4 papers
On the convergence of PINNs for inverse source problem in the complex Ginzburg-Landau equation
Xing Cheng, Zhiyuan Li, Mengmeng Zhang +1
This paper addresses the problem of recovering the spatial profile of the source in the complex Ginzburg-Landau equation from regional observation data at fixed times. We establish…
Conditional well-posedness and data-driven method for identifying the dynamic source in a coupled diffusion system from one single boundary measurement
Chunlong Sun, Mengmeng Zhang, Zhidong Zhang
This work considers the inverse dynamic source problem arising from the time-domain fluorescence diffuse optical tomography (FDOT). We recover the dynamic distributions of fluoroph…
Solving the inverse potential problem in the parabolic equation by the deep neural networks method
Mengmeng Zhang, Zhidong Zhang
In this work, we consider an inverse potential problem in the parabolic equation, where the unknown potential is a space-dependent function and the used measurement is the final ti…
On the well-posedness of the time-fractional diffusion equation with Robin boundary condition
Mengmeng Zhang, Jijun Liu
The diffusion system with time-fractional order derivative is of great importance mathematically due to the nonlocal property of the fractional order derivative, which can be appli…