64 Reliable emulation of complex functionals by active learning with error control

Oregon Convention Center 

A statistical emulator can be used as a surrogate of complex physics-based calculations to drastically reduce the computational cost. Its effectiveness relies on accurately representing nonlinear response surfaces in high-dimensional input spaces. Traditional "space-filling" designs like random and Latin hypercube sampling lose efficiency with increased input dimensionality, impacting emulator accuracy. To overcome this issue, we introduce Active Learning with Error Control (ALEC) for reliably predicting complex functionals. ALEC is applicable to emulating expensive computer models with infinite-dimensional inputs, ensuring high-fidelity predictions with controlled errors. We derived a criterion to ensure that the fraction of samples with predictive errors larger than a threshold is small and develop an iterative algorithm to reduce the computational cost. We demonstrate the accuracy of ALEC by emulating classical density functional theory (cDFT) calculations, crucial in simulating thermodynamic properties of fluids. ALEC outperforms Gaussian process emulators with conventional designs and active learning methods with other criterion in accuracy and computational efficiency.

Active learning

Computational model emulation

Error control

Gaussian processes

High-dimensional input 

Uncertainty Quantification in Complex Systems Interest Group