Identifying Unknown Stochastic Dynamics via Finite expression methods
This addresses the need for interpretable and generalizable SDE models in scientific fields, though it appears incremental as it builds on existing symbolic and generative techniques.
The paper tackled the problem of modeling stochastic differential equations (SDEs) by introducing the Finite Expression Method (FEX), a symbolic learning approach that derives interpretable mathematical representations, and it demonstrated that FEX generalizes better and provides more accurate long-term predictions compared to neural network-based methods.
Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a combination of deterministic and stochastic terms. However, these models usually lack interpretability and have difficulty generalizing beyond their training domain. This paper introduces the Finite Expression Method (FEX), a symbolic learning approach designed to derive interpretable mathematical representations of the deterministic component of SDEs. For the stochastic component, we integrate FEX with advanced generative modeling techniques to provide a comprehensive representation of SDEs. The numerical experiments on linear, nonlinear, and multidimensional SDEs demonstrate that FEX generalizes well beyond the training domain and delivers more accurate long-term predictions compared to neural network-based methods. The symbolic expressions identified by FEX not only improve prediction accuracy but also offer valuable scientific insights into the underlying dynamics of the systems, paving the way for new scientific discoveries.