arXiv subjects

Minhyeok Ko

Publications and source records attributed to Minhyeok Ko.

4 recordsLinked to original sources

arXiv2026

Quadratic Point Estimate Method for Uncertainty Quantification with Dependent Non-Gaussian Inputs

As an extension of the Point Estimate Method (PEM) to evaluate probabilistic moments of quantities of interest (QoI) in general $n$-dimensional spaces, the Quadratic Point Estimate Method (QPEM) has been recently developed. This new method is defined to fully represent up to fifth-order input moments in the Gaussian space, providing general analytical expressions for sample locations and weights, without requiring any numerical optimization. The QPEM can significantly improve the estimation accuracy of the output QoI moments, in relation to PEM-based methods whose numbers of sigma points grow linearly with the problem dimension, while at the same time having an affordable and competitive computational cost up to a considerable number of dimensions. The QPEM is further enhanced in this work by enabling copula integration into the framework, which enables effective modeling of the joint input probability density function by estimating marginals and the dependence structure of the involved random variables. The validity and efficient performance of the copula-based QPEM are showcased against numerous other sampling methods in various examples considering two practical scenarios: (i) when the joint dependence structure can be inferred from data, and (ii) when only marginal distributions and correlation matrices are known.

math.NA↗

arXiv2026

Unscented KalmanNet: Structure-Preserving Deep Learning with Calibrated Posterior Uncertainty under Incomplete Physics and Unknown Noise

Nonlinear state estimation requires sequentially fusing model-based predictions with noisy measurements. Under imperfect dynamics and unknown, time-varying noise statistics, this fusion can degrade in both accuracy and statistical consistency. Existing learning-aided filters largely treat accuracy and uncertainty estimation separately, limiting their ability to correct model-mismatch-induced bias while retaining an explicit, calibrated posterior covariance. This paper introduces Unscented KalmanNet (UKN), a model-based deep learning architecture that extends the Unscented Kalman Filter (UKF) with learned mechanisms for these two sources of filtering error while preserving explicit posterior covariance propagation. NoiseNet learns time-varying process and measurement covariances as bounded multiplicative corrections to baseline covariances, guaranteeing positive definiteness, while GainNet learns a bounded residual correction to the analytical UKF gain to compensate for model-mismatch-induced bias. A calibration-aware training objective couples state error with posterior covariance and innovation consistency terms through adaptive weighting, jointly optimizing accuracy and calibration. UKN is benchmarked against UKF, KalmanNet, and Bayesian KalmanNet on three synthetic systems and real-flight UZH-FPV data. It achieves the lowest state-estimation error in all four examples and reduces RMSE by 26.4-49.7% compared with UKF in the synthetic cases. Leave-one-sequence-out cross-validation over 11 flights shows 22.4% and 34.3% reductions in mean position and velocity RMSE, respectively. UKN also yields the lowest fold-to-fold variability, with dimension-normalized NEES and empirical coverage closest to nominal values among covariance-reporting filters. These results show that structured learned adaptation improves estimation accuracy while retaining calibrated uncertainty.

cs.LG↗

arXiv2025

Med-PRM: Medical Reasoning Models with Stepwise, Guideline-verified Process Rewards

Large language models have shown promise in clinical decision making, but current approaches struggle to localize and correct errors at specific steps of the reasoning process. This limitation is critical in medicine, where identifying and addressing reasoning errors is essential for accurate diagnosis and effective patient care. We introduce Med-PRM, a process reward modeling framework that leverages retrieval-augmented generation to verify each reasoning step against established medical knowledge bases. By verifying intermediate reasoning steps with evidence retrieved from clinical guidelines and literature, our model can precisely assess the reasoning quality in a fine-grained manner. Evaluations on five medical QA benchmarks and two open-ended diagnostic tasks demonstrate that Med-PRM achieves state-of-the-art performance, with improving the performance of base models by up to 13.50% using Med-PRM. Moreover, we demonstrate the generality of Med-PRM by integrating it in a plug-and-play fashion with strong policy models such as Meerkat, achieving over 80\% accuracy on MedQA for the first time using small-scale models of 8 billion parameters. Our code and data are available at: https://med-prm.github.io/

cs.CL↗

arXiv2024

Quadratic Point Estimate Method for Probabilistic Moments Computation

This paper presents in detail the originally developed Quadratic Point Estimate Method (QPEM), aimed at efficiently and accurately computing the first four output moments of probabilistic distributions, using 2n^2+1 sample (or sigma) points, with n, the number of input random variables. The proposed QPEM particularly offers an effective, superior, and practical alternative to existing sampling and quadrature methods for low- and moderately-high-dimensional problems. Detailed theoretical derivations are provided proving that the proposed method can achieve a fifth or higher-order accuracy for symmetric input distributions. Various numerical examples, from simple polynomial functions to nonlinear finite element analyses with random field representations, support the theoretical findings and further showcase the validity, efficiency, and applicability of the QPEM, from low- to high-dimensional problems.

math.NA↗