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

The paper proposes a new interpretable machine learning approach for discovering unknown nonlinear ordinary differential equations from a single state trajectory. It differs from existing methods by deriving its formulation from Functional Analysis and Operator Theory and by defining a cost function as an integral distance between functions rather than a discrete error sum. An incremental learning algorithm enables online updates, allowing simultaneous identification of both system dynamics and external time‑varying forces, with numerical examples illustrating its benefits.

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