用物理约束神经网络实现单步生成，速度比现有方法快10倍以上。
PINGS: Physics-Informed Neural Network for Fast Generative Sampling
- 训练神经网络逼近扩散过程的反向动力学，采样只需一次前向计算。
- 在RTX 3090上生成1万样本仅需16.54毫秒，误差极小（MMD²=0.0188）。
- 适合需要快速生成且需可解释性的科学模拟场景，如热力学建模。
我们提出PINGS（Physics-Informed Neural Network for Fast Generative Sampling），一种通过训练物理信息神经网络来近似反向时间概率流动力学，将扩散采样过程退化为单次前向传播（NFE = 1）的框架。作为概念验证，我们学习从三维标准正态分布到非高斯混合模型（GMM）的直接映射。PINGS保持了目标分布结构，均值、协方差、偏度和峰度误差极小，多带宽核MMD² = 1.88 × 10⁻²。在RTX 3090上，生成10⁴个样本耗时仅16.54 ± 0.56毫秒，远快于DPM-Solver（10/20）的468–843毫秒和DDIM（50）的960毫秒。同时，在阻尼谐振子上对PINN/自动微分管道进行验证，均方误差降至10⁻⁵量级。相比快速但迭代的常微分方程求解器与直接映射方法（Flow、Rectified-Flow、Consistency），PINGS将生成采样视为带有端点约束的PINN残差问题，实现白盒、可微映射，且NFE=1。这些初步结果表明，PINGS是实现快速、函数化生成采样的有前景路径，未来可扩展至科学仿真（如快速量热法）。
原文摘要 · Abstract (English)
We introduce PINGS (Physics-Informed Neural Network for Fast Generative Sampling), a framework that amortizes diffusion sampling by training a physics-informed network to approximate reverse-time probability-flow dynamics, reducing sampling to a single forward pass (NFE = 1). As a proof of concept, we learn a direct map from a 3D standard normal to a non-Gaussian Gaussian Mixture Model (GMM). PINGS preserves the target's distributional structure (multi-bandwidth kernel $MMD^2 = 1.88 \times 10^{-2}$ with small errors in mean, covariance, skewness, and excess kurtosis) and achieves constant-time generation: $10^4$ samples in $16.54 \pm 0.56$ millisecond on an RTX 3090, versus 468-843 millisecond for DPM-Solver (10/20) and 960 millisecond for DDIM (50) under matched conditions. We also sanity-check the PINN/automatic-differentiation pipeline on a damped harmonic oscillator, obtaining MSEs down to $\mathcal{O}(10^{-5})$. Compared to fast but iterative ODE solvers and direct-map families (Flow, Rectified-Flow, Consistency), PINGS frames generative sampling as a PINN-style residual problem with endpoint anchoring, yielding a white-box, differentiable map with NFE = 1. These proof-of-concept results position PINGS as a promising route to fast, function-based generative sampling with potential extensions to scientific simulation (e.g., fast calorimetry).
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。