# Multi-model Ensemble Analysis with Neural Network Gaussian Processes

arXiv: https://arxiv.org/abs/2202.04152 · HTML: https://mlsanity.com/paper/2202.04152/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 55 references that are in the map.
- First posted on arXiv 8 Feb 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [Deep Convolutional Networks as shallow Gaussian Processes](https://mlsanity.com/paper/1808.05587/) (2018)
- [Harnessing the Power of Infinitely Wide Deep Nets on Small-data Tasks](https://mlsanity.com/paper/1910.01663/) (2019)
- [The Recurrent Neural Tangent Kernel](https://mlsanity.com/paper/2006.10246/) (2020)
- [A multi-resolution approximation for massive spatial datasets](https://mlsanity.com/paper/1507.04789/) (2015)
- [Mediated Experts for Deep Convolutional Networks](https://mlsanity.com/paper/1511.06072/) (2015)

## Built on by (most cited first, 2 of 2)

- [Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modeling](https://mlsanity.com/paper/2402.18846/) (2024)
- [Quantifying uncertainty in climate projections with conformal ensembles](https://mlsanity.com/paper/2408.06642/) (2024)

## Abstract (arXiv)

Multi-model ensemble analysis integrates information from multiple climate models into a unified projection. However, existing integration approaches based on model averaging can dilute fine-scale spatial information and incur bias from rescaling low-resolution climate models. We propose a statistical approach, called NN-GPR, using Gaussian process regression (GPR) with an infinitely wide deep neural network based covariance function. NN-GPR requires no assumptions about the relationships between models, no interpolation to a common grid, no stationarity assumptions, and automatically downscales as part of its prediction algorithm. Model experiments show that NN-GPR can be highly skillful at surface temperature and precipitation forecasting by preserving geospatial signals at multiple scales and capturing inter-annual variability. Our projections particularly show improved accuracy and uncertainty quantification skill in regions of high variability, which allows us to cheaply assess tail behavior at a 0.44^circ/50 km spatial resolution without a regional climate model (RCM). Evaluations on reanalysis data and SSP245 forced climate models show that NN-GPR produces similar, overall climatologies to the model ensemble while better capturing fine scale spatial patterns. Finally, we compare NN-GPR's regional predictions against two RCMs and show that NN-GPR can rival the performance of RCMs using only global model data as input.