Qi Sun

Qi Sun, Xuejun Xu, Haotian Yi

Non-overlapping domain decomposition methods are natural for solving interface problems arising from various disciplines, however, the numerical simulation requires technical analysis and is often available only with the use of high-quality grids, thereby impeding their use in more complicated situations. To remove the burden of mesh generation and to effectively tackle with the interface jump conditions, a novel mesh-free scheme, i.e., Dirichlet-Neumann learning algorithm, is proposed in this work to solve the benchmark elliptic interface problem with high-contrast coefficients as well as irregular interfaces. By resorting to the variational principle, we carry out a rigorous error analysis to evaluate the discrepancy caused by the boundary penalty treatment for each decomposed subproblem, which paves the way for realizing the Dirichlet-Neumann algorithm using neural network extension operators. The effectiveness and robustness of our proposed methods are demonstrated experimentally through a series of elliptic interface problems, achieving better performance over other alternatives especially in the presence of erroneous flux prediction at interface.

Yicheng Zhan, Liang Shi, Wojciech Matusik et al.

Emerging learned holography approaches have enabled faster and high-quality hologram synthesis, setting a new milestone toward practical holographic displays. However, these learned models require training a dedicated model for each set of display-scene parameters. To address this shortcoming, our work introduces a highly configurable learned model structure, synthesizing 3D holograms interactively while supporting diverse display-scene parameters. Our family of models relying on this structure can be conditioned continuously for varying novel scene parameters, including input images, propagation distances, volume depths, peak brightnesses, and novel display parameters of pixel pitches and wavelengths. Uniquely, our findings unearth a correlation between depth estimation and hologram synthesis tasks in the learning domain, leading to a learned model that unlocks accurate 3D hologram generation from 2D images across varied display-scene parameters. We validate our models by synthesizing high-quality 3D holograms in simulations and also verify our findings with two different holographic display prototypes. Moreover, our family of models can synthesize holograms with a 2x speed-up compared to the state-of-the-art learned holography approaches in the literature.