Learning Neural Optimal Interpolation Models and Solvers

TL;DR

This paper introduces a neural optimal interpolation framework that learns scalable, efficient models and solvers for complex, high-dimensional, and noisy spatio-temporal data, outperforming existing methods especially with high missing data.

Contribution

It proposes a neural OI scheme using variational formulation, auto-encoders, and trainable iterative solvers, theoretically equivalent to classical OI and applicable to non-linear, multimodal problems.

Findings

Demonstrates the neural OI's ability to learn efficient, scalable models from synthetic data.

Shows significant performance improvements over state-of-the-art methods on real satellite data.

Validates convergence of the trainable solver to classical OI solutions.

Abstract

The reconstruction of gap-free signals from observation data is a critical challenge for numerous application domains, such as geoscience and space-based earth observation, when the available sensors or the data collection processes lead to irregularly-sampled and noisy observations. Optimal interpolation (OI), also referred to as kriging, provides a theoretical framework to solve interpolation problems for Gaussian processes (GP). The associated computational complexity being rapidly intractable for n-dimensional tensors and increasing numbers of observations, a rich literature has emerged to address this issue using ensemble methods, sparse schemes or iterative approaches. Here, we introduce a neural OI scheme. It exploits a variational formulation with convolutional auto-encoders and a trainable iterative gradient-based solver. Theoretically equivalent to the OI formulation, the trainable solver asymptotically converges to the OI solution when dealing with both stationary and non-stationary linear spatio-temporal GPs. Through a bi-level optimization formulation, we relate the learning step and the selection of the training loss to the theoretical properties of the OI, which is an unbiased estimator with minimal error variance. Numerical experiments for 2D+t synthetic GP datasets demonstrate the relevance of the proposed scheme to learn computationally-efficient and scalable OI models and solvers from data. As illustrated for a real-world interpolation problems for satellite-derived geophysical dynamics, the proposed framework also extends to non-linear and multimodal interpolation problems and significantly outperforms state-of-the-art interpolation methods, when dealing with very high missing data rates.