Physics Informed Neural Networks (PINNs) are a type of function approximators that use both data-driven supervised neural networks to learn the model of the dynamics of a physical system, and mathematical equations of the physical laws governing that system. PINNs have the benefit of being data-driven to train a model, but also of being able to assure consistency with the physics, and to extrapolate accurately beyond the range of data that currently accessible. As a result, PINNs can provide models that are more reliable while using less data. Specifically, the PINNs objective is to learn the solutions of a systems of equations using supervised learning on the available data and incorporating the knowledge of physical laws and constraints into the training process. However, solving single differential equations with a PINN may be relatively simple, solving systems of coupled differential equations may not be so simple. In this study, I present a neural network model specialized in solving differential equations of enzyme kinetics that has the main characteristic of being a demonstrative simple case of coupled equations system. The study focuses mainly on the theoretical aspects of the definition of a physics-informed loss function and shows a case study that highlights the challenges still to be overcome in solving systems of coupled differential equations.

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使用物理信息神经网络的常微分方程学习系统：酶动力学的案例研究

物理信息神经网络 (PINN) 是一种函数逼近器，它使用数据驱动的监督神经网络来学习物理系统的动力学模型以及控制该系统的物理定律的数学方程。PINN 的优点是由数据驱动来训练模型，而且能够确保与物理的一致性，并在当前可访问的数据范围之外进行准确推断。因此，PINN 可以提供更可靠的模型，同时使用更少的数据。具体来说，PINN 的目标是通过对可用数据进行监督学习，并将物理定律和约束知识纳入训练过程来学习方程组的解。然而，用 PINN 求解单个微分方程可能相对简单，但求解耦合微分方程组可能就不那么简单了。在这项研究中，我提出了一个专门用于求解酶动力学微分方程的神经网络模型，其主要特征是耦合方程系统的演示性简单情况。该研究主要关注物理信息损失函数定义的理论方面，并展示了一个案例研究，强调了在求解耦合微分方程组时仍需克服的挑战。