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

• URL: http://arxiv.org/abs/2506.11683v1
• Date: Fri, 13 Jun 2025 11:20:49 GMT
• Title: On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiologic boundary conditions
• Authors: Chloe H. Choi, Andrea Zanoni, Daniele E. Schiavazzi, Alison L. Marsden,
• Abstract summary: We focus on Bayesian parameter estimation and explore different methods to reduce the computational cost of sampling from the posterior distribution.<n>A common approach is to construct a surrogate model for the high-fidelity simulation itself.<n>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.
• Score: 0.7499722271664147
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Diffusion models for multivariate subsurface generation and efficient probabilistic inversion [0.0]
  Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks.<n>We introduce a likelihood approximation accounting for the noise-contamination that is inherent in diffusion modeling.<n>Our tests show significantly improved statistical robustness, enhanced sampling of the posterior probability density function.
  arXiv  Detail & Related papers  (2025-07-21T17:10:16Z)
• Amortized Posterior Sampling with Diffusion Prior Distillation [55.03585818289934]
  Amortized Posterior Sampling is a novel variational inference approach for efficient posterior sampling in inverse problems.<n>Our method trains a conditional flow model to minimize the divergence between the variational distribution and the posterior distribution implicitly defined by the diffusion model.<n>Unlike existing methods, our approach is unsupervised, requires no paired training data, and is applicable to both Euclidean and non-Euclidean domains.
  arXiv  Detail & Related papers  (2024-07-25T09:53:12Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Solving Inverse Problems with Model Mismatch using Untrained Neural Networks within Model-based Architectures [14.551812310439004]
  We introduce an untrained forward model residual block within the model-based architecture to match the data consistency in the measurement domain for each instance. Our approach offers a unified solution that is less parameter-sensitive, requires no additional data, and enables simultaneous fitting of the forward model and reconstruction in a single pass.
  arXiv  Detail & Related papers  (2024-03-07T19:02:13Z)
• Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization [45.72323731094864]
  We present a theoretical framework to analyze two-layer neural network-based diffusion models. We prove that training shallow neural networks for score prediction can be done by solving a single convex program. Our results provide a precise characterization of what neural network-based diffusion models learn in non-asymptotic settings.
  arXiv  Detail & Related papers  (2024-02-03T00:20:25Z)
• A Deep Unrolling Model with Hybrid Optimization Structure for Hyperspectral Image Deconvolution [50.13564338607482]
  We propose a novel optimization framework for the hyperspectral deconvolution problem, called DeepMix.<n>It consists of three distinct modules, namely, a data consistency module, a module that enforces the effect of the handcrafted regularizers, and a denoising module.<n>This work proposes a context aware denoising module designed to sustain the advancements achieved by the cooperative efforts of the other modules.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Multi-fidelity Hierarchical Neural Processes [79.0284780825048]
  Multi-fidelity surrogate modeling reduces the computational cost by fusing different simulation outputs. We propose Multi-fidelity Hierarchical Neural Processes (MF-HNP), a unified neural latent variable model for multi-fidelity surrogate modeling. We evaluate MF-HNP on epidemiology and climate modeling tasks, achieving competitive performance in terms of accuracy and uncertainty estimation.
  arXiv  Detail & Related papers  (2022-06-10T04:54:13Z)
• Sparse Bayesian Learning for Complex-Valued Rational Approximations [0.03392423750246091]
  Surrogate models are used to alleviate the computational burden in engineering tasks. These models show a strongly non-linear dependence on their input parameters. We apply a sparse learning approach to the rational approximation.
  arXiv  Detail & Related papers  (2022-06-06T12:06:13Z)
• RMFGP: Rotated Multi-fidelity Gaussian process with Dimension Reduction for High-dimensional Uncertainty Quantification [12.826754199680474]
  Multi-fidelity modelling enables accurate inference even when only a small set of accurate data is available. By combining the realizations of the high-fidelity model with one or more low-fidelity models, the multi-fidelity method can make accurate predictions of quantities of interest. This paper proposes a new dimension reduction framework based on rotated multi-fidelity Gaussian process regression and a Bayesian active learning scheme.
  arXiv  Detail & Related papers  (2022-04-11T01:20:35Z)
• Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements [62.997667081978825]
  characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI. We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
  arXiv  Detail & Related papers  (2021-11-15T09:08:27Z)
• Estimation of Bivariate Structural Causal Models by Variational Gaussian Process Regression Under Likelihoods Parametrised by Normalising Flows [74.85071867225533]
  Causal mechanisms can be described by structural causal models. One major drawback of state-of-the-art artificial intelligence is its lack of explainability.
  arXiv  Detail & Related papers  (2021-09-06T14:52:58Z)
• A Twin Neural Model for Uplift [59.38563723706796]
  Uplift is a particular case of conditional treatment effect modeling. We propose a new loss function defined by leveraging a connection with the Bayesian interpretation of the relative risk. We show our proposed method is competitive with the state-of-the-art in simulation setting and on real data from large scale randomized experiments.
  arXiv  Detail & Related papers  (2021-05-11T16:02:39Z)
• Jointly Modeling and Clustering Tensors in High Dimensions [6.072664839782975]
  We consider the problem of jointly benchmarking and clustering of tensors. We propose an efficient high-maximization algorithm that converges geometrically to a neighborhood that is within statistical precision.
  arXiv  Detail & Related papers  (2021-04-15T21:06:16Z)
• Using Bayesian deep learning approaches for uncertainty-aware building energy surrogate models [0.0]
  Machine learning surrogate models are trained to emulate slow, high-fidelity engineering simulation models. Deep learning models exist that follow the Bayesian paradigm. We show that errors can be reduced by up to 30% when the 10% of samples with the highest uncertainty are transferred to the high-fidelity model.
  arXiv  Detail & Related papers  (2020-10-05T15:04:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.