3 papers
math-ph2025
Mathematical and numerical studies on ground states of trapped unitary Fermi gases
Yongyong Cai, Xinran Ruan, Yanzhi Zhang
We mathematically and numerically study the ground states of unitary Fermi gases. Starting from the three-dimensional nonlinear Schrödinger equation that contains a quantum pressu…
math.NA2025
Nonlocal modeling of spatial fractional diffusion with truncated interaction domains and truncated kernel function singularity
Shiping Zhou, Yanzhi Zhang, Max Gunzburger
Parabolic partial differential equations (PDEs) are in ubiquitous, very effective use to model diffusion processes. However, there are many applications (e.g., such as in hydrology…
cs.LG2025
Discretization-independent multifidelity operator learning for partial differential equations
Jacob Hauck, Yanzhi Zhang
We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for input and output function distributio…