Infinite-Fidelity Coregionalization for Physical Simulation

TL;DR

This paper introduces Infinite Fidelity Coregionalization (IFC), a novel method for multi-fidelity modeling that captures continuous, infinite fidelities in physical simulations, enabling interpolation and extrapolation beyond training data.

Contribution

The paper proposes a continuous fidelity modeling approach using neural ODEs and tensor-Gaussian variational inference, extending multi-fidelity modeling to infinite fidelities.

Findings

Outperforms existing methods on benchmark physics tasks

Enables accurate interpolation and extrapolation of fidelities

Scalable inference for large-scale outputs

Abstract

Multi-fidelity modeling and learning are important in physical simulation-related applications. It can leverage both low-fidelity and high-fidelity examples for training so as to reduce the cost of data generation while still achieving good performance. While existing approaches only model finite, discrete fidelities, in practice, the fidelity choice is often continuous and infinite, which can correspond to a continuous mesh spacing or finite element length. In this paper, we propose Infinite Fidelity Coregionalization (IFC). Given the data, our method can extract and exploit rich information within continuous, infinite fidelities to bolster the prediction accuracy. Our model can interpolate and/or extrapolate the predictions to novel fidelities, which can be even higher than the fidelities of training data. Specifically, we introduce a low-dimensional latent output as a continuous function of the fidelity and input, and multiple it with a basis matrix to predict high-dimensional solution outputs. We model the latent output as a neural Ordinary Differential Equation (ODE) to capture the complex relationships within and integrate information throughout the continuous fidelities. We then use Gaussian processes or another ODE to estimate the fidelity-varying bases. For efficient inference, we reorganize the bases as a tensor, and use a tensor-Gaussian variational posterior to develop a scalable inference algorithm for massive outputs. We show the advantage of our method in several benchmark tasks in computational physics.