arXiv subjects

Jacob Hauck

Publications and source records attributed to Jacob Hauck.

2 recordsLinked to original sources

arXiv2026

Score-Based Generative Data Assimilation for Integrating Aggregated Surveillance Data into Agent-Based Models in Epidemic Tracking

Reliable epidemic monitoring often requires inferring regional infection burden and transmission heterogeneity from noisy, spatially aggregated, and potentially sparse surveillance data. Agent-based models (ABMs) are attractive for this task because they represent individual behavior, contact heterogeneity, and localized interventions, but these same features make them difficult to calibrate online. We develop a generative AI-based data-assimilation (GenDA) framework for partially observed epidemic ABMs that estimates both the epidemic state and a heterogeneous parameter field while respecting the gap between observable macrostates and latent agent-level microstates. GenDA combines a training-free, score-based generative update for macrostate correction with a direct parameter update based on macrostate discrepancies, followed by a macro-micro reassignment step that restores consistency with the ABM. In controlled and geographically explicit synthetic experiments, the framework recovers regional epidemic burden, dominant hotspot structures, and effective transmission heterogeneity from aggregated observations, while improving post-assimilation forecasts relative to state-only assimilation.

math.NA↗

arXiv2025

Discretization-independent multifidelity operator learning for partial differential equations

We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for input and output function distributions. We introduce the concepts of \textit{numerical operator learning} and \textit{discretization independence}, which clarify the relationship between theoretical formulations and practical realizations of operator learning models. Our model is discretization-independent, making it particularly effective for multifidelity learning. We establish theoretical approximation guarantees, demonstrating uniform universal approximation under strong assumptions on the input functions and statistical approximation under weaker conditions. To our knowledge, this is the first comprehensive study that investigates how discretization independence enables robust and efficient multifidelity operator learning. We validate our method through extensive numerical experiments involving both local and nonlocal PDEs, including time-independent and time-dependent problems. The results show that multifidelity training significantly improves accuracy and computational efficiency. Moreover, multifidelity training further enhances empirical discretization independence.

cs.LG↗