用物理约束的神经算子，18小时变秒级预测液滴在复杂表面的扩散动态。
Droplet-LNO: Physics-Informed Laplace Neural Operators for Accurate Prediction of Droplet Spreading Dynamics on Complex Surfaces
- 基于拉普拉斯变换构建物理感知函数基，天然捕捉指数型动态变化。
- 在接触角20°~160°的多表面数据上，预测精度超越5种先进方法。
- 适合需快速高保真模拟的微流控、喷墨打印等工程场景。
液滴在固体表面的铺展是广泛应用于喷墨打印、喷雾冷却和生物医学微流体系统中的经典多物理场问题。然而，精确的计算流体动力学（CFD）模拟极为耗时，单次瞬态计算需18至24小时。本文提出物理信息拉普拉斯神经算子（PI-LNO），其核心是将拉普拉斯积分变换函数作为可学习的物理信息函数基。通过与五种前沿方法（UNet、UNet-AM、DeepONet、PI-UNet、LNO）的全面对比实验验证，该模型能原生建模铺展过程的指数型瞬态行为。基于TensorFlow实现的PI-LNO，在接触角θ_s ∈ [20,160] 的多表面CFD数据上训练，采用结合数据拟合（MSE、MAE、RMSE）与纳维-斯托克斯、卡恩-希里哈德方程及因果性约束的物理正则化复合损失函数。
原文摘要 · Abstract (English)
Spreading of liquid droplets on solid substrates constitutes a classic multiphysics problem with widespread applications ranging from inkjet printing, spray cooling, to biomedical microfluidic systems. Yet, accurate computational fluid dynamic (CFD) simulations are prohibitively expensive, taking more than 18 to 24 hours for each transient computation. In this paper, Physics-Informed Laplace Operator Neural Network (PI-LNO) is introduced, representing a novel architecture where the Laplace integral transform function serves as a learned physics-informed functional basis. Extensive comparative benchmark studies were performed against five other state-of-the-art approaches: UNet, UNet with attention modules (UNet-AM), DeepONet, Physics-Informed UNet (PI-UNet), and Laplace Neural Operator (LNO). Through complex Laplace transforms, PI-LNO natively models the exponential transient dynamics of the spreading process. A TensorFlow-based PI-LNO is trained on multi-surface CFD data spanning contact angles $θ_s ε[20,160]$, employing a physics-regularized composite loss combining data fidelity (MSE, MAE, RMSE) with Navier-Stokes, Cahn-Hilliard, and causality constraints.
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