The Physics Is the Network: Fast, Training-Free Neural Emulation
Training-free PolyNets emulate known polynomial physics with solver-level accuracy and strong GPU ensemble scaling.
The paper introduces PolyNets that combine a continuous-time neural representation of polynomial dynamics with a recurrent network for discrete-time integration. When governing coefficients are known, the tensor graph needs no training and preserves the prescribed numerical scheme while running efficiently on hardware. Using the one-dimensional Korteweg-de Vries equation, PolyNet matches CPU and GPU finite-difference Runge-Kutta accuracy, including amplitudes outside the training conditions of three learned neural baselines. Tests cover grid resolutions, one million dispersively scaled time steps, and ensembles of up to 10,000 trajectories, with roughly constant GPU throughput.
- Known polynomial coefficients let PolyNet run without training.
- Compared on the Korteweg-de Vries equation against CPU and GPU solvers.
- Accuracy matches numerical solvers beyond trained models' amplitude range.
- GPU throughput stays roughly flat and ensembles scale to 10,000 trajectories.
From the original article
1 min read at arxiv.orgNeural 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.
By Luka Todorovic · arxiv.org
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