10 accepted papers
As a lightweight model for sequence processing, an LSSL that uses the HiPPO matrix has been proposed. In this paper, as the continuous limit of the HiPPO Matrix, we propose Continuized-HiPPO Operator. Furthermore, as examples of advantages obtained by using this operator, we show that one can analyz…
The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks (DNNs) for learning such a mapping, enabling the learning of solution operators of partial differential equations (PDEs…
Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by selecting suitable points is essential for accelerating the learnin…
Deep learning has achieved great success in modeling dynamical systems, providing data-driven simulators to predict complex phenomena, even without known governing equations. However, existing models have two major limitations: their narrow focus on mechanical systems and their tendency to treat sys…
Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory. It is known that physical phenomena based on these theories have an energy conservation law or a dissipation law. Therefore, in the simulations of such phys…
Many real-world dynamical systems are associated with first integrals (a.k.a. invariant quantities), which are quantities that remain unchanged over time. The discovery and understanding of first integrals are fundamental and important topics both in the natural sciences and in industrial applicatio…
Many physical phenomena are described by Hamiltonian mechanics using an energy function (Hamiltonian). Recently, the Hamiltonian neural network, which approximates the Hamiltonian by a neural network, and its extensions have attracted much attention. This is a very powerful method, but theoretical s…
In recent years, substantial research on the methods for learning Hamiltonian equations has been conducted. Although these approaches are very promising, the commonly used representation of the Hamilton equation uses the generalized momenta, which are generally unknown. Therefore, the training data…
A neural network model of a differential equation, namely neural ODE, has enabled the learning of continuous-time dynamical systems and probabilistic distributions with high accuracy. The neural ODE uses the same network repeatedly during a numerical integration. The memory consumption of the backpr…
Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws. Recent developments in neural networks have enabled the mimicking of the energy conservation law by learning the underlyi…