Stochastic systems: estimation, identification and adaptive control
Stochastic systems: estimation, identification and adaptive control
Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Environmental Modelling & Software
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
Environmental Modelling & Software
Position Paper: A general framework for Dynamic Emulation Modelling in environmental problems
Environmental Modelling & Software
Network-Based Consensus Averaging With General Noisy Channels
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
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The computational complexity of numerical models can be broken down into contributions ranging from spatial, temporal and stochastic resolution, e.g., spatial grid resolution, time step size and number of repeated simulations dedicated to quantify uncertainty. Controlling these resolutions allows keeping the computational cost at a tractable level whilst still aiming at accurate and robust predictions. The objective of this work is to introduce a framework that optimally allocates the available computational resources in order to achieve highest accuracy associated with a given prediction goal. Our analysis is based on the idea to jointly consider the discretization errors and computational costs of all individual model dimensions (physical space, time, parameter space). This yields a cost-to-error surface which serves to aid modelers in finding an optimal allocation of the computational resources (ORA). As a pragmatic way to proceed, we propose running small cost-efficient pre-investigations in order to estimate the joint cost-to-error surface, then fit underlying complexity and error models, decide upon a computational design for the full simulation, and finally to perform the designed simulation at near-optimal costs-to-accuracy ratio. We illustrate our approach with three examples from subsurface hydrogeology and show that the computational costs can be substantially reduced when allocating computational resources wisely and in a situation-specific and task-specific manner. We conclude that the ORA depends on a multitude of parameters, assumptions and problem-specific features and, hence, ORA needs to be determined carefully prior to each investigation.