AI-Supported Dynamic System Identification: Recognizing a Differential Equation from Response Data

Abstract

The paper proposes an approach to modeling dynamic systems by identifying the governing differential equations based on system responses. The work answers the question whether Artificial Neural Networks (ANNs) can be trained to recognize and infer symbolic representations of differential equations, just observing the response data. The proposed method consists of a two-stage pipeline. The first stage - Structural identification, when governing differential equation (DE) type recognition occurs. The stage is implemented as Transducer which transforms data from one representation to another while preserving the semantic content. The method takes advantage of the heuristic mechanism, bridging the gap between human cognition and machine learning. The second stage - Parametric identification, when the inferred equation coefficients are refined. Experiments were conducted using surrogate datasets generated from various classes of differential equations typical for oscillatory systems. The results demonstrate that trained ANN can effectively classify DEs, while the refinement process might provide an accurate parameter estimation.