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

arXiv: https://arxiv.org/abs/2608.10011 · HTML: https://mlsanity.com/paper/2608.10011/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 46 references that are in the map.
- First posted on arXiv 8 Aug 2026.

## Builds on (most cited first, 12 of 12)

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- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [PaPaGei: Open Foundation Models for Optical Physiological Signals](https://mlsanity.com/paper/2410.20542/) (2024)
- [PPG2ABP: Translating Photoplethysmogram (PPG) Signals to Arterial Blood Pressure (ABP) Waveforms using Fully Convolutional Neural Networks](https://mlsanity.com/paper/2005.01669/) (2020)
- [Versatile Cardiovascular Signal Generation with a Unified Diffusion Transformer](https://mlsanity.com/paper/2505.22306/) (2025)
- [BP-DeepONet: A new method for cuffless blood pressure estimation using the physcis-informed DeepONet](https://mlsanity.com/paper/2402.18886/) (2024)
- [INN-PAR: Invertible Neural Network for PPG to ABP Reconstruction](https://mlsanity.com/paper/2409.09021/) (2024)

## Abstract (arXiv)

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 τWK=R2 C, and the characteristic-impedance coordinate kappa=R1 C. Across 945499 intraoperative windows from 2562 patients, HIPNO predicts τwave, 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.