A Multi-Fidelity Parametric Framework for Reduced-Order Modeling using Optimal Transport-based Interpolation: Applications to Diffused-Interface Two-Phase Flows

TL;DR

This paper presents a non-intrusive, data-driven reduced-order modeling framework using optimal transport for multi-fidelity and parametric two-phase flow problems, enhancing accuracy and efficiency.

Contribution

It extends displacement interpolation to complex two-phase flows, constructing surrogate models with hierarchical multi-fidelity interpolation for parameter-dependent systems.

Findings

Framework effectively corrects low-fidelity models to match high-fidelity data.

Hierarchical interpolation enables efficient exploration of parameter space.

Method is suitable for complex, nonlinear two-phase flow simulations.

Abstract

This work introduces a data-driven, non-intrusive reduced-order modeling (ROM) framework that leverages Optimal Transport (OT) for multi-fidelity and parametric problems in two-phase flows modelling. Building upon the success of displacement interpolation for data augmentation in handling nonlinear dynamics, we extend its application to more complex and practical scenarios. The framework is designed to correct a computationally inexpensive low-fidelity (LF) model to match an accurate high-fidelity (HF) one by capturing its temporal evolution via displacement interpolation while preserving the problem's physical consistency. The framework is further extended to address systems dependent on a physical parameter, for which we construct a surrogate model using a hierarchical, two-level interpolation strategy. First, it creates synthetic HF checkpoints via displacement interpolation in the parameter space. Second, the residual between these synthetic HF checkpoints and a true LF solution is interpolated in the time domain using the multi-fidelity OT-based methodology. This strategy provides a robust and efficient way to explore the parameter space and to obtain a refined description of the dynamical system. The potential of the method is discussed in the context of complex and computationally expensive diffuse-interface methods for two-phase flow simulations, which are characterized by moving interfaces and nonlinear evolution, and challenging to be dealt with traditional ROM techniques.