Giacomo Bottacini | Searcharxiv

arXiv2026

Neural Markov chain Monte Carlo: Bayesian inversion via normalizing flows and variational autoencoders

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and (ii) are characterized by intractable or unavailable likelihood functions. The posterior probability distribution over quantities of interest is estimated via differential evolution Metropolis sampling, empowered by learnable mappings. First, a variational autoencoder performs probabilistic feature extraction from observational data. The resulting latent structure inherently quantifies uncertainty, capturing deviations between the actual data-generating process and the training data distribution. At each step of the MCMC random walk, the algorithm jointly samples from the data-informed latent distribution and the space of parameters to be inferred. These samples are fed into a neural likelihood estimator based on normalizing flows, specifically real-valued non-volume preserving transformations. The scaling and translation functions of the affine coupling layers are modeled by neural networks conditioned on the unknown parameters, allowing the representation of arbitrary observation likelihoods. The proposed methodology is validated on two case studies: (i) structural health monitoring of a railway bridge for damage detection, localization, and quantification, and (ii) estimation of the conductivity field in a steady-state Darcy's groundwater flow problem. The results demonstrate the efficiency of the inference strategy, while ensuring that model-reality mismatches do not yield overconfident, yet inaccurate, estimates.

cs.CE↗

arXiv2025

MAGIC-Flow: Multiscale Adaptive Conditional Flows for Generation and Interpretable Classification

Generative modeling has emerged as a powerful paradigm for representation learning, but its direct applicability to challenging fields like medical imaging remains limited: mere generation, without task alignment, fails to provide a robust foundation for clinical use. We propose MAGIC-Flow, a conditional multiscale normalizing flow architecture that performs generation and classification within a single modular framework. The model is built as a hierarchy of invertible and differentiable bijections, where the Jacobian determinant factorizes across sub-transformations. We show how this ensures exact likelihood computation and stable optimization, while invertibility enables explicit visualization of sample likelihoods, providing an interpretable lens into the model's reasoning. By conditioning on class labels, MAGIC-Flow supports controllable sample synthesis and principled class-probability estimation, effectively aiding both generative and discriminative objectives. We evaluate MAGIC-Flow against top baselines using metrics for similarity, fidelity, and diversity. Across multiple datasets, it addresses generation and classification under scanner noise, and modality-specific synthesis and identification. Results show MAGIC-Flow creates realistic, diverse samples and improves classification. MAGIC-Flow is an effective strategy for generation and classification in data-limited domains, with direct benefits for privacy-preserving augmentation, robust generalization, and trustworthy medical AI.

cs.LG↗