PolyNets 无需训练即可模拟物理：以 KdV 方程验证 GPU 并行仿真
The Physics Is the Network: Fast, Training-Free Neural Emulation
这篇 arXiv 论文提出 PolyNets，系数已知时不用训练就能做神经仿真，在 KdV 方程上精度追平数值求解器，还吃满 GPU 并行，做科学计算的朋友可以看看思路。
论文提出 PolyNets，把多项式动力学的连续时间神经表示与简单循环网络耦合，用于离散时间积分。在控制方程系数已知时，整个张量图无需训练即可构建，并保留指定的数值格式。作者用一维 KdV 方程对比 CPU/GPU 有限差分 Runge-Kutta 求解器和三种训练过的神经模型，覆盖 10^6 个时间步、最多 10^4 条轨迹的系综，以解析孤立子解为参照。PolyNets 在振幅超出训练条件的场景下精度与数值求解器相当，且 GPU 吞吐量在测试分辨率范围内近似恒定。
The Physics Is the Network: Fast, Training-Free Neural Emulation
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.
