An adaptive sampling algorithm for data-generation to build a data-manifold for physical problem surrogate modeling

TL;DR

This paper introduces an adaptive sampling algorithm that iteratively generates input data to better represent the response manifold of physical models, improving surrogate model accuracy over traditional methods like Latin Hypercube Sampling.

Contribution

The novel adaptive sampling algorithm (ASADG) enhances data generation for physical models, leading to more accurate surrogate models by iteratively refining input data based on the manifold's geometry.

Findings

ASADG outperforms LHS in representing the response manifold.

The algorithm achieves better surrogate model accuracy with the same data size.

Efficient data generation for complex physical models demonstrated.

Abstract

Physical models classically involved Partial Differential equations (PDE) and depending of their underlying complexity and the level of accuracy required, and known to be computationally expensive to numerically solve them. Thus, an idea would be to create a surrogate model relying on data generated by such solver. However, training such a model on an imbalanced data have been shown to be a very difficult task. Indeed, if the distribution of input leads to a poor response manifold representation, the model may not learn well and consequently, it may not predict the outcome with acceptable accuracy. In this work, we present an Adaptive Sampling Algorithm for Data Generation (ASADG) involving a physical model. As the initial input data may not accurately represent the response manifold in higher dimension, this algorithm iteratively adds input data into it. At each step the barycenter of each simplicial complex, that the manifold is discretized into, is added as new input data, if a certain threshold is satisfied. We demonstrate the efficiency of the data sampling algorithm in comparison with LHS method for generating more representative input data. To do so, we focus on the construction of a harmonic transport problem metamodel by generating data through a classical solver. By using such algorithm, it is possible to generate the same number of input data as LHS while providing a better representation of the response manifold.