arXiv：cs.LG· Luka Todorovic, Kaushal Gianchandani, Sai Ravela·· 4 小时前
PolyNets：无需训练的快速神经仿真
The Physics Is the Network: Fast, Training-Free Neural Emulation
AI 导读
研究提出 PolyNets，将多项式动力学的连续时间神经表示与离散时间积分的简单循环网络耦合，在已知控制系数时张量图无需训练即可保持预设数值格式。在一维 Korteweg-de Vries 方程上，其精度与 CPU、GPU 有限差分 Runge-Kutta 求解器相当，并在训练条件之外的振幅下依然有效。
正文
Abstract:Neural emulation need not require learning a substitute for known physics. We investigate PolyNets that couple a continuous-time neural representation of polynomial dynamics with a simple recurrent network for discrete-time integration. When the governing coefficients are known, the resulting tensor graph requires no training and preserves the prescribed numerical scheme while enabling efficient hardware execution and parallel simulation. Using the one-dimensional Korteweg-de Vries equation, we compare PolyNet with CPU and GPU finite-difference Runge-Kutta solvers and three trained neural models: a state-map emulator, a physics-informed predictor, and a learned-tendency integrator. Analytical soliton solutions provide a reference for amplitude and phase errors across grid resolutions, 10^6 dispersively scaled time steps, ensembles of up to 10^4 trajectories, and varying initial amplitudes. PolyNet achieves accuracy comparable to the numerical solvers, including at amplitudes outside the learned models' training conditions. It combines this fidelity with high GPU throughput, approximately constant over the tested resolution range, and favorable ensemble scaling.
| Subjects: | Machine Learning (cs.LG); Systems and Control (eess.SY); Chaotic Dynamics (nlin.CD); Applications (stat.AP) |
| MSC classes: | 76-10, 65P20 |
| ACM classes: | J.2 |
| Cite as: | arXiv:2610.20525 [cs.LG] |
| (or arXiv:2610.20525v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.20525 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Sai Ravela [view email]
[v1]
Wed, 14 Oct 2026 17:24:48 UTC (2,263 KB)
来源：arXiv：cs.LG · arxiv.org