PINGS: Physics-Informed Neural Network for Fast Generative Sampling
This addresses the need for faster generative sampling in machine learning, though it is incremental as it builds on existing diffusion and PINN methods.
The paper tackled the problem of slow sampling in diffusion models by introducing PINGS, a physics-informed neural network framework that reduces sampling to a single forward pass, achieving constant-time generation of 10^4 samples in 16.54 milliseconds with preserved distributional accuracy (MMD^2 = 1.88e-2).
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).