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We develop a distributed stochastic gradient descent algorithm for solving non-convex optimization problems under the assumption that the local objective functions are twice continuously differentiable with Lipschitz continuous gradients…

In this paper, we propose a deep learning-based method, deep Euler method (DEM) to solve ordinary differential equations. DEM significantly improves the accuracy of the Euler method by approximating the local truncation error with deep…

Distributed training of GNNs enables learning on massive graphs (e.g., social and e-commerce networks) that exceed the storage and computational capacity of a single machine. To reach performance comparable to centralized training,…

We learn recurrent neural network optimizers trained on simple synthetic functions by gradient descent. We show that these learned optimizers exhibit a remarkable degree of transfer in that they can be used to efficiently optimize a broad…

Many real-world physics and engineering problems arise in geometrically complex domains discretized by meshes for numerical simulations. The nodes of these potentially irregular meshes naturally form point clouds whose limited tractability…

Differentially private stochastic gradient descent (DP-SGD) is broadly considered to be the gold standard for training and fine-tuning neural networks under differential privacy (DP). With the increasing availability of high-quality…

In the last decade, deep learning has contributed to advances in a wide range computer vision tasks including texture analysis. This paper explores a new approach for texture segmentation using deep convolutional neural networks, sharing…

Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…

Gradients of neural networks can be computed efficiently for any architecture, but some applications require differential operators with higher time complexity. We describe a family of restricted neural network architectures that allow…

We introduce a distributed spatio-temporal artificial neural network architecture (DISTANA). It encodes mesh nodes using recurrent, neural prediction kernels (PKs), while neural transition kernels (TKs) transfer information between…

We develop a data-driven machine learning approach to identifying parameters with steady-state solutions, locating such solutions, and determining their linear stability for systems of ordinary differential equations and dynamical systems…

Partial differential equations (PDEs) form the mathematical foundation for modeling physical systems in science and engineering, where numerical solutions demand rigorous accuracy-efficiency tradeoffs. Mesh movement techniques address this…

Computer vision algorithms with pixel-wise labeling tasks, such as semantic segmentation and salient object detection, have gone through a significant accuracy increase with the incorporation of deep learning. Deep segmentation methods…

We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity,…

Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…

We investigate scaling and efficiency of the deep neural network multigrid method (DNN-MG). DNN-MG is a novel neural network-based technique for the simulation of the Navier-Stokes equations that combines an adaptive geometric multigrid…

In this paper we propose a method to generate suitably refined finite element meshes using neural networks. As a model problem we consider a linear elasticity problem on a planar domain (possibly with holes) having a polygonal boundary. We…

Neural operators offer an effective framework for learning solutions of partial differential equations for many physical systems in a resolution-invariant and data-driven manner. Existing neural operators, however, often suffer from…

State-based peridynamic models provide an important extension of bond-based models that allow the description of general linearly elastic materials. Meshfree discretizations of these nonlocal models are attractive due to their ability to…

Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…