Related papers: A Domain Decomposition Deep Neural Network Method …

Monocular depth estimation (MDE) has attracted intense study due to its low cost and critical functions for robotic tasks such as localization, mapping and obstacle detection. Supervised approaches have led to great success with the advance…

The decoupling of multivariate functions is a powerful modeling paradigm for learning multivariate input-output relations from data. For the single-layer case, established CPD-based methods are available, but the multi-layer case remained…

In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational…

Modeling fracture is computationally expensive even in computational simulations of two-dimensional problems. Hence, scaling up the available approaches to be directly applied to large components or systems crucial for real applications…

Owing to the complicated characteristics of 5G communication system, designing RF components through mathematical modeling becomes a challenging obstacle. Moreover, such mathematical models need numerous manual adjustments for various…

Multiscale problems are challenging for neural network-based discretizations of differential equations, such as physics-informed neural networks (PINNs). This can be (partly) attributed to the so-called spectral bias of neural networks. To…

We present a class of algorithms capable of directly training deep neural networks with respect to large families of task-specific performance measures such as the F-measure and the Kullback-Leibler divergence that are structured and…

We present a domain decomposition approach for the simulation of charge transport in heterojunction semiconductors. The problem is characterized by a large variation of primary variables across an interface region of a size much smaller…

Mosaic Flow is a novel domain decomposition method designed to scale physics-informed neural PDE solvers to large domains. Its unique approach leverages pre-trained networks on small domains to solve partial differential equations on large…

Anytime multi-agent path finding (MAPF) is a promising approach to scalable path optimization in multi-agent systems. MAPF-LNS, based on Large Neighborhood Search (LNS), is the current state-of-the-art approach where a fast initial solution…

Many different deep networks have been used to approximate, accelerate or improve traditional image operators, such as image smoothing, super-resolution and denoising. Among these traditional operators, many contain parameters which need to…

We introduce a deep neural network based method for solving a class of elliptic partial differential equations. We approximate the solution of the PDE with a deep neural network which is trained under the guidance of a probabilistic…

The alternating current optimal power flow (AC-OPF) problem is critical to power system operations and planning, but it is generally hard to solve due to its nonconvex and large-scale nature. This paper proposes a scalable decomposition…

Artificial neural networks typically have a fixed, non-linear activation function at each neuron. We have designed a novel form of piecewise linear activation function that is learned independently for each neuron using gradient descent.…

Learning operators mapping between infinite-dimensional Banach spaces via neural networks has attracted a considerable amount of attention in recent years. In this paper, we propose an interfaced operator network (IONet) to solve parametric…

In this chapter, we investigate the bending behavior of a perforated nanobeam subjected to sinusoidal loading using an efficient and computationally robust Physics-Informed Functional Link Constrained Framework with Domain Mapping (DFL-TFC)…

Solving high dimensional partial differential equations (PDEs) has historically posed a considerable challenge when utilizing conventional numerical methods, such as those involving domain meshes. Recent advancements in the field have seen…

Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…

Resting-state functional magnetic resonance imaging (rs-fMRI) and its derived functional connectivity networks (FCNs) have become critical for understanding neurological disorders. However, collaborative analyses and the generalizability of…

Multi-Agent Path Finding (MAPF) is a fundamental coordination problem in large-scale robotic and cyber-physical systems, where multiple agents must compute conflict-free trajectories with limited computational and communication resources.…