Department of Earth System Science, University of California, Irvine, California 92697-3100, USA.
Department of Earth and Environmental Engineering, Columbia University, New York, New York 10027, USA.
Phys Rev Lett. 2021 Mar 5;126(9):098302. doi: 10.1103/PhysRevLett.126.098302.
Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic constraints in neural networks via constraints in the architecture or the loss function. Applied to convective processes for climate modeling, architectural constraints enforce conservation laws to within machine precision without degrading performance. Enforcing constraints also reduces errors in the subsets of the outputs most impacted by the constraints.
神经网络可以高精度地模拟非线性物理系统，但在违反基本约束时，可能会产生不符合物理事实的结果。在这里，我们通过架构或损失函数中的约束，引入了一种在神经网络中强制实施非线性分析约束的系统方法。应用于气候建模的对流过程，架构约束可在不降低性能的情况下将守恒定律强制到机器精度范围内。实施约束还可以减少受约束影响最大的输出子集的误差。
