Physics-based network speeds up accurate neural equation simulation
The Physics Is the Network: Fast, Training-Free Neural Emulation
Machine Learning
Summary
Most neural emulators for physical systems need to be trained on data, but this paper shows a way to simulate known physical dynamics without training at all. The authors combine a neural network design with known physics equations to create a fast, exact model for simulating waves that doesn't lose accuracy. Their method performs as precisely as traditional numerical solvers and runs efficiently on graphics hardware. This approach works well even when conditions go beyond what trained models can handle.
What this means in practice
- •For simulation engineers: Run high-throughput, accurate simulations of wave dynamics without costly neural network training or reduced fidelity.
- •For hardware acceleration teams: Deploy physics-preserving neural network emulators to leverage GPUs for scalable and parallelizable simulation workloads.
Authors
Luka Todorovic, Kaushal Gianchandani, Sai Ravela
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.