Lagrangian Neural Networks (LNNs) are a powerful tool for addressing physical systems, particularly those governed by conservation laws. LNNs can parametrize the Lagrangian of a system to predict trajectories with nearly conserved energy. These techniques have proven effective in unconstrained systems as well as those with holonomic constraints. In this work, we adapt LNN techniques to mechanical systems with nonholonomic constraints. We test our approach on some well-known examples with nonholonomic constraints, showing that incorporating these restrictions into the neural network's learning improves not only trajectory estimation accuracy but also ensures adherence to constraints and exhibits better energy behavior compared to the unconstrained counterpart.

翻译：拉格朗日神经网络是处理物理系统，特别是受守恒定律支配系统的有力工具。该网络能够参数化系统的拉格朗日量，从而预测具有近似守恒能量的轨迹。这些技术已在无约束系统及完整约束系统中被证明是有效的。在本研究中，我们将拉格朗日神经网络技术应用于具有非完整约束的力学系统。我们在若干具有非完整约束的经典示例上测试了所提出的方法，结果表明：将此类约束融入神经网络的学习过程，不仅提高了轨迹估计的精度，而且确保了约束条件的满足，同时相较于无约束模型展现出更优的能量特性。