arXiv subjects

Xujia Zhu

Publications and source records attributed to Xujia Zhu.

4 recordsLinked to original sources

arXiv2026

Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates

Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration. However, a systematic end-to-end differentiable formulation for coupling deep-learning-based reduced-order surrogates with variational parameter estimation remains underdeveloped. In this work, we introduce a physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation. The proposed autoencoder-based approach yields a differentiable surrogate that maps physical parameters to predicted flow fields through a latent representation. The observable supervision is used during offline training to encourage the latent variables to retain information correlated with system parameters, while the online inverse problem is solved in the parameter space through the surrogate-induced observation operator. The method is evaluated on two computational-fluid-dynamics benchmarks. The results show that reconstruction accuracy alone is insufficient for inverse modeling, owing to the lack of end-to-end differentiability or physics awareness for variational parameter calibration. Quantitative latent-space analysis further shows that observable supervision improves case-level separability and temporal organization of latent representations. Experiments with realistic measurement settings, including noisy, low-resolution, randomly masked, and block-wise partial observations, demonstrate the robustness of the proposed framework and show that it generally reduces calibration error and variability compared with the standard surrogate models.

cs.LG↗

arXiv2026

Uncertainty functionals revisited: Concavity and Jensen's inequality

This article presents a theoretical study of uncertainty functionals on general measurable spaces. These functionals are fundamental in experimental design and global sensitivity analysis, where they are used to quantify variability and information content in probabilistic models. As first articulated in DeGroot's seminal 1962 article, a natural requirement is that uncertainty should decrease on average when additional information is obtained. This requirement is equivalent to the probabilistic form of Jensen's inequality on the space of probability measures. Our main results show that concavity is necessary but not sufficient for Jensen's inequality to hold whenever the underlying measurable space is infinite. We also provide practicable sufficient conditions under which the desired property holds. These results contribute to a clearer mathematical foundation for uncertainty quantification. Several open questions are formulated.

math.ST↗

arXiv2026

Amortized Variational Inference for Logistic Regression with Missing Covariates

Missing covariate data pose a significant challenge to statistical inference and machine learning, particularly for classification tasks like logistic regression. Classical iterative approaches (EM, multiple imputation) are often computationally intensive, sensitive to high missingness rates, and limited in uncertainty propagation. Recent deep generative models based on VAEs show promise but rely on complex latent representations. We propose Amortized Variational Inference for Logistic Regression (AV-LR), a unified end-to-end framework for binary logistic regression with missing covariates. AV-LR integrates a probabilistic generative model with a simple amortized inference network, trained jointly by maximizing the evidence lower bound. Unlike competing methods, AV-LR performs inference directly in the space of missing data without additional latent variables, using a single inference network and a linear layer that jointly estimate regression parameters and the missingness mechanism. AV-LR achieves estimation accuracy comparable to or better than state-of-the-art EM-like algorithms, with significantly lower computational cost. It naturally extends to missing-not-at-random settings by explicitly modeling the missingness mechanism. Empirical results on synthetic and real-world datasets confirm its effectiveness and efficiency across various missing-data scenarios.

cs.LG↗

arXiv2025

Maximum Likelihood for Logistic Regression Model with Incomplete and Hybrid-Type Covariates

Logistic regression is a fundamental and widely used statistical method for modeling binary outcomes based on covariates. However, the presence of missing data, particularly in settings involving hybrid covariates (a mix of discrete and continuous variables), poses significant challenges. In this paper, we propose a novel Expectation-Maximization based algorithm tailored for parameter estimation in logistic regression models with missing hybrid covariates. The proposed method is specifically designed to handle these complexities, delivering efficient parameter estimates. Through comprehensive simulations and real-world application, we demonstrate that our approach consistently outperforms traditional methods, achieving superior accuracy and reliability.

stat.ME↗