# Multi-fidelity Hierarchical Neural Processes

arXiv: https://arxiv.org/abs/2206.04872 · HTML: https://mlsanity.com/paper/2206.04872/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 43 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 19 of 19)

- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Multi-fidelity Bayesian Optimisation with Continuous Approximations](https://mlsanity.com/paper/1703.06240/) (2017)
- [Multi-fidelity Bayesian Neural Networks: Algorithms and Applications](https://mlsanity.com/paper/2012.13294/) (2020)
- [Sequential Neural Processes](https://mlsanity.com/paper/1906.10264/) (2019)
- [Deep Gaussian Processes for Multi-fidelity Modeling](https://mlsanity.com/paper/1903.07320/) (2019)
- [Multi-Fidelity Bayesian Optimization via Deep Neural Networks](https://mlsanity.com/paper/2007.03117/) (2020)
- [The Functional Neural Process](https://mlsanity.com/paper/1906.08324/) (2019)
- [Doubly Stochastic Variational Inference for Neural Processes with Hierarchical Latent Variables](https://mlsanity.com/paper/2008.09469/) (2020)
- [Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities](https://mlsanity.com/paper/2102.13403/) (2021)
- [On transfer learning of neural networks using bi-fidelity data for uncertainty propagation](https://mlsanity.com/paper/2002.04495/) (2020)
- [Overview of Gaussian process based multi-fidelity techniques with variable relationship between fidelities](https://mlsanity.com/paper/2006.16728/) (2020)
- [Multi-fidelity modeling with different input domain definitions using Deep Gaussian Processes](https://mlsanity.com/paper/2006.15924/) (2020)
- [Deep Multi-fidelity Gaussian Processes](https://mlsanity.com/paper/1604.07484/) (2016)
- [Batch Multi-Fidelity Bayesian Optimization with Deep Auto-Regressive Networks](https://mlsanity.com/paper/2106.09884/) (2021)

## Built on by (most cited first, 15 of 15)

- [Spectral Diffusion Processes](https://mlsanity.com/paper/2209.14125/) (2022)
- [The Neural Process Family: Survey, Applications and Perspectives](https://mlsanity.com/paper/2209.00517/) (2022)
- [Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modeling](https://mlsanity.com/paper/2402.18846/) (2024)
- [Disentangled Multi-Fidelity Deep Bayesian Active Learning](https://mlsanity.com/paper/2305.04392/) (2023)
- [Infinite-Fidelity Coregionalization for Physical Simulation](https://mlsanity.com/paper/2207.00678/) (2022)
- [Entity Aware Modelling: A Survey](https://mlsanity.com/paper/2302.08406/) (2023)
- [Multi-fidelity climate model parameterization for better generalization and extrapolation](https://mlsanity.com/paper/2309.10231/) (2023)
- [Practical multi-fidelity machine learning: fusion of deterministic and Bayesian models](https://mlsanity.com/paper/2407.15110/) (2024)
- [GAR: Generalized Autoregression for Multi-Fidelity Fusion](https://mlsanity.com/paper/2301.05729/) (2023)
- [Diffusion-Generative Multi-Fidelity Learning for Physical Simulation](https://mlsanity.com/paper/2311.05606/) (2023)
- [MFBind: a Multi-Fidelity Approach for Evaluating Drug Compounds in Practical Generative Modeling](https://mlsanity.com/paper/2402.10387/) (2024)
- [Progressive multi-fidelity learning with neural networks for physical system predictions](https://mlsanity.com/paper/2510.13762/) (2025)
- [Assessing the performance of correlation-based multi-fidelity neural emulators](https://mlsanity.com/paper/2512.02868/) (2025)
- [MF-LAL: Drug Compound Generation Using Multi-Fidelity Latent Space Active Learning](https://mlsanity.com/paper/2410.11226/) (2024)
- [Real-Time Performance Analysis of Multi-Fidelity Residual Physics-Informed Neural Process-Based State Estimation for Robotic Systems](https://mlsanity.com/paper/2511.08231/) (2025)

## Abstract (arXiv)

Science and engineering fields use computer simulation extensively. These simulations are often run at multiple levels of sophistication to balance accuracy and efficiency. Multi-fidelity surrogate modeling reduces the computational cost by fusing different simulation outputs. Cheap data generated from low-fidelity simulators can be combined with limited high-quality data generated by an expensive high-fidelity simulator. Existing methods based on Gaussian processes rely on strong assumptions of the kernel functions and can hardly scale to high-dimensional settings. We propose Multi-fidelity Hierarchical Neural Processes (MF-HNP), a unified neural latent variable model for multi-fidelity surrogate modeling. MF-HNP inherits the flexibility and scalability of Neural Processes. The latent variables transform the correlations among different fidelity levels from observations to latent space. The predictions across fidelities are conditionally independent given the latent states. It helps alleviate the error propagation issue in existing methods. MF-HNP is flexible enough to handle non-nested high dimensional data at different fidelity levels with varying input and output dimensions. We evaluate MF-HNP on epidemiology and climate modeling tasks, achieving competitive performance in terms of accuracy and uncertainty estimation. In contrast to deep Gaussian Processes with only low-dimensional (< 10) tasks, our method shows great promise for speeding up high-dimensional complex simulations (over 7000 for epidemiology modeling and 45000 for climate modeling).