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Frequency multiplier estimates for the linearized relativistic Boltzmann operator without angular cutoff
Namely, it is crucial to obtain the sharp asymptotics for the frequency multiplier to obtain this coercivity that has never been established before.
Analysis of PDEs
Sobolev Training for the Neural Network Solutions of PDEs
Inspired by the recent studies that incorporate derivative information for the training of neural networks, we develop a loss function that guides a neural network to reduce the error in the corresponding Sobolev space.
The model reduction of the Vlasov-Poisson-Fokker-Planck system to the Poisson-Nernst-Planck system via the Deep Neural Network Approach
The model reduction of a mesoscopic kinetic dynamics to a macroscopic continuum dynamics has been one of the fundamental questions in mathematical physics since Hilbert's time.
Trend to Equilibrium for the Kinetic Fokker-Planck Equation via the Neural Network Approach
The issue of the relaxation to equilibrium has been at the core of the kinetic theory of rarefied gas dynamics.
