论文标题
稀疏的合成整合神经网络
Sparse Symplectically Integrated Neural Networks
论文作者
论文摘要
我们介绍了稀疏的符合性整合的神经网络（SSINNS），这是一种从数据中学习汉密尔顿动态系统的新型模型。 Ssinns将四阶符合性整合与通过数学上优雅的函数空间获得的稀疏回归获得的汉密尔顿的学习参数化结合在一起。这允许可解释的模型，这些模型结合了符合性归纳偏见并具有较低的内存要求。我们评估了四个古典哈密顿动力学问题的SSINN：Hénon-Heiles系统，非线性耦合振荡器，多粒子质量弹力系统和摆系统。我们的结果表明，在系统预测和能源的保护方面都有希望，通常比当前最新的黑盒预测技术按数量级优于当前的最新黑盒预测技术。此外，Ssinns从高度有限和嘈杂的数据中成功收敛到真正的管理方程式，证明了在发现新的物理管理方程式中的潜在适用性。
We introduce Sparse Symplectically Integrated Neural Networks (SSINNs), a novel model for learning Hamiltonian dynamical systems from data. SSINNs combine fourth-order symplectic integration with a learned parameterization of the Hamiltonian obtained using sparse regression through a mathematically elegant function space. This allows for interpretable models that incorporate symplectic inductive biases and have low memory requirements. We evaluate SSINNs on four classical Hamiltonian dynamical problems: the Hénon-Heiles system, nonlinearly coupled oscillators, a multi-particle mass-spring system, and a pendulum system. Our results demonstrate promise in both system prediction and conservation of energy, often outperforming the current state-of-the-art black-box prediction techniques by an order of magnitude. Further, SSINNs successfully converge to true governing equations from highly limited and noisy data, demonstrating potential applicability in the discovery of new physical governing equations.
