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Found 7 papers, 0 papers with code
Weak Collocation Regression for Inferring Stochastic Dynamics with Lévy Noise
In this work, we propose a Weak Collocation Regression (WCR) to explicitly reveal unknown stochastic dynamical systems, i. e., the Stochastic Differential Equation (SDE) with both $\alpha$-stable L\'{e}vy noise and Gaussian noise, from discrete aggregate data.
A note on the adjoint method for neural ordinary differential equation network
Perturbation and operator adjoint method are used to give the right adjoint form rigourously.
Reconstruction of dynamical systems from data without time labels
In this paper, we study the method to reconstruct dynamical systems from data without time labels.
Weak Collocation Regression method: fast reveal hidden stochastic dynamics from high-dimensional aggregate data
Taking the collocations of Gaussian functions as the test functions in the weak form of the FP equation, we transfer the derivatives to the Gaussian functions and thus approximate the weak form by the expectational sum of the data.
BI-GreenNet: Learning Green's functions by boundary integral network
In addition, we also use the Green's function calculated by our method to solve a class of PDE, and also obtain high-precision solutions, which shows the good generalization ability of our method on solving PDEs.
A neural network framework for learning Green's function
Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs).
Revealing hidden dynamics from time-series data by ODENet
To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields.
