Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

TL;DR

This paper introduces a multi-resolution functional ANOVA model as a scalable and efficient alternative to Gaussian processes for large-scale, many-input computer experiments, with proven consistency and uncertainty quantification.

Contribution

The paper develops a novel multi-resolution functional ANOVA model with an overlapping group lasso estimation approach, enabling scalable emulation for high-dimensional, large-scale experiments.

Findings

Model achieves computational efficiency and high accuracy.

Quantifies uncertainty in predictions effectively.

Outperforms existing emulation tools in large-scale settings.

Abstract

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed multi-resolution functional ANOVA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy.