Related papers: Deep Learning for One-dimensional Consolidation
The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzing the loss functions of deep linear networks remains a…
This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
Deep neural networks (DNN) have an impressive ability to invert very complex models, i.e. to learn the generative parameters from a model's output. Once trained, the forward pass of a DNN is often much faster than traditional,…
Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…
As a prevalent distributed learning paradigm, Federated Learning (FL) trains a global model on a massive amount of devices with infrequent communication. This paper investigates a class of composite optimization and statistical recovery…
The lack of mathematical tractability of Deep Neural Networks (DNNs) has hindered progress towards having a unified convergence analysis of training algorithms, in the general setting. We propose a unified optimization framework for…
Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…
In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…
Reinforcement learning (RL) is attracting attention as an effective way to solve sequential optimization problems that involve high dimensional state/action space and stochastic uncertainties. Many such problems involve constraints…
In this paper, we perform Lyapunov based analysis of the loss function to derive an a priori upper bound on the settling time of deep neural networks. While previous studies have attempted to understand deep learning using control theory…
Deep neural networks (DNNs) have been introduced for designing wireless policies by approximating the mappings from environmental parameters to solutions of optimization problems. Considering that labeled training samples are hard to…
Singularly perturbed partial differential equations arise in many applications, including magnetohydrodynamic duct flows, chemical reaction transport systems, and Poisson Boltzmann electrostatics. These problems are characterized by sharp…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
Deep Learning has become one of the primary research areas in developing intelligent machines. Most of the well-known applications (such as Speech Recognition, Image Processing and NLP) of AI are driven by Deep Learning. Deep Learning…
State-of-the-art deep learning models have a parameter count that reaches into the billions. Training, storing and transferring such models is energy and time consuming, thus costly. A big part of these costs is caused by training the…
Recent years have witnessed the outstanding success of deep learning in various fields such as vision and natural language processing. This success is largely indebted to the massive size of deep learning models that is expected to increase…
We study regenerative stopping problems in which the system starts anew whenever the controller decides to stop and the long-term average cost is to be minimized. Traditional model-based solutions involve estimating the underlying process…
This paper presents an approach to trajectory-centric learning control based on contraction metrics and disturbance estimation for nonlinear systems subject to matched uncertainties. The approach uses deep neural networks to learn uncertain…
The extensive adoption of Deep Neural Networks has led to their increased utilization in challenging scientific visualization tasks. Recent advancements in building compressed data models using implicit neural representations have shown…