Related papers: A framework for structural shape optimization base…
Differentiable numerical simulations of physical systems have gained rising attention in the past few years with the development of automatic differentiation tools. This paper presents JAX-SSO, a differentiable finite element analysis…
An inexact accelerated stochastic Alternating Direction Method of Multipliers (AS-ADMM) scheme is developed for solving structured separable convex optimization problems with linear constraints. The objective function is the sum of a…
Modelers use automatic differentiation (AD) of computation graphs to implement complex Deep Learning models without defining gradient computations. Stochastic AD extends AD to stochastic computation graphs with sampling steps, which arise…
We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by…
Robust federated learning aims to maintain reliable performance despite the presence of adversarial or misbehaving workers. While state-of-the-art (SOTA) robust distributed gradient descent (Robust-DGD) methods were proven theoretically…
We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…
Modern supercomputers are increasingly relying on Graphic Processing Units (GPUs) and other accelerators to achieve exa-scale performance at reasonable energy usage. The challenge of exploiting these accelerators is the incompatibility…
Differentiable programming, enabled by automatic differentiation (AD), provides a robust framework for gradient-based optimization in computational plasma physics. While optimization is often only used towards design, we demonstrate that it…
Understanding low-dimensional structures within high-dimensional data is crucial for visualization, interpretation, and denoising in complex datasets. Despite the advancements in manifold learning techniques, key challenges-such as limited…
In scientific computation, it is often necessary to calculate higher-order derivatives of a function. Currently, two primary methods for higher-order automatic differentiation exist: symbolic differentiation and algorithmic automatic…
Deformable Attention Transformers (DAT) have shown remarkable performance in computer vision tasks by adaptively focusing on informative image regions. However, their data-dependent sampling mechanism introduces irregular memory access…
Predictive simulations are essential for applications ranging from weather forecasting to material design. The veracity of these simulations hinges on their capacity to capture the effective system dynamics. Massively parallel simulations…
Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive…
This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending…
Imaging Earth structure or seismic sources from seismic data involves minimizing a target misfit function, and is commonly solved through gradient-based optimization. The adjoint-state method has been developed to compute the gradient…
Quantitative low-energy electron diffraction [LEED $I(V)$] is a powerful method for surface-structure determination, based on a direct comparison of experimentally observed $I(V)$ data with computations for a structure model. As the…
As a well-known optimization framework, the Alternating Direction Method of Multipliers (ADMM) has achieved tremendous success in many classification and regression applications. Recently, it has attracted the attention of deep learning…
In this paper, we propose a general deep learning training framework XGrad which introduces weight prediction into the popular gradient-based optimizers to boost their convergence and generalization when training the deep neural network…
The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis, and tolerance calculation. An…
Aligning theoretical atomistic structural models of materials with available experimental data presents a significant challenge for disordered systems. The configurational space to navigate is vast, and faithful realizations require large…