Tae-Geun Kim

Tae-Geun Kim, Seong Chan Park

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

Tae-Geun Kim

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.

Taehyeun Kim, Tae-Geun Kim, Anouck Girard et al.

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.

Chang Min Hyun, Tae-Geun Kim, Kyounghun Lee

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.