On the construction of non-intrusive multifidelity models for computer codes with time-series output: Comparison of three paradigms on a transient thermal problem

• Multifidelity approaches for predicting codes with functional outputs • Overview of non-intrusive multifidelity techniques for simplified use • Practical guideline for meta-model selection • Comparative insights on multifidelity methods’ benefits and limitations • Comparison of methods on a 3D transient thermal problem This study evaluates three multifidelity meta-modeling approaches for time-varying systems: the Non-Intrusive Reduced Basis method (NIRB), the Gaussian Process Regression (GPR), and the Long Short-Term Memory Recurrent Neural Networks (LSTM). The focus is on predicting, in a small data context, the output of an expensive numerical code (high-fidelity version) that takes a parameter vector as input and produces a time-dependent function as output, leveraging one (or more) less expensive code(s) referred as low-fidelity versions. The goal is to analyze the strengths and limitations of these approaches in this context, and to make these three approaches accessible, even to non-specialists. To this end, we compare these methods based on prediction performance (accuracy), ease of hyper-parameter tuning, offline versus online computational costs, ability to quantify uncertainty, but also based on their complexity of implementation. The analysis also explores the advantages of using multiple codes and strategies for distributing computational costs across each code. Numerical experiments are conducted using a thermal model designed to predict surface heat fluxes and temperatures of a multi-layer wall based on its geometry and the thermal properties of its materials.