A Systematic Review of PDE-based models for advanced rendering in computer graphics: Methods, Architectures, and Future Research Directions

Abstract

Partial differential equation (PDE)-based models have emerged as a foundational paradigm for achieving physically accurate and computationally efficient rendering in modern computer graphics. These models enable the formulation of light transport, diffusion, wave propagation, and radiative transfer phenomena in mathematically rigorous ways, bridging the gap between realism and computational feasibility. This systematic review examines recent advancements in PDE-based rendering methods, focusing on numerical techniques, hybrid architectures, and integration with data-driven approaches such as machine learning. The paper analyzes state-of-the-art contributions from 2018 to 2025, highlighting how PDE formulations enhance global illumination, volumetric rendering, subsurface scattering, and neural rendering pipelines. Key findings reveal a shift toward hybrid frameworks combining PDE solvers with neural networks, improved discretization techniques for real-time performance, and the growing importance of differentiable rendering. The review contributes a structured synthesis of existing methodologies, identifies research gaps in scalability and generalization, and proposes future directions including AI-assisted PDE solvers and real-time physically based rendering systems.