In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep...
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This paper presents an advanced method for addressing the inverse kinematics and optimal path planning challenges in robot manipulators. The inverse kinematics problem involves determining the joint angles for a given...
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The long time behavior of the solutions of the generalized long-short wave equations with dissipation term is studied. The existence of global attractor of the initial periodic boundary value is proved by means of a u...
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The long time behavior of the solutions of the generalized long-short wave equations with dissipation term is studied. The existence of global attractor of the initial periodic boundary value is proved by means of a uniform a priori estimate for time. And also the dimensions of the global attractor are estimated.
This paper discusses the trajectory planning of a robot manipulator with computer algebra. In the operation of robot manipulators, it is important to make the trajectory of the end effector so that it does not collide...
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Decentralized optimization with time-varying networks is an emerging paradigm in machine learning. It saves remarkable communication overhead in large-scale deep training and is more robust in wireless scenarios espec...
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Social distancing is widely acknowledged as an effective public health policy combating the novel coronavirus. But extreme forms of social distancing like isolation and quarantine have costs and it is not clear how mu...
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We propose a method for solving the speech direction estimation problem by computer algebra. The method is based on the function approximation using the minimax polynomial. The minimax polynomial is obtained by an ite...
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Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between function...
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Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data. We propose a novel operator learning method, LOCA (Learning Operators with Coupled Attention), motivated from the recent success of the attention mechanism. In our architecture, the input functions are mapped to a finite set of features which are then averaged with attention weights that depend on the output query locations. By coupling these attention weights together with an integral transform, LOCA is able to explicitly learn correlations in the target output functions, enabling us to approximate nonlinear operators even when the number of output function measurements in the training set is very small. Our formulation is accompanied by rigorous approximation theoretic guarantees on the universal expressiveness of the proposed model. Empirically, we evaluate the performance of LOCA on several operator learning scenarios involving systems governed by ordinary and partial differential equations, as well as a black-box climate prediction problem. Through these scenarios we demonstrate state of the art accuracy, robustness with respect to noisy input data, and a consistently small spread of errors over testing data sets, even for out-of-distribution prediction tasks.
Spontaneous pattern formation plays an important role in a wide variety of natural phenomena and materials systems. A key ingredient for the occurrence of modulated phases is the presence of competing interactions, ge...
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Spontaneous pattern formation plays an important role in a wide variety of natural phenomena and materials systems. A key ingredient for the occurrence of modulated phases is the presence of competing interactions, generally of different physical origins. We demonstrate that in dipolar films, a prototypical system for pattern formation, patterns can be induced by dielectric effects alone. A rich phase diagram arises, where striped and circular morphologies emerge with geometric properties that can be controlled through variation of particle shape and substrate permittivity or permeability. These effects are particularly enhanced by metamaterial substrates.
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