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Dongeun Lee

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2 papers

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AAAI Conference 2024 Conference Paper

Operator-Learning-Inspired Modeling of Neural Ordinary Differential Equations

Woojin Cho
Seunghyeon Cho
Hyundong Jin
Jinsung Jeon
Kookjin Lee
Sanghyun Hong
Dongeun Lee
Jonghyun Choi

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for various downstream tasks, e.g., image classification, time series classification, image generation, etc. Its key part is how to model the time-derivative of the hidden state, denoted dh(t)/dt. People have habitually used conventional neural network architectures, e.g., fully-connected layers followed by non-linear activations. In this paper, however, we present a neural operator-based method to define the time-derivative term. Neural operators were initially proposed to model the differential operator of partial differential equations (PDEs). Since the time-derivative of NODEs can be understood as a special type of the differential operator, our proposed method, called branched Fourier neural operator (BFNO), makes sense. In our experiments with general downstream tasks, our method significantly outperforms existing methods.

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AAAI Conference 2021 Conference Paper

DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation

Jungeun Kim
Kookjin Lee
Dongeun Lee
Sheo Yon Jhin
Noseong Park

We present a method for learning dynamics of complex physical processes described by time-dependent nonlinear partial differential equations (PDEs). Our particular interest lies in extrapolating solutions in time beyond the range of temporal domain used in training. Our choice for a baseline method is physics-informed neural network (PINN) because the method parameterizes not only the solutions, but also the equations that describe the dynamics of physical processes. We demonstrate that PINN performs poorly on extrapolation tasks in many benchmark problems. To address this, we propose a novel method for better training PINN and demonstrate that our newly enhanced PINNs can accurately extrapolate solutions in time. Our method shows up to 72% smaller errors than existing methods in terms of the standard L2-norm metric.

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