error writing map file civilization emulator mac

However, once additional information is available in the form of measurement data, then a reliable and feasible framework for inverse modeling is indispensable to account for the uncertainty that remains after model calibration. Most versions of the surrogate methods named above need training runs of the original model to construct the surrogate. Surrogate representation of the original physical model can be very helpful to accelerate forward modeling and assess prior uncertainty. A recent paper compares various surrogate-based approaches using a common benchmark model for forward uncertainty quantification in carbon carbon dioxide storage. GPEs also offer representation via various kernels, and have gained popularity for such machine learning tasks as classification and regression problems. For that reason, GPEs are also known as Wiener–Kolmogorov prediction, after Norbert Wiener and Andrey Kolmogorov. Similar to polynomial chaos expansions, Gaussian process emulators (GPE), also known as Kriging for spatial prediction in the Geosciences, offer a linear representation through nonlinear kernels using fundamentals of probability theory. Advanced extensions towards sparse quadrature, sparse integration rules, or multi-element polynomial chaos approaches were applied to complex and computationally demanding applications.Īlternately to global or local polynomial representation, other kernels functions have been widely used in applied mathematics and machine learning. The conventional non-intrusive version of the polynomial chaos expansion or its generalization towards data-driven descriptions gained popularity during the last few decades because it can offer an efficient reduction of computational costs in uncertainty quantification. Classical machine learning approaches, such as artificial neural networks, require huge numbers of model evaluations.Ī reasonably fast approach to quantify forward uncertainty has been established by Wiener, projecting a full-complexity model onto orthogonal polynomial bases over the parameter space. Due to the high computational costs of the original numerical simulation required for training runs of such surrogates, constructing surrogate models is still challenging. The latter is the primary reason why a vast majority of ongoing research has been focusing on accelerating the forward model using surrogate models, such as response surfaces, emulators, meta-models, reduced-order models, etc.

The great difficulty here is to establish a consistent and feasible framework that can provide appropriate conceptual descriptions and can simultaneously maintain a reliable time frame of simulations. Due to the computational complexity of the underlying physical concepts, numerical simulation models are often too expensive for applications tasks related to uncertainty quantification, risk assessment and stochastic model calibration. The greatest challenge of the scientific modeling workflow is to construct reliable and feasible models that can adequately describe underlying physical concepts and, at the same time, account for uncertainty. The relative entropy-based strategy demonstrates superior performance to the Bayesian model evidence-based strategy. We conclude that Bayesian model evidence-based and relative entropy-based strategies outperform the entropy-based strategy because the latter can be misleading during the BAL. The paper shows evidence of convergence against a reference solution and demonstrates quantification of post-calibration uncertainty by comparing the introduced three strategies. We illustrate the performance of our three strategies using analytical- and carbon-dioxide benchmarks. The first strategy relies on Bayesian model evidence that indicates the GPE’s quality of matching the measurement data, the second strategy is based on relative entropy that indicates the relative information gain for the GPE, and the third is founded on information entropy that indicates the missing information in the GPE. We introduce three BAL strategies that adaptively identify training sets for the GPE using information-theoretic arguments.

The current paper offers a fully Bayesian view on GPEs for Bayesian inference accompanied by Bayesian active learning (BAL). Constructing such a surrogate is very challenging and, in the context of Bayesian inference, the training runs should be well invested. Gaussian process emulators (GPE) are a machine learning approach that replicates computational demanding models using training runs of that model.

Error writing map file civilization emulator mac