Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. It is mainly considered as a powerful tool with high flexibility to approximate functions. This paper pro...
Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. It is mainly considered as a powerful tool with high flexibility to approximate functions. This paper proposes a generalized NURBS based approach to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains by using physics-informed neural networks (PINNs). Our approach is based on a posteriori error estimation in which the adjoint problem is solved for the error localization to formulate an error estimator within the framework of neural network. An efficient and easy to implement algorithm is developed to obtain a posteriori error estimate for multiple goal functionals by employing the dual-weighted residual approach, which is followed by the computation of both primal and adjoint solutions using the neural network. The present study shows that such a data-driven model based learning has superior approximation of quantities of interest even with relatively less training data. Moreover, we illustrate the versatility of activation functions in achieving better learning capabilities and improving convergence rates, especially at the early training stage, and also in increasing solutions accuracies. The novel algorithmic developments are substantiated with several numerical test examples. It has been demonstrated that deep neural networks have distinct advantages over shallow neural networks, and the techniques for enhancing convergence have also been reviewed.
In this study, N-Structured based InAs/AlSb/GaSb Type-II Superlattice pbin type detector structures are investigated. These systems make absorption in infrared region in electromagnetic spectrum as detectors. Structur...
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We demonstrate a relation between Nielsen’s approach toward circuit complexity and Krylov complexity through a particular construction of quantum state space geometry. We start by associating Kähler structures o...
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We demonstrate a relation between Nielsen’s approach toward circuit complexity and Krylov complexity through a particular construction of quantum state space geometry. We start by associating Kähler structures on the full projective Hilbert space of low rank algebras. This geometric structure of the states in the Hilbert space ensures that every unitary transformation of the associated algebras leave the metric and the symplectic forms invariant. We further associate a classical matter free Jackiw-Teitelboim gravity model with these state manifolds and show that the dilaton can be interpreted as the quantum mechanical expectation values of the symmetry generators. On the other hand, we identify the dilaton with the spread complexity over a Krylov basis thereby proposing a geometric perspective connecting two different notions of complexity.
Widely recognized as a thermally activated process, atomic stick-slip friction has been typically explained by Prandtl-Tomlinson model with thermal activation. Despite the limited success, theoretical predictions from...
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Widely recognized as a thermally activated process, atomic stick-slip friction has been typically explained by Prandtl-Tomlinson model with thermal activation. Despite the limited success, theoretical predictions from the classic model are primarily based on a one-dimensional (1D) assumption, which is generally not compatible with real experiments that are two-dimensional (2D) in nature. In this letter, a theoretical model based on 2D transition state theory has been derived and confirmed to be able to capture the 2D slip kinetics in atomic-scale friction experiments on crystalline surface with a hexagonal energy landscape. Moreover, we propose a reduced scheme that enables extraction of intrinsic interfacial parameters from 2D experiments approximately using the traditional 1D model. The 2D model provides a theoretical tool for understanding the rich kinetics of atomic-scale friction or other phenomena involving higher dimensional transitions.
The interaction between a jet and its surrounding medium plays a crucial role in various astrophysical phenomena, notably in star formation and jet deflection. Despite its significance, the detailed processes and fine...
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Recently we developed a local and constructive algorithm based on Lie algebraic methods for compressing Trotterized evolution under Hamiltonians that can be mapped to free fermions [1, 2]. The compression algorithm yi...
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We propose the coarse-grained spectral projection method (CGSP), a deep learning-assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show CGSP can extract spectral c...
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We establish a scale separation of Kolmogorov width type between subspaces of a given Banach space under the condition that a sequence of linear maps converges much faster on one of the subspaces. The general techniqu...
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We introduce DeePKS-kit, an open-source software package for developing machine learning based energy and density functional models. DeePKS-kit is interfaced with PyTorch, an open-source machine learning library, and ...
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We introduce the Deep Post–Hartree–Fock (DeePHF) method, a machine learning-based scheme for constructing accurate and transferable models for the ground-state energy of electronic structure problems. DeePHF predict...
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