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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.
Temporal Difference Learning for High-Dimensional PIDEs with Jumps
In this paper, we propose a deep learning framework for solving high-dimensional partial integro-differential equations (PIDEs) based on the temporal difference learning.
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.
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