Joon-Hyuk Ko

Taeyoung Kim, Joon-Hyuk Ko · eth-zurich

We propose an architecture that augments the Flux Neural Operator (Flux NO), which combines the classical finite volume method (FVM) with neural operators, with ViT-based context injection. Our model is formulated as a hypernetwork: it extracts solution dynamics over a finite temporal window, encodes them with a recurrent Vision Transformer, and generates the parameters of a context-conditioned neural operator. This enables the model to infer and solve conservation laws without explicit access to the governing equation or PDE coefficients. Experimentally, we show that the proposed method preserves the robustness, generalization ability, and long-time prediction advantages of Flux NO over standard neural operators, while delivering reliable numerical solutions across a broad range of conservative systems, including previously unseen fluxes. Our code is available at https://github.com/xx257xx/CONTEXT_FLUX_NO.

Joon-Hyuk Ko, Hankyul Koh, Nojun Park et al.

Neural Ordinary Differential Equations (NeuralODEs) present an attractive way to extract dynamical laws from time series data, as they bridge neural networks with the differential equation-based modeling paradigm of the physical sciences. However, these models often display long training times and suboptimal results, especially for longer duration data. While a common strategy in the literature imposes strong constraints to the NeuralODE architecture to inherently promote stable model dynamics, such methods are ill-suited for dynamics discovery as the unknown governing equation is not guaranteed to satisfy the assumed constraints. In this paper, we develop a new training method for NeuralODEs, based on synchronization and homotopy optimization, that does not require changes to the model architecture. We show that synchronizing the model dynamics and the training data tames the originally irregular loss landscape, which homotopy optimization can then leverage to enhance training. Through benchmark experiments, we demonstrate our method achieves competitive or better training loss while often requiring less than half the number of training epochs compared to other model-agnostic techniques. Furthermore, models trained with our method display better extrapolation capabilities, highlighting the effectiveness of our method.

Hankyul Koh, Joon-hyuk Ko, Wonho Jhe

We propose the Moderate Adaptive Linear Unit (MoLU), a novel activation function for deep neural networks, defined analytically as: f(x)=x \times (1+tanh(x))/2. MoLU combines mathematical elegance with empirical effectiveness, exhibiting superior performance in terms of prediction accuracy, convergence speed, and computational efficiency. Due to its C-infinity smoothness, i.e. infinite differentiability and analyticity, MoLU is expected to mitigate issues such as vanishing or exploding gradients, making it suitable for a broad range of architectures and applications, including large language models (LLMs), Neural Ordinary Differential Equations (Neural ODEs), Physics-Informed Neural Networks (PINNs), and Convolutional Neural Networks (CNNs). Empirical evaluations show that MoLU consistently achieves faster convergence and improved final accuracy relative to widely used activation functions such as GeLU, SiLU, and Mish. These properties position MoLU as a promising and robust candidate for general-purpose activation across diverse deep learning paradigms.

Joon-Hyuk Ko, Andrus Giraldo, Deok-Sun Lee

Chaotic systems pose fundamental challenges for data-driven dynamics discovery, as small modeling errors lead to exponentially growing trajectory discrepancies. Since exact long-term prediction is unattainable, it is natural to ask what a good surrogate model for chaotic dynamics is. Prior work has largely focused either on reproducing the Jacobian of the underlying dynamics, which governs local expansion and contraction rates, or on training surrogate models that reproduce the ground-truth dynamics' long-term statistical behavior. In this work, we propose a new framework that aims to bridge these two paradigms by training surrogate dynamics models with accurate Jacobians and long-term statistical properties. Our method constructs a local covering of a chaotic attractor in phase space and analyzes the expansion and contraction of these coverings under the dynamics. The surrogate model is trained by minimizing the maximum mean discrepancy between the pushforward distributions of the coverings under the surrogate and ground-truth dynamics. Experiments show that our method significantly improves Jacobian accuracy while remaining competitive with state-of-the-art statistically accurate dynamics learning methods. Our code is fully available at https://anonymous.4open.science/r/neighborwatch.

QHwan Kim, Joon-Hyuk Ko, Sunghoon Kim et al.

The characterization of drug-protein interactions is crucial in the high-throughput screening for drug discovery. The deep learning-based approaches have attracted attention because they can predict drug-protein interactions without trial-and-error by humans. However, because data labeling requires significant resources, the available protein data size is relatively small, which consequently decreases model performance. Here we propose two methods to construct a deep learning framework that exhibits superior performance with a small labeled dataset. At first, we use transfer learning in encoding protein sequences with a pretrained model, which trains general sequence representations in an unsupervised manner. Second, we use a Bayesian neural network to make a robust model by estimating the data uncertainty. As a result, our model performs better than the previous baselines for predicting drug-protein interactions. We also show that the quantified uncertainty from the Bayesian inference is related to the confidence and can be used for screening DPI data points.