科研成果

Numerical resolution of moderately high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality for the classical numerical methods including finite difference, finite element and spectral methods. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by tracking the deterministic motion, random jump, resampling and reweighting of particles. Real-valued weighted particles are adopted by SPM to approximate the high-dimensional solution, which automatically adjusts the point distribution to intimate the relevant feature of the solution. A piecewise constant reconstruction with virtual uniform grid is employed to evaluate the nonlinear terms, which fully exploits the intrinsic adaptive characteristic of SPM. Combining both, SPM can achieve the goal of adaptive sampling in time. Numerical experiments on the 6-D Allen-Cahn equation and the 7- D Hamiltonian-Jacobi-Bellman equation demonstrate the potential of SPM in solving moderately high-dimensional nonlinear PDEs efficiently while maintaining an acceptable accuracy

<p>This perspective article highlights the pressing necessity to focus on heterogeneity in organ-specific aging, emphasizing the influence of environmental and climate changes, as well as social interactions, on the aging process of individual organs. It explores innovative and integrative strategies tailored to the unique aging mechanisms of different organs, aiming to preserve their biological clocks. By emphasizing the importance of addressing organ-specific vulnerabilities, the article calls for transcending traditional pharmacological treatments and organ transplants. It proposes a comprehensive approach that combines environmental management, social support systems, and advanced technological interventions to improve the well-being and longevity of aging populations.</p>