PINGS: Physics-Informed Neural Network for Fast Generative Sampling

• URL: http://arxiv.org/abs/2509.11284v1
• Date: Sun, 14 Sep 2025 14:22:33 GMT
• Title: PINGS: Physics-Informed Neural Network for Fast Generative Sampling
• Abstract summary: We introduce PINGS, a framework that amortizes diffusion sampling by training a physics-informed network to approximate reverse-time probability-flow dynamics.<n>As a proof of concept, we learn a direct map from a 3D standard normal to a non-Gaussian Gaussian Mixture Model (GMM)<n>PINGS frames generative sampling as a PINN-style residual problem with endpoint anchoring, yielding a white-box, differentiable map with NFE = 1.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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).

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