As a usual component in virtual scenes, water surface plays an important role in various graphical applications, including special effects, video games, and virtual reality. Although recent years have witnessed significant progress based on Navier-Stokes equations and simplified water models, large-scale water surface waves with high-frequency visual details remain computationally expensive for interactive applications. This article proposes a novel frequency-aware neural network to synthesize consistent and detailed water surface waves from low-resolution input. At its core, our approach leverage the wavelet transformation theory over space, frequency and direction, and incremental supervision to decompose the 4D amplitude function into multiple smaller subproblems. Specifically, we first customize four subnetworks and corresponding loss functions for super-resolution of spatial resolution, temporal evolution, wave direction subdivision, and wave number, respectively. Then, to enforce the upsampling along each dimension orthogonal to each other, we introduce a cooperative training scheme to fine-tune and integrate the proposed subnetworks with carefully designed training dataset. Our method can visually enhance high-resolution spatial details, temporal coherence, interactions with complex boundaries, and various wave patterns with flexible control along multiple dimensions. Through extensive experiments, our method arrives at 13× speedup for 32× upsampling of various simulation scenarios. We also validate the effectiveness and robustness of our method to produce realistic water surface waves toward artistic innovation.

Desiccation cracking of soil-like materials is a common phenomenon in natural dry environment, however, it remains a challenge to model and simulate complicated multi-physical processes inside the porous structure. With the goal of tracking such physical evolution accurately, we propose an MPM based method to simulate volumetric shrinkage and crack during moisture diffusion. At the physical level, we introduce Richards equations to evolve the dynamic moisture field to model evaporation and diffusion in unsaturated soils, with which a elastoplastic model is established to simulate strength changes and volumetric shrinkage via a novel saturation-based hardening strategy during plastic treatment. At the algorithmic level, we develop an MPM-fashion numerical solver for the proposed physical model and achieve stable yet efficient simulation towards delicate deformation and fracture. At the geometric level, we propose a correlating stretching criteria and a saturation-aware extrapolation scheme to extend existing surface reconstruction for MPM, producing visual compelling soil appearance. Finally, we manifest realistic simulation results based on the proposed method with several challenging scenarios, which demonstrates usability and efficiency of our method.