# The Physics Is the Network: Fast, Training-Free Neural Emulation

arXiv: https://arxiv.org/abs/2610.20525 · HTML: https://mlsanity.com/paper/2610.20525/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 17 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Builds on (most cited first, 8 of 8)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Data Driven Governing Equations Approximation Using Deep Neural Networks](https://mlsanity.com/paper/1811.05537/) (2018)
- [Out-of-Distribution Generalization for Neural Physics Solvers](https://mlsanity.com/paper/2601.19091/) (2026)
- [Neural Integration of Continuous Dynamics](https://mlsanity.com/paper/1911.10309/) (2019)
- [Solver-Integrated Adversarial Attacking and Training of Neural Operators](https://mlsanity.com/paper/2510.18989/) (2025)

## Abstract (arXiv)

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.