Physics-Informed Neural Networks (PINNs) are an attractive tool for partial-observation problems in biology, where the governing dynamics are known but some compartments cannot be measured. Chemotherapy pharmacokinetics (PK) is a clean instance: drug concentration in plasma is routinely measured, but concentration in tissue -- which determines tumour kill and off-target toxicity -- is not. We benchmark a PINN against the standard clinical baseline (nonlinear least-squares on the analytical biexponential plasma solution, hereafter NLS) and a physics-agnostic neural baseline (a data-only MLP) on two PK problems. On the linear two-compartment problem, NLS is near-optimal; the PINN matches it to within a small constant factor while also producing the tissue curve in a single training pass, whereas the data-only MLP fails on tissue by roughly 10x. On a Michaelis-Menten extension (saturable elimination), the biexponential closed form no longer exists, so NLS is mis-specified and silently returns meaningless rate constants. The PINN instead exposes a deeper fact: the Michaelis-Menten two-compartment model is non-identifiable from plasma alone, and the PINN reports this honestly by converging to a basin with k12 -> 0. Adding two sparse tissue observations largely resolves identifiability: across five seeds the PINN recovers k21 to within 1% of truth and Vmax, Km to within one standard-deviation bar, while k12 moves in the correct direction (0.02 -> 0.82) but remains ~2 sigma below truth -- a recovery the closed-form NLS estimator cannot attempt at all, because its biexponential ansatz describes only plasma. Our claim is not that PINNs beat NLS. It is that PINNs offer a uniform recipe that ties the textbook estimator on the textbook problem, exposes structural identifiability that the textbook estimator hides, and absorbs heterogeneous measurements within a single loss.

翻译：物理信息神经网络（PINNs）是生物学部分观测问题中的一种有吸引力的工具，在这类问题中，控制动力学已知但部分隔室无法测量。化疗药代动力学（PK）是一个典型的实例：血浆中的药物浓度可常规测量，但组织中的浓度（决定肿瘤杀伤和非靶向毒性）无法测量。我们在两个PK问题上将PINN与标准临床基线（基于解析双指数血浆解的非线性最小二乘法，以下简称NLS）和物理无关的神经基线（纯数据MLP）进行了基准测试。在线性双隔室问题中，NLS接近最优；PINN以较小的常数因子与其匹配，同时能在单次训练过程中生成组织曲线，而纯数据MLP在组织预测上误差约为10倍。在米氏方程扩展（可饱和消除）情况下，双指数闭合形式不再存在，因此NLS被错误指定并静默返回无意义的速率常数。PINN反而揭示了一个更深层次的事实：米氏双隔室模型仅凭血浆数据不可识别，而PINN通过收敛到k12→0的盆地诚实报告了这一点。添加两个稀疏的组织观测值在很大程度上解决了可识别性问题：在五个随机种子下，PINN恢复的k21与真实值误差在1%以内，Vmax和Km在一个标准差范围内，而k12向正确方向移动（0.02→0.82），但仍比真实值低约2个标准差——这种恢复是闭合形式的NLS估算器完全无法尝试的，因为其双指数假设仅描述血浆。我们的论点并非PINN优于NLS，而是PINN提供了一种统一的方案：它在教科书问题上与教科书估算器持平，揭示了教科书估算器隐藏的结构可识别性，并将异质测量值整合到单一损失函数中。