8 papers
Dirac-Interconnected Neural Elements: Discovering Modularity in Physical Systems Without Reduction
Reiho Li, Razmik Arman Khosrovian, Takaharu Yaguchi +2
Deep learning has shown remarkable success in the data-driven modeling of dynamical systems. Much of its success is attributed not to the flexibility of neural networks but to indu…
GRFBrain: Graph-Structured Rectified Flows for EEG Dynamic Modeling
Haohui Jia, Zheng Chen, Jathurshan Pradeepkumar +4
Forecasting time-varying functional connectivity from electroencephalography (EEG) requires modeling both history-dependent trends and structured variability across channels. Condi…
PINNs Failure Modes are Overfitting
Nigel T. Andersen, Takashi Matsubara
Physics-Informed Neural Networks (PINNs) are a common class of machine learning-based partial differential equation (PDE) solvers which train a network to represent a solution by m…
Symplectic Neural Operators for Learning Infinite Dimensional Hamiltonian Systems
Yeang Makara, Yusuke Tanaka, Takashi Matsubara +1
The modeling and simulation of infinite-dimensional Hamiltonian systems are central problems in mathematical physics and engineering, however they pose significant computational an…
ODEBrain: Continuous-Time EEG Graph for Modeling Dynamic Brain Networks
Haohui Jia, Zheng Chen, Lingwei Zhu +6
Modeling neural population dynamics is crucial for foundational neuroscientific research and various clinical applications. Conventional latent variable methods typically model con…
RepSPD: Enhancing SPD Manifold Representation in EEGs via Dynamic Graphs
Haohui Jia, Zheng Chen, Lingwei Zhu +4
Decoding brain activity from electroencephalography (EEG) is crucial for neuroscience and clinical applications. Among recent advances in deep learning for EEG, geometric learning…
Learning Hamiltonian Density Using DeepONet
Baige Xu, Yusuke Tanaka, Takashi Matsubara +1
In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for…
Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domains
Razmik Arman Khosrovian, Takaharu Yaguchi, Hiroaki Yoshimura +1
Deep learning has achieved great success in modeling dynamical systems, providing data-driven simulators to predict complex phenomena, even without known governing equations. Howev…