# KITINet: Kinetics Theory Inspired Network Architectures with PDE Simulation Approaches Source: [KITINet: Kinetics Theory Inspired Network Architectures with PDE Simulation Approaches]() Collection index: [llms.txt]() Data updated: 2025-10-26T04:45:08.569Z Authors: Mingquan Feng, Yifan Fu, Tongcheng Zhang, Yu Jiang, Yixin Huang, Junchi Yan Published: 2025-05-23T13:58:29.000Z ## Abstract Despite the widely recognized success of residual connections in modern neural networks, their design principles remain largely heuristic. This paper introduces KITINet (Kinetics Theory Inspired Network), a novel architecture that reinterprets feature propagation through the lens of non-equilibrium particle dynamics and partial differential equation (PDE) simulation. At its core, we propose a residual module that models feature updates as the stochastic evolution of a particle system, numerically simulated via a discretized solver for the Boltzmann transport equation (BTE). This formulation mimics particle collisions and energy exchange, enabling adaptive feature refinement via physics-informed interactions. Additionally, we reveal that this mechanism induces network parameter condensation during training, where parameters progressively concentrate into a sparse subset of dominant channels. Experiments on scientific computation (PDE operator), image classification (CIFAR-10/100), and text classification (IMDb/SNLI) show consistent improvements over classic network baselines, with negligible increase of FLOPs. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()