# Infinite-Fidelity Coregionalization for Physical Simulation

arXiv: https://arxiv.org/abs/2207.00678 · HTML: https://mlsanity.com/paper/2207.00678/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 1 Jul 2022.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Deep Multi-Fidelity Active Learning of High-dimensional Outputs](https://mlsanity.com/paper/2012.00901/) (2020)
- [Scheduling Techniques for Liver Segmentation: ReduceLRonPlateau Vs OneCycleLR](https://mlsanity.com/paper/2202.06373/) (2022)
- [Multi-fidelity Hierarchical Neural Processes](https://mlsanity.com/paper/2206.04872/) (2022)
- [Multi-resolution Multi-task Gaussian Processes](https://mlsanity.com/paper/1906.08344/) (2019)
- [Non-linear process convolutions for multi-output Gaussian processes](https://mlsanity.com/paper/1810.04632/) (2018)
- [Residual Gaussian Process: A Tractable Nonparametric Bayesian Emulator for Multi-fidelity Simulations](https://mlsanity.com/paper/2104.03743/) (2021)

## Built on by (most cited first, 7 of 7)

- [Multi-Resolution Active Learning of Fourier Neural Operators](https://mlsanity.com/paper/2309.16971/) (2023)
- [Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modeling](https://mlsanity.com/paper/2402.18846/) (2024)
- [Multi-Fidelity Methods for Optimization: A Survey](https://mlsanity.com/paper/2402.09638/) (2024)
- [Diffusion-Generative Multi-Fidelity Learning for Physical Simulation](https://mlsanity.com/paper/2311.05606/) (2023)
- [MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning](https://mlsanity.com/paper/2410.11226/) (2024)
- [COMPOL: A Unified Neural Operator Framework for Scalable Multi-Physics Simulations](https://mlsanity.com/paper/2501.17296/) (2025)
- [Multi-Fidelity Flow Matching: Cascaded Refinement of PDE Solutions](https://mlsanity.com/paper/2605.16118/) (2026)

## Abstract (arXiv)

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.