HIPNO: Symmetry-Aware Physics-Informed Neural Operators for Noninvasive Hemodynamic Inference

2026-08-08

AI Summary

Current non-invasive signals struggle to accurately infer hemodynamic states, primarily due to scale symmetry in the observation model that renders parameters unidentifiable. This work proposes a symmetry-aware physics-informed neural operator that explicitly models the symmetry group of the hemodynamic system and parameterizes the network in the quotient space to eliminate scale ambiguity, thereby enabling disentanglement of physical parameters and recovery of absolute scale. Built upon the three-element Windkessel model, the method supports counterfactual interventions and precise state estimation. Evaluated across 2,562 patients and 945,499 intraoperative windows, it reduces the log-scale error in vascular decay time prediction by 32%, achieves over 90% accuracy in counterfactual response, and maintains high fidelity in mean arterial pressure estimation.

Abstract

Continuous hemodynamic monitoring guides treatment decisions in surgery and intensive care. However, gold-standard signals are only measured in severe cases due to risks associated with invasive measurement. In this work, we introduce HIPNO (Hemodynamic Inference via Physics-informed Neural Operators) to recover hemodynamic state from ubiquitous, non-invasive signals and expand access to advanced monitoring. HIPNO addresses a problem of scale symmetry in physics-informed hemodynamic inference, where different combinations of flow, resistance, and compliance can generate the same observed pressure. We identify the symmetry group of the observation model and parameterize the network in its quotient space. For the 3-element Windkessel model, the quotient coordinates are the compliance-normalized flow $U=Q/C$, the decay time constant $τ_{WK}=R_2 C$, and the characteristic-impedance coordinate $κ=R_1 C$. Across 945499 intraoperative windows from 2562 patients, HIPNO predicts $τ_{wave}$, a proxy for vascular decay derived from pressure, with 32% lower error on the log scale than a population baseline while preserving mean arterial pressure accuracy. Because vascular decay and flow drive occupy separate coordinates, counterfactual perturbations produce the expected directional responses in at least 90% of windows in almost all prespecified scenarios, a separation unavailable to pressure-only baselines. The coordinates are also used as inputs to a calibration model for monitored cardiac output. Finally, the formulation identifies the external compliance or flow reference required to recover absolute physical scale.

Problem

• scale symmetry
• hemodynamic inference
• noninvasive monitoring
• physics-informed learning
• Windkessel model

Innovation

• symmetry-aware
• physics-informed neural operators
• hemodynamic inference
• quotient space parameterization
• noninvasive monitoring