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Daniele E. Schiavazzi

Publications and source records attributed to Daniele E. Schiavazzi.

At least 19 recordsLinked to original sources
arXiv2026

Rule-based and reinforcement-learning policies for resource allocation in a pediatric echo lab: a simulation study

Scheduling echocardiographic examinations in a hospital setting presents significant challenges due to non-deterministic factors such as patient no-shows, variable arrival times, and heterogeneous exam durations, as well as asymmetric resource constraints between fetal and non-fetal patient streams. Fetal cases involve specialized ultrasound examinations performed during pregnancy, whereas non-fetal cases correspond to general diagnostic echocardiography services. Using one week (184 patients) of operational data from the Echo Laboratory at Stanford University's Lucile Packard Children's Hospital, we estimate patient no-show probabilities and derive empirical distributions of arrival times and exam durations, and use them to build a discrete-event stochastic simulation model using SimPy, exposed through an open-source Gymnasium interface (https://github.com/desResLab/echo_rl). As a baseline for policy optimization, we systematically compare two scheduling paradigms: on-the-fly allocation, in which patients are served according to their arrival time without prior reservations, and reservation-based allocation, in which varying proportions of resources are preassigned. We consider a hospital with seven ultrasound rooms (one equipped for both fetal and non-fetal exams, six for non-fetal exams only) and six sonographers (four qualified for both exam types, two for non-fetal exams only). In this setting, on-the-fly allocation markedly reduces the average patient waiting time compared with every reservation-based configuration tested. Building on this foundation, we train a Dueling Double Deep Q-Network (DQN) with prioritized experience replay to approximate an optimal dynamic on-the-fly allocation policy. The learned RL policy is comparable to, but does not outperform, the best on-the-fly rule-based policy.

cs.LG↗
arXiv2026

Conditional Normalizing Flows for Forward and Backward Joint State and Parameter Estimation

Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters -- show performance degradation when applied to nonlinear systems whose uncertainty follows arbitrary non-Gaussian, and potentially multi-modal distributions. This study reviews recent approaches to state estimation via nonlinear filtering based on conditional normalizing flows, where the conditional embedding is generated by standard MLP architectures, transformers or selective state-space models (like Mamba-SSM). In addition, we test the effectiveness of an optimal-transport-inspired kinetic loss term in mitigating overparameterization in flows consisting of a large collection of transformations. We investigate the performance of these approaches on applications relevant to autonomous driving and patient population dynamics, paying special attention to how they handle time inversion and chained predictions. Finally, we assess the performance of various conditioning strategies for an application to real-world COVID-19 joint SIR system forecasting and parameter estimation.

stat.ML↗
arXiv2026

Model synthesis and identifiability analysis of stiff chemical reaction systems with inVAErt networks

We consider the problem of learning data-driven replicas for stiff systems of ordinary differential equations arising in chemical kinetics that can be evaluated with high computational efficiency. We first focus on training emulators for families of reaction equations under varying reaction rates, using conditional residual networks or long-short term memory architectures. We then apply a recently proposed data-driven framework known as ``inVAErt networks'' to address the ill-posed inverse problem of inferring reaction rates, integration time, and possibly initial conditions from a target set of species concentrations - a problem that has received relatively little attention in the literature. The proposed approach is demonstrated on chemical systems with reversible and irreversible kinetics, spanning 2 to 20 differential equations, 3 to 20 chemical species, and 3 to 25 reaction rate parameters. Relative root mean squared errors produced by the proposed emulators range from $10^{-5}$ for lower-dimensional systems to $10^{-4}$ and $10^{-3}$ for an air pollution model and a hydrogen-air reaction system, respectively. Manifolds of non-identifiable reaction rates recovered by the proposed approach can be analytically verified for simple systems and are consistent with local identifiability analysis in higher dimensions.

cs.LG↗
arXiv2026

FalconBC: Flow matching for Amortized inference of Latent-CONditioned physiologic Boundary Conditions

Boundary condition tuning is a fundamental step in patient-specific cardiovascular modeling. Despite an increase in offline training cost, recent methods in data-driven variational inference can efficiently estimate the joint posterior distribution of boundary conditions, with amortization of training efforts over clinical targets. However, even the most modern approaches fall short in two important scenarios: open-loop models with known mean flow and assumed waveform shapes, and anatomies affected by vascular lesions where segmentation influences the reachability of pressure or flow split targets. In both cases, boundary conditions cannot be tuned in isolation. We introduce a general amortized inference framework based on probabilistic flow that treats clinical targets, inflow features, and point cloud embeddings of patient-specific anatomies as either conditioning variables or quantities to be jointly estimated. We demonstrate the approach on two patient-specific models: an aorto-iliac bifurcation with varying stenosis locations and severity, and a coronary arterial tree.

cs.LG↗
arXiv2026

Enabling stratified sampling in high dimensions via nonlinear dimensionality reduction

We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far, has focused on models with a limited number of inputs due to the challenges of creating uniform partitions in high dimensions. To overcome these challenges, we propose a simple methodology for constructing an effective stratification of the input domain that is adapted to the model response. Our approach leverages neural active manifolds, a recently introduced nonlinear dimensionality reduction technique based on neural networks that identifies a one-dimensional manifold capturing most of the model variability. The resulting one-dimensional latent space is mapped to the unit interval, where stratification is performed with respect to the uniform distribution. The corresponding strata in the original input space are then recovered through the neural active manifold, generating partitions that tend to follow the level sets of the model. We show that our approach is effective in high dimensions and can be used to further reduce the variance of multifidelity Monte Carlo estimators.

math.NA↗
arXiv2025

On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiological boundary conditions

Solving inverse problems in cardiovascular modeling is particularly challenging due to the high computational cost of running high-fidelity simulations. In this work, we focus on Bayesian parameter estimation and explore different methods to reduce the computational cost of sampling from the posterior distribution by leveraging low-fidelity approximations. A common approach is to construct a surrogate model for the high-fidelity simulation itself. Another is to build a surrogate for the discrepancy between high- and low-fidelity models. This discrepancy, which is often easier to approximate, is modeled with either a fully connected neural network or a nonlinear dimensionality reduction technique that enables surrogate construction in a lower-dimensional space. A third possible approach is to treat the discrepancy between the high-fidelity and surrogate models as random noise and estimate its distribution using normalizing flows. This allows us to incorporate the approximation error into the Bayesian inverse problem by modifying the likelihood function. We validate five different methods which are variations of the above on analytical test cases by comparing them to posterior distributions derived solely from high-fidelity models, assessing both accuracy and computational cost. Finally, we demonstrate our approaches on two cardiovascular examples of increasing complexity: a lumped-parameter Windkessel model and a patient-specific three-dimensional anatomy.

stat.ML↗
arXiv2025

Assessing the performance of correlation-based multi-fidelity neural emulators

Outer loop tasks such as optimization, uncertainty quantification or inference can easily become intractable when the underlying high-fidelity model is computationally expensive. Similarly, data-driven architectures typically require large datasets to perform predictive tasks with sufficient accuracy. A possible approach to mitigate these challenges is the development of multi-fidelity emulators, leveraging potentially biased, inexpensive low-fidelity information while correcting and refining predictions using scarce, accurate high-fidelity data. This study investigates the performance of multi-fidelity neural emulators, neural networks designed to learn the input-to-output mapping by integrating limited high-fidelity data with abundant low-fidelity model solutions. We investigate the performance of such emulators for low and high-dimensional functions, with oscillatory character, in the presence of discontinuities, for collections of models with equal and dissimilar parametrization, and for a possibly large number of potentially corrupted low-fidelity sources. In doing so, we consider a large number of architectural, hyperparameter, and dataset configurations including networks with a different amount of spectral bias (Multi-Layered Perceptron, Siren and Kolmogorov Arnold Network), various mechanisms for coordinate encoding, exact or learnable low-fidelity information, and for varying training dataset size. We further analyze the added value of the multi-fidelity approach by conducting equivalent single-fidelity tests for each case, quantifying the performance gains achieved through fusing multiple sources of information.

cs.LG↗
arXiv2025

Neural active manifolds: nonlinear dimensionality reduction for uncertainty quantification

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.

math.NA↗
arXiv2025

On the accuracy of implicit neural representations for cardiovascular anatomies and hemodynamic fields

Implicit neural representations (INRs, also known as neural fields) have recently emerged as a powerful framework for knowledge representation, synthesis, and compression. By encoding fields as continuous functions within the weights and biases of deep neural networks-rather than relying on voxel- or mesh-based structured or unstructured representations-INRs offer both resolution independence and high memory efficiency. However, their accuracy in domain-specific applications remains insufficiently understood. In this work, we assess the performance of state-of-the-art INRs for compressing hemodynamic fields derived from numerical simulations and for representing cardiovascular anatomies via signed distance functions. We investigate several strategies to mitigate spectral bias, including specialized activation functions, both fixed and trainable positional encoding, and linear combinations of nonlinear kernels. On realistic, space- and time-varying hemodynamic fields in the thoracic aorta, INRs achieved remarkable compression ratios of up to approximately 230, with maximum absolute errors of 1 mmHg for pressure and 5-10 cm/s for velocity, without extensive hyperparameter tuning. Across 48 thoracic aortic anatomies, the average and maximum absolute anatomical discrepancies were below 0.5 mm and 1.6 mm, respectively. Overall, the SIREN, MFN-Gabor, and MHE architectures demonstrated the best performance. Source code and data is available at https://github.com/desResLab/nrf.

cs.LG↗
arXiv2024

Personalized and uncertainty-aware coronary hemodynamics simulations: From Bayesian estimation to improved multi-fidelity uncertainty quantification

Simulations of coronary hemodynamics have improved non-invasive clinical risk stratification and treatment outcomes for coronary artery disease, compared to relying on anatomical imaging alone. However, simulations typically use empirical approaches to distribute total coronary flow amongst the arteries in the coronary tree. This ignores patient variability, the presence of disease, and other clinical factors. Further, uncertainty in the clinical data often remains unaccounted for in the modeling pipeline. We present an end-to-end uncertainty-aware pipeline to (1) personalize coronary flow simulations by incorporating branch-specific coronary flows as well as cardiac function; and (2) predict clinical and biomechanical quantities of interest with improved precision, while accounting for uncertainty in the clinical data. We assimilate patient-specific measurements of myocardial blood flow from CT myocardial perfusion imaging to estimate branch-specific coronary flows. We use adaptive Markov Chain Monte Carlo sampling to estimate the joint posterior distributions of model parameters with simulated noise in the clinical data. Additionally, we determine the posterior predictive distribution for relevant quantities of interest using a new approach combining multi-fidelity Monte Carlo estimation with non-linear, data-driven dimensionality reduction. Our framework recapitulates clinically measured cardiac function as well as branch-specific coronary flows under measurement uncertainty. We substantially shrink the confidence intervals for estimated quantities of interest compared to single-fidelity and state-of-the-art multi-fidelity Monte Carlo methods. This is especially true for quantities that showed limited correlation between the low- and high-fidelity model predictions. Moreover, the proposed estimators are significantly cheaper to compute for a specified confidence level or variance.

physics.flu-dyn↗
arXiv2024

InVAErt networks for amortized inference and identifiability analysis of lumped parameter hemodynamic models

Estimation of cardiovascular model parameters from electronic health records (EHR) poses a significant challenge primarily due to lack of identifiability. Structural non-identifiability arises when a manifold in the space of parameters is mapped to a common output, while practical non-identifiability can result due to limited data, model misspecification, or noise corruption. To address the resulting ill-posed inverse problem, optimization-based or Bayesian inference approaches typically use regularization, thereby limiting the possibility of discovering multiple solutions. In this study, we use inVAErt networks, a neural network-based, data-driven framework for enhanced digital twin analysis of stiff dynamical systems. We demonstrate the flexibility and effectiveness of inVAErt networks in the context of physiological inversion of a six-compartment lumped parameter hemodynamic model from synthetic data to real data with missing components.

math.NA↗
arXiv2024

Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology

When predicting physical phenomena through simulation, quantification of the total uncertainty due to multiple sources is as crucial as making sure the underlying numerical model is accurate. Possible sources include irreducible aleatoric uncertainty due to noise in the data, epistemic uncertainty induced by insufficient data or inadequate parameterization, and model-form uncertainty related to the use of misspecified model equations. Physics-based regularization interacts in nontrivial ways with aleatoric, epistemic and model-form uncertainty and their combination, and a better understanding of this interaction is needed to improve the predictive performance of physics-informed digital twins that operate under real conditions. With a specific focus on biological and physiological models, this study investigates the decomposition of total uncertainty in the estimation of states and parameters of a differential system simulated with MC X-TFC, a new physics-informed approach for uncertainty quantification based on random projections and Monte-Carlo sampling. MC X-TFC is applied to a six-compartment stiff ODE system, the CVSim-6 model, developed in the context of human physiology. The system is analyzed by progressively removing data while estimating an increasing number of parameters and by investigating total uncertainty under model-form misspecification of non-linear resistance in the pulmonary compartment. In particular, we focus on the interaction between the formulation of the discrepancy term and quantification of model-form uncertainty, and show how additional physics can help in the estimation process. The method demonstrates robustness and efficiency in estimating unknown states and parameters, even with limited, sparse, and noisy data. It also offers great flexibility in integrating data with physics for improved estimation, even in cases of model misspecification.

cs.LG↗
arXiv2024

Bayesian Windkessel calibration using optimized 0D surrogate models

Boundary condition (BC) calibration to assimilate clinical measurements is an essential step in any subject-specific simulation of cardiovascular fluid dynamics. Bayesian calibration approaches have successfully quantified the uncertainties inherent in identified parameters. Yet, routinely estimating the posterior distribution for all BC parameters in 3D simulations has been unattainable due to the infeasible computational demand. We propose an efficient method to identify Windkessel parameter posteriors using results from a single high-fidelity three-dimensional (3D) model evaluation. We only evaluate the 3D model once for an initial choice of BCs and use the result to create a highly accurate zero-dimensional (0D) surrogate. We then perform Sequential Monte Carlo (SMC) using the optimized 0D model to derive the high-dimensional Windkessel BC posterior distribution. We validate this approach in a publicly available dataset of N=72 subject-specific vascular models. We found that optimizing 0D models to match 3D data a priori lowered their median approximation error by nearly one order of magnitude. In a subset of models, we confirm that the optimized 0D models still generalize to a wide range of BCs. Finally, we present the high-dimensional Windkessel parameter posterior for different measured signal-to-noise ratios in a vascular model using SMC. We further validate that the 0D-derived posterior is a good approximation of the 3D posterior. The minimal computational demand of our method using a single 3D simulation, combined with the open-source nature of all software and data used in this work, will increase access and efficiency of Bayesian Windkessel calibration in cardiovascular fluid dynamics simulations.

cs.CE↗
arXiv2024

Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques

We study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity Monte Carlo estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

stat.ME↗
arXiv2024

Global sensitivity analysis with multifidelity Monte Carlo and polynomial chaos expansion for carotid artery haemodynamics

Computational models of the cardiovascular system are increasingly used for the diagnosis, treatment, and prevention of cardiovascular disease. Before being used for translational applications, the predictive abilities of these models need to be thoroughly demonstrated through verification, validation, and uncertainty quantification. When results depend on multiple uncertain inputs, sensitivity analysis is typically the first step required to separate relevant from unimportant inputs, and is key to determine an initial reduction on the problem dimensionality that will significantly affect the cost of all downstream analysis tasks. For computationally expensive models with numerous uncertain inputs, sample-based sensitivity analysis may become impractical due to the substantial number of model evaluations it typically necessitates. To overcome this limitation, we consider recently proposed Multifidelity Monte Carlo estimators for Sobol' sensitivity indices, and demonstrate their applicability to an idealized model of the common carotid artery. Variance reduction is achieved combining a small number of three-dimensional fluid-structure interaction simulations with affordable one- and zero-dimensional reduced order models. These multifidelity Monte Carlo estimators are compared with traditional Monte Carlo and polynomial chaos expansion estimates. Specifically, we show consistent sensitivity ranks for both bi- (1D/0D) and tri-fidelity (3D/1D/0D) estimators, and superior variance reduction compared to traditional single-fidelity Monte Carlo estimators for the same computational budget. As the computational burden of Monte Carlo estimators for Sobol' indices is significantly affected by the problem dimensionality, polynomial chaos expansion is found to have lower computational cost for idealized models with smooth stochastic response.

stat.AP↗
arXiv2023

A Probabilistic Neural Twin for Treatment Planning in Peripheral Pulmonary Artery Stenosis

The substantial computational cost of high-fidelity models in numerical hemodynamics has, so far, relegated their use mainly to offline treatment planning. New breakthroughs in data-driven architectures and optimization techniques for fast surrogate modeling provide an exciting opportunity to overcome these limitations, enabling the use of such technology for time-critical decisions. We discuss an application to the repair of multiple stenosis in peripheral pulmonary artery disease through either transcatheter pulmonary artery rehabilitation or surgery, where it is of interest to achieve desired pressures and flows at specific locations in the pulmonary artery tree, while minimizing the risk for the patient. Since different degrees of success can be achieved in practice during treatment, we formulate the problem in probability, and solve it through a sample-based approach. We propose a new offline-online pipeline for probabilsitic real-time treatment planning which combines offline assimilation of boundary conditions, model reduction, and training dataset generation with online estimation of marginal probabilities, possibly conditioned on the degree of augmentation observed in already repaired lesions. Moreover, we propose a new approach for the parametrization of arbitrarily shaped vascular repairs through iterative corrections of a zero-dimensional approximant. We demonstrate this pipeline for a diseased model of the pulmonary artery tree available through the Vascular Model Repository.

physics.med-ph↗
arXiv2023

InVAErt networks: a data-driven framework for model synthesis and identifiability analysis

Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to other aspects of system synthesis including model inversion and identifiability. We introduce inVAErt (pronounced "invert") networks, a comprehensive framework for data-driven analysis and synthesis of parametric physical systems which uses a deterministic encoder and decoder to represent the forward and inverse solution maps, a normalizing flow to capture the probabilistic distribution of system outputs, and a variational encoder designed to learn a compact latent representation for the lack of bijectivity between inputs and outputs. We formally investigate the selection of penalty coefficients in the loss function and strategies for latent space sampling, since we find that these significantly affect both training and testing performance. We validate our framework through extensive numerical examples, including simple linear, nonlinear, and periodic maps, dynamical systems, and spatio-temporal PDEs.

cs.LG↗
arXiv2023

LINFA: a Python library for variational inference with normalizing flow and annealing

Variational inference is an increasingly popular method in statistics and machine learning for approximating probability distributions. We developed LINFA (Library for Inference with Normalizing Flow and Annealing), a Python library for variational inference to accommodate computationally expensive models and difficult-to-sample distributions with dependent parameters. We discuss the theoretical background, capabilities, and performance of LINFA in various benchmarks. LINFA is publicly available on GitHub at https://github.com/desResLab/LINFA.

cs.LG↗