aiqbench analysis
This research introduces PolyNets, a novel architecture that couples continuous-time polynomial dynamics with recurrent networks to simulate physical systems without requiring training when governing equations are known. By preserving standard numerical schemes like Runge-Kutta while leveraging GPU parallelism, the method achieves high-fidelity soliton simulations comparable to traditional solvers but with superior ensemble scaling and throughput. The approach represents a significant step toward efficient, hardware-accelerated scientific computing that integrates neural methods directly into physics-based workflows.
The Physics Is the Network: Fast, Training-Free Neural Emulation
arXiv:2610.20525v1 Announce Type: new 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.
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.
Machine Learning (cs.LG); Systems and Control (eess.SY); Chaotic Dynamics (nlin.CD); Applications (stat.AP)
arXiv:2610.20525 [cs.LG]
(or arXiv:2610.20525v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.20525 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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