论文标题
简约的神经网络学习可解释的物理定律
Parsimonious neural networks learn interpretable physical laws
论文作者
论文摘要
机器学习在物理科学中起着越来越多的作用，并且在将领域知识嵌入模型中已取得了重大进展。较少探索的是它用来发现数据可解释的物理定律。我们提出了简约的神经网络（PNN），将神经网络与进化优化相结合，以找到平衡准确性与简约的模型。通过开发经典力学模型并预测基本特性材料的熔化温度来证明该方法的功能和多功能性。在第一个示例中，可以很容易地将结果的PNN解释为牛顿的第二定律，称为非平凡的时间集成商，表现出时间可逆性并保留了能量，在这种情况下，parsimony对于从数据中提取基础对称性至关重要。在第二种情况下，PNN不仅找到了著名的Lindemann熔化法律，而且还以帕累托的简约意义与准确性相比，新的关系胜过它。
Machine learning is playing an increasing role in the physical sciences and significant progress has been made towards embedding domain knowledge into models. Less explored is its use to discover interpretable physical laws from data. We propose parsimonious neural networks (PNNs) that combine neural networks with evolutionary optimization to find models that balance accuracy with parsimony. The power and versatility of the approach is demonstrated by developing models for classical mechanics and to predict the melting temperature of materials from fundamental properties. In the first example, the resulting PNNs are easily interpretable as Newton's second law, expressed as a non-trivial time integrator that exhibits time-reversibility and conserves energy, where the parsimony is critical to extract underlying symmetries from the data. In the second case, the PNNs not only find the celebrated Lindemann melting law, but also new relationships that outperform it in the pareto sense of parsimony vs. accuracy.
