Physics-Informed Neural Operators for Parameter Inference in Multi-vessel Cardiovascular Networks

Accurate, patient-specific haemodynamic assessment is limited by the cost of computational solvers and the sparsity of clinical measurements. We demonstrate that physics-informed neural operator surrogates can emulate multi-vessel 1D haemodynamics with sufficient accuracy and speed to enable Bayesian parameter inference and non-invasive pressure estimation in a clinically relevant setting.

We construct neural operator surrogates for a 17-vessel 1D systemic arterial network with prescribed inflow and structured-tree outflow, using DeepONet, POD-DeepONet and Fourier Neural Operator (FNO) architectures that map inflow waveforms and biophysical parameters (vessel stiffnesses and microvascular properties) to flow and pressure fields. Conservation laws, PDE residuals and bifurcation conditions are incorporated via physics-informed loss terms. To generate realistic inflow boundary conditions from limited clinical data, we compare generative models and adopt a Wasserstein autoencoder. The best-performing surrogate is embedded in a Bayesian pipeline to perform MCMC-based parameter inference and non-invasive pressure prediction for two Fontan patients using sparse 4D flow MRI waveforms.

The physics-informed FNO architecture achieved the lowest median relative errors across all vessels and markedly reduced maximum errors compared with purely data-driven training. In synthetic inverse tests, the PINO recovered vascular parameters more accurately than DeepONet and POD-DeepONet. For two Fontan patients, the calibrated model reproduced measured flow waveforms and yielded brachial pressure predictions consistent with cuff measurements, together with posterior uncertainty bands.

Physics-informed neural operators can emulate multi-vessel haemodynamics with high accuracy at a fraction of the computational cost of traditional solvers. Coupled with Bayesian inference, the proposed framework enables practical, uncertainty-aware estimation of vascular parameters and non-invasive pressure waveforms from sparse clinical flow data.