arXiv subjects

Seho Park

Publications and source records attributed to Seho Park.

7 recordsLinked to original sources

arXiv2026

Optimal Convergence Rate for Periodic Homogenization of Rearrangement-Invariant Convex Hamilton--Jacobi Equations in Infinite Dimensions

We prove the optimal convergence rate $O(\varepsilon)$ for periodic homogenization of convex Hamilton-Jacobi equations arising from infinite systems of indistinguishable particles on the torus, under the assumption that the initial data depend only on the mean configuration. This extends the finite-dimensional result [1], which is based on the large-time behavior of the Lagrangian action metric and a curve-surgery argument. Here, these tools cannot be applied directly because minimizing curves live in an infinite-dimensional Hilbert space, where local compactness and finite-dimensional topology are unavailable. We overcome this difficulty by cutting the finite-dimensional mean-time projection of a minimizing curve and gluing the lifted pieces in the Hilbert space using the compact quotient induced by periodicity and rearrangement invariance. We conclude with an example showing that this rate is sharp.

math.AP↗

arXiv2026

Periodic Homogenization of Hamilton-Jacobi Equations for Infinite Systems of Indistinguishable Particles

We study the homogenization of first-order Hamilton-Jacobi equations on an infinite-dimensional Hilbert space, motivated by systems of infinitely many indistinguishable particles on the torus. A central difficulty is that the analysis takes place in an infinite-dimensional setting, where the compactness arguments available in finite dimensions break down. The problem is further complicated by the possible nonconvexity of the Hamiltonian, which prevents the direct use of variational methods. Under suitable assumptions on the Hamiltonian and the initial data, we characterize the effective Hamiltonian through an associated cell problem and prove that the solutions converge to those of the limiting equation at rate $O(\varepsilon^{1/3})$. This yields a qualitative and quantitative homogenization result for a class of possibly nonconvex Hamilton-Jacobi equations in infinite dimensions.

math.AP↗

arXiv2025

Retrieval Augmented Large Language Model System for Comprehensive Drug Contraindications

The versatility of large language models (LLMs) has been explored across various sectors, but their application in healthcare poses challenges, particularly in the domain of pharmaceutical contraindications where accurate and reliable information is required. This study enhances the capability of LLMs to address contraindications effectively by implementing a Retrieval Augmented Generation (RAG) pipeline. Utilizing OpenAI's GPT-4o-mini as the base model, and the text-embedding-3-small model for embeddings, our approach integrates Langchain to orchestrate a hybrid retrieval system with re-ranking. This system leverages Drug Utilization Review (DUR) data from public databases, focusing on contraindications for specific age groups, pregnancy, and concomitant drug use. The dataset includes 300 question-answer pairs across three categories, with baseline model accuracy ranging from 0.49 to 0.57. Post-integration of the RAG pipeline, we observed a significant improvement in model accuracy, achieving rates of 0.94, 0.87, and 0.89 for contraindications related to age groups, pregnancy, and concomitant drug use, respectively. The results indicate that augmenting LLMs with a RAG framework can substantially reduce uncertainty in prescription and drug intake decisions by providing more precise and reliable drug contraindication information.

cs.AI↗

arXiv2024

Learning Networked Dynamical System Models with Weak Form and Graph Neural Networks

This paper presents a sequence of two approaches for the data-driven control-oriented modeling of networked systems, i.e., the systems that involve many interacting dynamical components. First, a novel deep learning approach named the weak Latent Dynamics Model (wLDM) is developed for learning generic nonlinear dynamics with control. Leveraging the weak form, the wLDM enables more numerically stable and computationally efficient training as well as more accurate prediction, when compared to conventional methods such as neural ordinary differential equations. Building upon the wLDM framework, we propose the weak Graph Koopman Bilinear Form (wGKBF) model, which integrates geometric deep learning and Koopman theory to learn latent space dynamics for networked systems, especially for the challenging cases having multiple timescales. The effectiveness of the wLDM framework and wGKBF model are demonstrated on three example systems of increasing complexity - a controlled double pendulum, the stiff Brusselator dynamics, and an electrified aircraft energy system. These numerical examples show that the wLDM and wGKBF achieve superior predictive accuracy and training efficiency as compared to baseline models. Parametric studies provide insights into the effects of hyperparameters in the weak form. The proposed framework shows the capability to efficiently capture control-dependent dynamics in these systems, including stiff dynamics and multi-physics interactions, offering a promising direction for learning control-oriented models of complex networked systems.

eess.SY↗

arXiv2023

Comparing weighting and imputation methods for enhancing statistical inference of health surveys given administrative claims data

National surveys of the healthcare system in the United States were conducted to characterize the structure of healthcare system and investigate the impact of evidence-based innovations in healthcare systems on healthcare services. Administrative data is additionally available to researchers raising the question of whether inferences about healthcare organizations based on the survey data can be enhanced by incorporating information from auxiliary data. Administrative data can provide information for dealing with under-coverage-bias and non-response in surveys and for capturing more sub-populations. In this study, we focus on the use of administrative claims data to improve estimates about means of survey items for the finite population. Auxiliary information from the claims data is incorporated using multiple imputation to impute values of non-responding or non-surveyed organizations. We derive multiple versions of imputation strategy, and the logical development of methodology is compared to two incumbent approaches: a naïve analysis that ignores the sampling probabilities and a traditional survey analysis weighting by the inverses of the sampling probabilities. , and illustrate the methods using data from The National Survey of Healthcare Organizations and Systems and The Centers for Medicare & Medicaid Services Medicare claims data to make inferences about relationships of characteristics of healthcare organizations and healthcare services they provide.

stat.ME↗

arXiv2023

Pseudo-clustering for combining data sets with multiple hierarchies

Multi-level modeling is an important approach for analyzing complex survey data using multi-stage sampling. However, estimation of multi-level models can be challenging when we combine several datasets with distinct hierarchies with sampling weights. This paper presents a method for combining multiple datasets with different hierarchical structures due to distinct informative sampling designs for the same survey. To develop an approach with complete generality, we propose to define a pseudo-cluster, a cluster containing only a singleton observation, to unify the data structure and thereby enable estimation of multi-level models incorporating sampling weights across the combined sample. We justify incorporating sampling weights at each level of the hierarchical model and in doing-so define a pseudo-likelihood estimation procedure. Simulation studies are used to illustrate the effect of incorporating sampling designs in this challenging multi-level modeling scenario. We demonstrate in the simulation studies that considering a linear mixed model with sampling weights provides unbiased estimates of model parameters and enhances the estimation of the variance components of the random effects. The proposed method is illustrated through a novel application from the National Survey of Healthcare Organizations and Systems that sought to determine which organizational characteristics or traits, as measured in the surveys, have the strongest average relationship to the percentage of depression and anxiety diagnoses in physician practices in the US.

stat.ME↗

arXiv2020

Combining Non-probability and Probability Survey Samples Through Mass Imputation

This paper presents theoretical results on combining non-probability and probability survey samples through mass imputation, an approach originally proposed by Rivers (2007) as sample matching without rigorous theoretical justification. Under suitable regularity conditions, we establish the consistency of the mass imputation estimator and derive its asymptotic variance formula. Variance estimators are developed using either linearization or bootstrap. Finite sample performances of the mass imputation estimator are investigated through simulation studies and an application to analyzing a non-probability sample collected by the Pew Research Centre.

stat.ME↗