Physics-Informed Kolmogorov-Arnold Networks (PIKANs) are gaining attention as an effective counterpart to the original multilayer perceptron-based Physics-Informed Neural Networks (PINNs). Both representation models can address inverse problems and facilitate gray-box system identification. However, a comprehensive understanding of their performance in terms of accuracy and speed remains underexplored. In particular, we introduce a modified PIKAN architecture, tanh-cPIKAN, which is based on Chebyshev polynomials for parametrization of the univariate functions with an extra nonlinearity for enhanced performance. We then present a systematic investigation of how choices of the optimizer, representation, and training configuration influence the performance of PINNs and PIKANs in the context of systems pharmacology modeling. We benchmark a wide range of first-order, second-order, and hybrid optimizers, including various learning rate schedulers. We use the new Optax library to identify the most effective combinations for learning gray-boxes under ill-posed, non-unique, and data-sparse conditions. We examine the influence of model architecture (MLP vs. KAN), numerical precision (single vs. double), the need for warm-up phases for second-order methods, and sensitivity to the initial learning rate. We also assess the optimizer scalability for larger models and analyze the trade-offs introduced by JAX in terms of computational efficiency and numerical accuracy. Using two representative systems pharmacology case studies - a pharmacokinetics model and a chemotherapy drug-response model - we offer practical guidance on selecting optimizers and representation models/architectures for robust and efficient gray-box discovery. Our findings provide actionable insights for improving the training of physics-informed networks in biomedical applications and beyond.

翻译：物理信息柯尔莫哥洛夫-阿诺德网络（PIKANs）作为基于原始多层感知器的物理信息神经网络（PINNs）的有效对应模型正受到关注。这两种表示模型均能解决反问题并促进灰箱系统辨识。然而，对其在精度与速度方面性能的综合理解仍显不足。本文特别提出一种改进的PIKAN架构——tanh-cPIKAN，其基于切比雪夫多项式对单变量函数进行参数化，并通过额外非线性增强性能。我们系统研究了优化器选择、表示模型及训练配置如何影响PINNs与PIKANs在系统药理学建模中的表现。我们对包括多种学习率调度器在内的一阶、二阶及混合优化器进行了广泛基准测试，并利用新型Optax库识别在病态、非唯一及数据稀疏条件下学习灰箱系统的最有效组合。我们探究了模型架构（MLP与KAN）、数值精度（单精度与双精度）、二阶方法预热阶段的需求以及初始学习率敏感性的影响，同时评估了优化器对大型模型的扩展性，并分析了JAX在计算效率与数值精度间的权衡。通过两个代表性系统药理学案例研究——药代动力学模型与化疗药物响应模型，我们为稳健高效的灰箱发现提供了关于优化器与表示模型/架构选择的实践指导。本研究结果为生物医学及其他领域物理信息网络的训练改进提供了可操作的见解。