arXiv:2607.18787cs.CV2026-07被引 1

用图像模型模拟多种物理系统,无需专门求解器。

Image Editing Models are Numerical Solvers

论文配图:Image Editing Models are Numerical Solvers
图 1 · 摘自论文原文
  • 将物理方程转为图像编码,用预训练模型求解
  • 覆盖椭圆方程到纳维-斯托克斯等10类问题,效果良好
  • 适合快速原型验证,不适用于长期混沌系统

我们研究预训练生成式图像编辑模型能否作为通用数值模拟接口。物理输入与解以图像形式呈现,材料属性、扩散率等标量参数通过轻量适配器输入。利用已有的数值与解析求解器进行监督,采用相同架构和训练流程,处理了异质椭圆方程、受迫热传导与伯格斯演化、复杂金兹堡-朗道动力学、二维纳维-斯托克斯预测、势流、弹性力学、射线传播时间、相场断裂及熵正则最优传输等任务。结果表明,当每项任务通过合适视觉编码表达时,预训练图像模型可有效表示多种静态与动态物理映射,包括不稳定与激波行为。本工作为能力探索,非旨在超越专用求解器。同时揭示根本限制:图像与隐空间表示使数值范围选择复杂化,难以直接施加控制方程或守恒律;柯尔莫哥洛夫-西瓦辛斯基实验失败表明,表示误差导致混沌系统的长时序模拟无法有效进行。

原文摘要 · Abstract (English)

We investigate whether a pretrained generative image-editing model can provide a common interface for numerical simulation. Physical inputs and solutions are rendered as images, while scalar quantities such as material properties, diffusivity, and loading parameters enter through lightweight adapters. Using established numerical and analytic solvers for supervision, we apply the same architecture and training protocol to heterogeneous elliptic equations, forced heat and Burgers evolution, complex Ginzburg-Landau dynamics, two-dimensional Navier-Stokes prediction, potential flow, elasticity, eikonal travel time, phase-field fracture, and entropic optimal transport. The results show that a pretrained image model can represent diverse static and time-dependent physical mappings, including unstable and shock-like behavior, when each task is expressed through a suitable visual encoding. This work is a capability study rather than an attempt to surpass specialized solvers. It also identifies fundamental constraints: image and latent representations complicate numerical range selection and direct enforcement of governing equations or invariants, while a failed Kuramoto-Sivashinsky experiment indicates that representation errors prevent meaningful long-horizon simulation of chaotic systems.

物理模拟图像模型数值求解生成模型

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。