perform a global-sensitivity analysis of the resulting behavioral dataset using the active-subspace method, which requires approximating the local sensitivities of the target quantity with respect to all parameters at all sampled locations in parameter space. The Gaussian Process Emulator implicitly provides an analytical expression for this gradient, thus improving the accuracy of the active-subspace construction. When applying the GPE-based preselection, 70–90% of the samples were confirmed to be behavioral by running the full model, whereas only 0.5% of the samples were behavioral in standard Monte-Carlo sampling without preselection. The GPE method also provided local sensitivities at minimal additional costs.

GNN-Surrogate: A Hierarchical and Adaptive Graph Neural Network for Parameter Space Exploration of Unstructured-Mesh Ocean Simulations

“…Its major limitation is that the simulation output is only visualized with several predefined visual mappings, meaning scientists cannot adjust visual mappings to find features of interest after models have been trained. Second, researchers have also used different techniques such as machine learning [4], [5] and Gaussian process [21], [22] to predict raw data using surrogate models. Hazarika et al [4] trained a surrogate model to approximate the yeast cell polarization simulation model in the NNVA system.…”

“…Urban et al [21] proposed a Latin hypercube to improve the quality of a Gaussian process emulator on a simple Earth system model. For ensemblebased sensitivity analysis, Erdal et al [22] used a Gaussian process emulator and active subspaces to sample behavioral model parameters. However, these data-level methods do not directly work for our unstructured-mesh simulations since they learn the mapping between the simulation parameters and the raw simulation data on regular grids.…”

Unraveling biogeochemical complexity through better integration of experiments and modeling

“…Ensuring that parameters are highly identiable, given the available experimental data, requires that the information content of this data is balanced with the degree of the employed parameter variability; that is, it requires that the model calibration is "well-posed" or "well-determined". 15 To gauge this, it is essential that scientists employ either parameter sensitivity analyses, which do not require the model to be calibrated, [41][42][43][44][45] or methods for quantifying parameter uncertainty. [46][47][48][49][50][51][52][53] Without the application of such analyses, models are poorly described and potentially meaninglessand they would indeed become merely a tting exercise.…”

“…49 Machine learning algorithms may also hold the promise of reducing computational costs. 45,63 As the eld of Bayesian inference is rapidly evolving, more efficient techniques can be expected to become available in the future.…”

Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles

“…In civil engineering, structural reliability is assessed using the well-developed co cept of limit states [59,60], which clearly defines the design quantiles of resistance and t In civil engineering, SA is focused on the stability of steel frames [20], deflection of concrete beams with correlated inputs [21], multiple-criteria decision-making (MCDM) [22], structural response to stochastic dynamic loads [23], rheological properties of asphalt [24], thermal performance of facades [25], strength of reinforced concrete beams [26], use of machines during the construction of tunnels [27], stress-based topology of structural frames [28], seismic response of steel plate shear walls [29], deformation of retaining walls [30], multiple-attribute decision making (MADM) [31], efficiency of the operations of transportation companies [32], unbalanced bidding prices in construction projects [33], shear buckling strength [34], reliability index β of steel girders [35], system reliability [36], seismic response and fragility of transmission toners [37], shear strength of corrugated web panels [38], inelastic response of conical shells [39], fatigue limit state [40], corrosion depth [41], building-specific seismic loss [42], vibration response of train-bridge coupled systems [43], shear strength of reinforced concrete beam-column joints [44], forecasts of groundwater levels [45], equivalent rock strength [46], vertical displacement and maximum axial force of piles [47], regional-scale subsurface flow [48], ultimate limit state of cross-beam structures [49], serviceability limit state of structures [50], deflection of steel frames…”