This paper presents a comprehensive investigation into the applicability and performance of two prominent growth models, namely, the Verhulst model and the Montroll model, in the context of modeling tumor cell growth dynamics. Leveraging the power of Physics-Informed Neural Networks (PINNs), we aim to assess and compare the predictive capabilities of these models against experimental data obtained from the growth patterns of tumor cells. We employed a dataset comprising detailed measurements of tumor cell growth to train and evaluate the Verhulst and Montroll models. By integrating PINNs, we not only account for experimental noise but also embed physical insights into the learning process, enabling the models to capture the underlying mechanisms governing tumor cell growth. Our findings reveal the strengths and limitations of each growth model in accurately representing tumor cell proliferation dynamics. Furthermore, the study sheds light on the impact of incorporating physics-informed constraints on the model predictions. The insights gained from this comparative analysis contribute to advancing our understanding of growth models and their applications in predicting complex biological phenomena, particularly in the realm of tumor cell proliferation.

中文翻译：

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使用物理信息神经网络 (PINN) 进行肿瘤细胞生长建模

本文对两种著名的生长模型（即 Verhulst 模型和 Montroll 模型）在肿瘤细胞生长动力学建模的背景下的适用性和性能进行了全面研究。利用物理信息神经网络（PINN）的力量，我们的目标是根据从肿瘤细胞生长模式获得的实验数据来评估和比较这些模型的预测能力。我们使用包含肿瘤细胞生长详细测量结果的数据集来训练和评估 Verhulst 和 Montroll 模型。通过集成 PINN，我们不仅可以解释实验噪声，还可以将物理见解嵌入到学习过程中，使模型能够捕获控制肿瘤细胞生长的潜在机制。我们的研究结果揭示了每种生长模型在准确表示肿瘤细胞增殖动态方面的优势和局限性。此外，该研究揭示了纳入物理约束对模型预测的影响。从这种比较分析中获得的见解有助于增进我们对生长模型及其在预测复杂生物现象中的应用的理解，特别是在肿瘤细胞增殖领域。