The existence or not of pathologies in the context of Lagrangian theory is studied with the aid of Machine Learning algorithms. Using an example in the framework of classical mechanics, we make a proof of concept, that the construction of new physical theories using machine learning is possible. Specifically, we utilize a fully-connected, feed-forward neural network architecture, aiming to discriminate between “healthy” and “nonhealthy” Lagrangians, without explicitly extracting the relevant equations of motion. The network, after training, is used as a fitness function in the concept of a genetic algorithm and new healthy Lagrangians are constructed. These new Lagrangians are different from the Lagrangians contained in the initial data set. Hence, searching for Lagrangians possessing a number of pre-defined properties is significantly simplified within our approach. The framework employed in this work can be used to explore more complex physical theories, such as generalizations of General Relativity in gravitational physics, or constructions in solid state physics, in which the standard procedure can be laborious.

中文翻译：

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用机器学习建立健康的拉格朗日理论

借助机器学习算法研究拉格朗日理论背景下的病理是否存在。使用经典力学框架中的一个例子，我们做一个概念证明，使用机器学习构建新的物理理论是可能的。具体来说，我们利用完全连接的前馈神经网络架构，旨在区分“健康”和“非健康”拉格朗日函数，而无需明确提取相关的运动方程。该网络在训练后被用作遗传算法概念中的适应度函数，并构建新的健康拉格朗日函数。这些新的拉格朗日量不同于初始数据集中包含的拉格朗日量。因此，在我们的方法中，搜索具有许多预定义属性的拉格朗日函数大大简化了。这项工作中采用的框架可用于探索更复杂的物理理论，例如广义相对论在引力物理学中的推广，