Multi-Fidelity Delayed Acceptance: hierarchical MCMC sampling for Bayesian inverse problems combining multiple solvers through deep neural networks

• URL: http://arxiv.org/abs/2512.16430v1
• Date: Thu, 18 Dec 2025 11:32:16 GMT
• Title: Multi-Fidelity Delayed Acceptance: hierarchical MCMC sampling for Bayesian inverse problems combining multiple solvers through deep neural networks
• Authors: Filippo Zacchei, Paolo Conti, Attilio Alberto Frangi, Andrea Manzoni,
• Abstract summary: Inverse uncertainty quantification (UQ) tasks are computationally demanding when dealing with physics-based models.<n>Data-driven surrogate models may help reduce evaluation costs, but their utility is often limited by the expense of generating high-fidelity data.<n>We propose a Multi-Fidelity Delayed Acceptance scheme for Bayesian inverse problems.
• Score: 0.3499870393443268
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Inverse uncertainty quantification (UQ) tasks such as parameter estimation are computationally demanding whenever dealing with physics-based models, and typically require repeated evaluations of complex numerical solvers. When partial differential equations are involved, full-order models such as those based on the Finite Element Method can make traditional sampling approaches like Markov Chain Monte Carlo (MCMC) computationally infeasible. Although data-driven surrogate models may help reduce evaluation costs, their utility is often limited by the expense of generating high-fidelity data. In contrast, low-fidelity data can be produced more efficiently, although relying on them alone may degrade the accuracy of the inverse UQ solution. To address these challenges, we propose a Multi-Fidelity Delayed Acceptance scheme for Bayesian inverse problems. Extending the Multi-Level Delayed Acceptance framework, the method introduces multi-fidelity neural networks that combine the predictions of solvers of varying fidelity, with high fidelity evaluations restricted to an offline training stage. During the online phase, likelihood evaluations are obtained by evaluating the coarse solvers and passing their outputs to the trained neural networks, thereby avoiding additional high-fidelity simulations. This construction allows heterogeneous coarse solvers to be incorporated consistently within the hierarchy, providing greater flexibility than standard Multi-Level Delayed Acceptance. The proposed approach improves the approximation accuracy of the low fidelity solvers, leading to longer sub-chain lengths, better mixing, and accelerated posterior inference. The effectiveness of the strategy is demonstrated on two benchmark inverse problems involving (i) steady isotropic groundwater flow, (ii) an unsteady reaction-diffusion system, for which substantial computational savings are obtained.

Related papers

• Robust low-rank estimation with multiple binary responses using pairwise AUC loss [0.0]
  Multiple binary responses arise in many modern data-analytic problems.<n>Low-rank models offer a natural way to encode latent dependence across tasks.<n>Existing methods for binary data are largely likelihood-based and focus on pointwise classification.
  arXiv  Detail & Related papers  (2026-01-13T15:00:10Z)
• Deep Learning and Elicitability for McKean-Vlasov FBSDEs With Common Noise [2.421459418045937]
  We present a novel numerical method for solving McKean-Vlasov forward-backward differential equations (MV-FBSDEs) with common noise.<n>The key innovation involves elicitability to derive a path-wise loss function, enabling efficient training of neural networks to approximate both the backward process and the conditional expectations arising from common noise.<n>We validate the algorithm on a systemic risk inter-bank borrowing and lending model, where analytical solutions exist, demonstrating accurate recovery of the true solution.
  arXiv  Detail & Related papers  (2025-12-16T23:39:31Z)
• Bifidelity Karhunen-Loève Expansion Surrogate with Active Learning for Random Fields [0.4899818550820576]
  We present a bifidelity Karhunen-Loeve expansion (KLE) surrogate model for field-valued quantities of interest (QoIs) under uncertain inputs.<n>We form an active learning strategy that adaptively selects new HF evaluations based on the surrogate's generalization error.<n>New HF samples are then acquired by maximizing an expected improvement criterion, targeting regions of high surrogate error.
  arXiv  Detail & Related papers  (2025-11-05T04:14:44Z)
• Adaptive Machine Learning-Driven Multi-Fidelity Stratified Sampling for Failure Analysis of Nonlinear Stochastic Systems [0.0]
  We introduce a multi-fidelity stratified sampling scheme with adaptive machine learning metamodels for estimating small failure probabilities.<n>A high-fidelity dataset is used to train a deep learning-based metamodel, which then serves as a cost-effective and highly correlated low-fidelity model.<n>An unbiased estimate of the strata-wise failure probabilities is obtained using a multi-fidelity Monte Carlo framework.
  arXiv  Detail & Related papers  (2025-08-01T16:04:21Z)
• Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum [78.27945336558987]
  Decentralized server (DFL) eliminates reliance on client-client architecture.<n>Non-smooth regularization is often incorporated into machine learning tasks.<n>We propose a novel novel DNCFL algorithm to solve these problems.
  arXiv  Detail & Related papers  (2025-04-17T08:32:25Z)
• Theoretical Insights in Model Inversion Robustness and Conditional Entropy Maximization for Collaborative Inference Systems [89.35169042718739]
  collaborative inference enables end users to leverage powerful deep learning models without exposure of sensitive raw data to cloud servers.<n>Recent studies have revealed that these intermediate features may not sufficiently preserve privacy, as information can be leaked and raw data can be reconstructed via model inversion attacks (MIAs)<n>This work first theoretically proves that the conditional entropy of inputs given intermediate features provides a guaranteed lower bound on the reconstruction mean square error (MSE) under any MIA.<n>Then, we derive a differentiable and solvable measure for bounding this conditional entropy based on the Gaussian mixture estimation and propose a conditional entropy algorithm to enhance the inversion robustness
  arXiv  Detail & Related papers  (2025-03-01T07:15:21Z)
• Preconditioned Inexact Stochastic ADMM for Deep Model [35.37705488695026]
  This paper develops an algorithm, PISA, which enables scalable parallel computing and supports various preconditions.<n>It converges under the sole assumption of Lipschitz continuity of the gradient on a bounded region, removing the need for other conditions commonly imposed by methods.<n>It demonstrates its superior numerical performance compared to various state-of-the-art iterations.
  arXiv  Detail & Related papers  (2025-02-15T12:28:51Z)
• Adaptive Sampled Softmax with Inverted Multi-Index: Methods, Theory and Applications [79.53938312089308]
  The MIDX-Sampler is a novel adaptive sampling strategy based on an inverted multi-index approach.<n>Our method is backed by rigorous theoretical analysis, addressing key concerns such as sampling bias, gradient bias, convergence rates, and generalization error bounds.
  arXiv  Detail & Related papers  (2025-01-15T04:09:21Z)
• Finite-Time Convergence and Sample Complexity of Actor-Critic Multi-Objective Reinforcement Learning [20.491176017183044]
  This paper tackles the multi-objective reinforcement learning (MORL) problem. It introduces an innovative actor-critic algorithm named MOAC which finds a policy by iteratively making trade-offs among conflicting reward signals.
  arXiv  Detail & Related papers  (2024-05-05T23:52:57Z)
• Optimization Guarantees of Unfolded ISTA and ADMM Networks With Smooth Soft-Thresholding [57.71603937699949]
  We study optimization guarantees, i.e., achieving near-zero training loss with the increase in the number of learning epochs. We show that the threshold on the number of training samples increases with the increase in the network width.
  arXiv  Detail & Related papers  (2023-09-12T13:03:47Z)
• 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)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)

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.