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Data-Driven Learning of Unknown Nonlinear Differential Equations Using Functional Analysis

arXiv · AI, language, vision and robotics · article · Sep 3, 2026 · UTC

In this paper, the problem of data-driven discovery of nonlinear ordinary differential equations (ODEs) is recast, and a new interpretable machine learning (ML) method is proposed. The proposed method aims to learn the unknown vector field of nonlinear dynamics without prior knowledge of the system's physics from only one single state trajectory's data. The proposed method has two fundamental differences with existing methods: 1) the formulation presented in this method is derived based on Functional Analysis and Operator Theory, and 2) the cost function is constructed in the function space as

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