A Bayesian Approach for Discovering Time- Delayed Differential Equation from Data
This addresses a challenging modeling problem for complex dynamic systems, offering a robust and scalable solution, though it appears incremental as it builds on Bayesian inference with sparsity-promoting priors.
The paper tackles the problem of inferring time-delayed differential equations from noisy data, presenting BayTiDe, a Bayesian method that identifies arbitrarily large time delays with accuracy proportional to data resolution and achieves computational savings.
Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem due to the inherent nonlinearity, uncertainty, and noise in real-world systems. Conventional equation discovery methods often exhibit limitations when dealing with large time delays, relying on deterministic techniques or optimization-based approaches that may struggle with scalability and robustness. In this paper, we present BayTiDe - Bayesian Approach for Discovering Time-Delayed Differential Equations from Data, that is capable of identifying arbitrarily large values of time delay to an accuracy that is directly proportional to the resolution of the data input to it. BayTiDe leverages Bayesian inference combined with a sparsity-promoting discontinuous spike-and-slab prior to accurately identify time-delayed differential equations. The approach accommodates arbitrarily large time delays with accuracy proportional to the input data resolution, while efficiently narrowing the search space to achieve significant computational savings. We demonstrate the efficiency and robustness of BayTiDe through a range of numerical examples, validating its ability to recover delayed differential equations from noisy data.