A unified perspective of Gaussian process approximation for differential equations
For researchers in scientific computing and machine learning, this provides a consolidated foundation for understanding and advancing GP-based numerical methods.
The paper unifies diverse Gaussian process-based methods for differential equations under a single probabilistic framework, enabling both parameter estimation and solution approximation.
The use of Gaussian processes for approximating differential equations has expanded rapidly, leading to a growing, diverse, and fragmented body of numerical methods. We present a unified Bayesian perspective that places these techniques within a common probabilistic framework, based on a derivative matching interpretation for incorporating differential equation constraints into likelihood. This unified perspective supports both parameter estimation and solution approximation, and shows how a range of existing methods can be understood within it. This work aims to consolidate current developments and provide a foundation for future research.