Clinical measurements such as blood pressures and respiration rates are critical in diagnosing and monitoring patient outcomes. It is an important component of biomedical data, which can be used to train transformer-based language models (LMs) for improving healthcare delivery. It is, however, unclear whether LMs can effectively interpret and use clinical measurements. We investigate two questions: First, can LMs effectively leverage clinical measurements to answer related medical questions? Second, how to enhance an LM's performance on medical question-answering (QA) tasks that involve measurements? We performed a case study on blood pressure readings (BPs), a vital sign routinely monitored by medical professionals. We evaluated the performance of four LMs: BERT, BioBERT, MedAlpaca, and GPT-3.5, on our newly developed dataset, BPQA (Blood Pressure Question Answering). BPQA contains $100$ medical QA pairs that were verified by medical students and designed to rely on BPs . We found that GPT-3.5 and MedAlpaca (larger and medium sized LMs) benefit more from the inclusion of BPs than BERT and BioBERT (small sized LMs). Further, augmenting measurements with labels improves the performance of BioBERT and Medalpaca (domain specific LMs), suggesting that retrieval may be useful for improving domain-specific LMs.

In this paper, we introduce an innovative approach for addressing Bayesian inverse problems through the utilization of physics-informed invertible neural networks (PI-INN). The PI-INN framework encompasses two sub-networks: an invertible neural network (INN) and a neural basis network (NB-Net). The primary role of the NB-Net lies in modeling the spatial basis functions characterizing the solution to the forward problem dictated by the underlying partial differential equation. Simultaneously, the INN is designed to partition the parameter vector linked to the input physical field into two distinct components: the expansion coefficients representing the forward problem solution and the Gaussian latent noise. If the forward mapping is precisely estimated, and the statistical independence between expansion coefficients and latent noise is well-maintained, the PI-INN offers a precise and efficient generative model for Bayesian inverse problems, yielding tractable posterior density estimates. As a particular physics-informed deep learning model, the primary training challenge for PI-INN centers on enforcing the independence constraint, which we tackle by introducing a novel independence loss based on estimated density. We support the efficacy and precision of the proposed PI-INN through a series of numerical experiments, including inverse kinematics, 1-dimensional and 2-dimensional diffusion equations, and seismic traveltime tomography. Specifically, our experimental results showcase the superior performance of the proposed independence loss in comparison to the commonly used but computationally demanding kernel-based maximum mean discrepancy loss.