In the evolving era of social robots, managing a swarm of autonomous agents to perform particular tasks has become essential for numerous industries. The task becomes more challenging for large-scale swarms and comple...
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We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenge...
ISBN:
(纸本)9798331314385
We propose the first learning scheme for functional differential equations (FDEs). FDEs play a fundamental role in physics, mathematics, and optimal control. However, the numerical analysis of FDEs has faced challenges due to its unrealistic computational costs and has been a long standing problem over decades. Thus, numerical approximations of FDEs have been developed, but they often oversimplify the solutions. To tackle these two issues, we propose a hybrid approach combining physics-informed neural networks (PINNs) with the cylindrical approximation. The cylindrical approximation expands functions and functional derivatives with an orthonormal basis and transforms FDEs into high-dimensional PDEs. To validate the reliability of the cylindrical approximation for FDE applications, we prove the convergence theorems of approximated functional derivatives and solutions. Then, the derived high-dimensional PDEs are numerically solved with PINNs. Through the capabilities of PINNs, our approach can handle a broader class of functional derivatives more efficiently than conventional discretization-based methods, improving the scalability of the cylindrical approximation. As a proof of concept, we conduct experiments on two FDEs and demonstrate that our model can successfully achieve typical L1 relative error orders of PINNs ~ 10-3. Overall, our work provides a strong backbone for physicists, mathematicians, and machine learning experts to analyze previously challenging FDEs, thereby democratizing their numerical analysis, which has received limited attention. Code is available at https://***/TaikiMiyagawa/FunctionalPINN.
In this article, we present the mathematical analysis of the convergence of the linearized Crank–Nicolson Galerkin method for a nonlinear Schrödinger problem related to a domain with a moving boundary. The conve...
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Demand generation is crucial for organizations, supplying sales teams with well-qualified commercial opportunities. Despite the wide variety of existing opportunity qualification methodologies, the subjective nature o...
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Sedimentary rocks are of great importance for the oil and gas industry. Spectral matching using known references made on hyperspectral images is one of the most rapid and cost effective alternatives for the detailed a...
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Artificial Intelligence (AI) and marketing have transformed consumer behavior and shopping experiences, especially through Recommender Systems (RSs) in e-commerce. RSs use algorithms to provide personalized recommenda...
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In the era of emerging technologies, the banks strive to provide a variety of innovations toward digital banking transformations. Hence, digital banking is the result rapid establishment of innovative digital banking ...
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Numerous tsunami disasters have happened in Indonesia as located across Ring of Fire, and it brings casualties to both the economy and welfare of the people in the event of their occurrence. Frequent tectonic earthqua...
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We revisit the perceptual crossing simulation studies, which are aimed at challenging methodological individualism in the analysis of social cognition by studying multi-agent real-time interactions. To date, all of th...
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The multivariate Spatiooral data challenges the analysts along the navigation and exploration of the information, using Data Analytics techniques. We present SPLORT, as a user-centered web-based solution for segmented...
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