Accurate and efficient modeling of soft-tissue interactions is fundamental for advancing surgical simulation, surgical robotics, and model-based surgical automation. To achieve real-time latency, classical Finite Element Method (FEM) solvers are often replaced with neural approximations; however, naively training such models in a fully data-driven manner without incorporating physical priors frequently leads to poor generalization and physically implausible predictions. We present a novel physics-informed neural simulation framework that enables real-time prediction of soft-tissue deformations under complex single- and multi-grasper interactions. Our approach integrates Kelvinlet-based analytical priors with large-scale FEM data, capturing both linear and nonlinear tissue responses. This hybrid design improves predictive accuracy and physical plausibility across diverse neural architectures while maintaining the low-latency performance required for interactive applications. We validate our method on challenging surgical manipulation tasks involving standard laparoscopic grasping tools, demonstrating substantial improvements in deformation fidelity and temporal stability over existing baselines. These results establish Kelvinlet-augmented learning as a principled and computationally efficient paradigm for real-time, physics-aware soft-tissue simulation in surgical AI.

翻译：软组织相互作用的精确高效建模是推进手术模拟、手术机器人及基于模型的手术自动化的基础。为实现实时延迟，经典有限元法求解器常被神经近似模型取代；然而，若在未融入物理先验的情况下完全以数据驱动方式训练此类模型，往往会导致泛化能力差及物理不可信的预测结果。本文提出一种新颖的物理信息神经模拟框架，能够实时预测复杂单抓持器与多抓持器相互作用下的软组织变形。该方法将基于开尔文核的解析先验与大规模有限元数据相结合，同时捕捉线性和非线性组织响应。这种混合设计在保持交互应用所需低延迟性能的同时，提升了不同神经架构的预测精度与物理合理性。我们在涉及标准腹腔镜抓持工具的外科操作任务上验证了所提方法，结果表明其在变形保真度与时间稳定性方面较现有基线方法有显著提升。这些成果确立了开尔文核增强学习作为一种原理清晰、计算高效的范式，可用于手术人工智能中实时且具有物理感知的软组织模拟。