arXiv subjects

Tae-Geun Kim

Publications and source records attributed to Tae-Geun Kim.

6 recordsLinked to original sources

arXiv2025

Learning Hamiltonian Dynamics with Bayesian Data Assimilation

In this paper, we develop a neural network-based approach for time-series prediction in unknown Hamiltonian dynamical systems. Our approach leverages a surrogate model and learns the system dynamics using generalized coordinates (positions) and their conjugate momenta while preserving a constant Hamiltonian. To further enhance long-term prediction accuracy, we introduce an Autoregressive Hamiltonian Neural Network, which incorporates autoregressive prediction errors into the training objective. Additionally, we employ Bayesian data assimilation to refine predictions in real-time using online measurement data. Numerical experiments on a spring-mass system and highly elliptic orbits under gravitational perturbations demonstrate the effectiveness of the proposed method, highlighting its potential for accurate and robust long-term predictions.

cs.LG↗

arXiv2024

Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics?

We propose a novel framework based on neural network that reformulates classical mechanics as an operator learning problem. A machine directly maps a potential function to its corresponding trajectory in phase space without solving the Hamilton equations. Most notably, while conventional methods tend to accumulate errors over time through iterative time integration, our approach prevents error propagation. Two newly developed neural network architectures, namely VaRONet and MambONet, are introduced to adapt the Variational LSTM sequence-to-sequence model and leverage the Mamba model for efficient temporal dynamics processing. We tested our approach with various 1D physics problems: harmonic oscillation, double-well potentials, Morse potential, and other potential models outside the training data. Compared to traditional numerical methods based on the fourth-order Runge-Kutta (RK4) algorithm, our model demonstrates improved computational efficiency and accuracy. Code is available at: https://github.com/Axect/Neural_Hamilton

cs.LG↗

arXiv2024

HyperbolicLR: Epoch insensitive learning rate scheduler

This study proposes two novel learning rate schedulers -- Hyperbolic Learning Rate Scheduler (HyperbolicLR) and Exponential Hyperbolic Learning Rate Scheduler (ExpHyperbolicLR) -- to address the epoch sensitivity problem that often causes inconsistent learning curves in conventional methods. By leveraging the asymptotic behavior of hyperbolic curves, the proposed schedulers maintain more stable learning curves across varying epoch settings. Specifically, HyperbolicLR applies this property directly in the epoch-learning rate space, while ExpHyperbolicLR extends it to an exponential space. We first determine optimal hyperparameters for each scheduler on a small number of epochs, fix these hyperparameters, and then evaluate performance as the number of epochs increases. Experimental results on various deep learning tasks (e.g., image classification, time series forecasting, and operator learning) demonstrate that both HyperbolicLR and ExpHyperbolicLR achieve more consistent performance improvements than conventional schedulers as training duration grows. These findings suggest that our hyperbolic-based schedulers offer a more robust and efficient approach to deep network optimization, particularly in scenarios constrained by computational resources or time.

cs.LG↗

arXiv2023

Unsupervised sequence-to-sequence learning for automatic signal quality assessment in multi-channel electrical impedance-based hemodynamic monitoring

This study proposes an unsupervised sequence-to-sequence learning approach that automatically assesses the motion-induced reliability degradation of the cardiac volume signal (CVS) in multi-channel electrical impedance-based hemodynamic monitoring. The proposed method attempts to tackle shortcomings in existing learning-based assessment approaches, such as the requirement of manual annotation for motion influence and the lack of explicit mechanisms for realizing motion-induced abnormalities under contextual variations in CVS over time. By utilizing long-short term memory and variational auto-encoder structures, an encoder--decoder model is trained not only to self-reproduce an input sequence of the CVS but also to extrapolate the future in a parallel fashion. By doing so, the model can capture contextual knowledge lying in a temporal CVS sequence while being regularized to explore a general relationship over the entire time-series. A motion-influenced CVS of low-quality is detected, based on the residual between the input sequence and its neural representation with a cut--off value determined from the two-sigma rule of thumb over the training set. Our experimental observations validated two claims: (i) in the learning environment of label-absence, assessment performance is achievable at a competitive level to the supervised setting, and (ii) the contextual information across a time series of CVS is advantageous for effectively realizing motion-induced unrealistic distortions in signal amplitude and morphology. We also investigated the capability as a pseudo-labeling tool to minimize human-craft annotation by preemptively providing strong candidates for motion-induced anomalies. Empirical evidence has shown that machine-guided annotation can reduce inevitable human-errors during manual assessment while minimizing cumbersome and time-consuming processes.

eess.SP↗

arXiv2022

DeeLeMa: Missing information search with Deep Learning for Mass estimation

We introduce DeeLeMa, a deep learning-based network for the analysis of energy and momentum in high-energy particle collisions. This novel approach is specifically designed to address the challenge of analyzing collision events with multiple invisible particles, which are prevalent in many high-energy physics experiments. DeeLeMa is constructed based on the kinematic constraints and symmetry of the event topologies. We show that DeeLeMa can robustly estimate mass distribution even in the presence of combinatorial uncertainties and detector smearing effects. The approach is flexible and can be applied to various event topologies by leveraging the relevant kinematic symmetries. This work opens up exciting opportunities for the analysis of high-energy particle collision data, and we believe that DeeLeMa has the potential to become a valuable tool for the high-energy physics community.

hep-ph↗

arXiv2022

Primordial Black Holes as a Factory of Axions: Extragalactic Photons from Axions

Primordial black holes (PBHs) are significant sources of axions and axion-like particles (ALPs), provided their Hawking temperature exceeds the particles' masses. Given the predominant decay of axions into photons, the enhanced photon spectrum they generate can be feasibly detected using sensitive detectors. This paper introduces a novel methodology that elucidates the decay process for particles to traverse and decay over cosmological timescales. Specifically, we derive estimations for the photon spectrum and flux, assuming a monochromatic mass spectrum and isotropic distribution for PBHs. Encouragingly, forthcoming detectors like e-ASTROGAM are well positioned to capture this signal.

hep-ph↗