Foundational optimization algorithms are the core driving force behind deep learning, evolving from early stochastic gradient descent (SGD) to the widely adopted Adam family. However, as the scale of ...
Efficient Shift-and-Invert Preconditioning for Multi-GPU Accelerated Density Functional Calculations
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Abstract: Bi-conjugate Gradient Method (BCG) has potential problems on slow convergence or divergence when complex linear equations are large-scale or coefficient matrix of complex linear equations is ...
Abstract: The Gauss-Seidel preconditioned conjugate gradient method applying to element-by-element finite-element method (EBE-FEM) is derived and the calculation process is presented in this paper.
ABSTRACT: In this paper, we propose an improved preconditioned algorithm for the conjugate gradient squared method (improved PCGS) for the solution of linear equations. Further, the logical structures ...
Least-squares reverse-time migration (LSRTM) can overcome the problems of low resolution and unbalanced amplitude energy of deep formation imaging in reverse-time migration (RTM); hence, it can obtain ...
tree-math makes it easy to implement numerical algorithms that work on JAX pytrees, such as iterative methods for optimization and equation solving. It does so by providing a wrapper class ...
A gradient preconditioning approach based on transmitted wave energy for least-squares reverse time migration (LSRTM) is proposed in this study. The gradient is preconditioned by using the energy of ...
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