The Physics Is the Network: Fast, Training-Free Neural Emulation
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.
Related
- Lazy training of quantum physics informed neural networks
- Preconditioned Physics-Informed Neural Operator Training
- Need for Speed: Fast and Accurate Pricing of American Options Using Parameterized Physics-Informed Neural Networks
- A Non-Monotone Preconditioned Trust-Region Method for Neural Network Training
- Comparison of a Parametric Physics-Informed Neural Network and a Tensorial Reduced-Order Model for the Shallow-Water Dam-Break Problem
BibTeX
@misc{todorovic2026physics,
title = {{The Physics Is the Network: Fast, Training-Free Neural Emulation}},
author = {Luka Todorovic and Kaushal Gianchandani and Sai Ravela},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20525},
eprint = {2610.20525},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20525},
}
RIS
TY - UNPB
TI - The Physics Is the Network: Fast, Training-Free Neural Emulation
AU - Luka Todorovic
AU - Kaushal Gianchandani
AU - Sai Ravela
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20525
UR - https://arxiv.org/abs/2610.20525
AB - 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.
ER -