Local parameter identification with neural ordinary differential equations

The data-driven methods extract the feature information from data to build system models, which enable estimation and identification of the systems and can be utilized for prognosis and health management(PHM). However, most data-driven models are still black-box models that cannot be interpreted. In this study, we use the neural ordinary differential equations(ODEs), especially the inherent computational relationships of a system added to the loss function calculation, to approximate the governing equations. In addition, a new strategy for identifying the local parameters of the system is investigated, which can be utilized for system parameter identification and damage detection. The numerical and experimental examples presented in the paper demonstrate that the strategy has high accuracy and good local parameter identification. Moreover, the proposed method has the advantage of being interpretable. It can directly approximate the underlying governing dynamics and be a worthwhile strategy for system identification and PHM.

ChemNODE: A neural ordinary differential equations framework for efficient chemical kinetic solvers

Solving for detailed chemical kinetics remains one of the major bottlenecks for computational fluid dynamics simulations of reacting flows using a finite-rate-chemistry approach.This has motivated the use of neural networks to predict stiff chemical source terms as functions of the thermochemical state of the combustion system.However,due to the nonlinearities and multi-scale nature of combustion,the predicted solution often diverges from the true solution when these machine learning models are coupled with a computational fluid dynamics solver.This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation solvers.In the present work,a novel neural ordinary differential equations approach to modeling chemical kinetics,termed as ChemNODE,is developed.In this machine learning framework,the chemical source terms predicted by the neural networks are integrated during training,and by computing the required derivatives,the neural network weights are adjusted accordingly to minimize the difference between the predicted and ground-truth solution.A proof-of-concept study is performed with ChemNODE for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions.It is shown that ChemNODE accurately captures the chemical kinetic behavior and reproduces the results obtained using the detailed kinetic mechanism at a fraction of the computational cost.

Synthetic PMU Data Creation Based on Generative Adversarial Network Under Time-varying Load Conditions

In this study,a machine learning based method is proposed for creating synthetic eventful phasor measurement unit(PMU)data under time-varying load conditions.The proposed method leverages generative adversarial networks to create quasi-steady states for the power system under slowly-varying load conditions and incorporates a framework of neural ordinary differential equations(ODEs)to capture the transient behaviors of the system during voltage oscillation events.A numerical example of a large power grid suggests that this method can create realistic synthetic eventful PMU voltage measurements based on the associated real PMU data without any knowledge of the underlying nonlinear dynamic equations.The results demonstrate that the synthetic voltage measurements have the key characteristics of real system behavior on distinct time scales.