Related papers: Multigoal-oriented dual-weighted-residual error es…

This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…

Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application,…

We propose a new algorithm for training deep neural networks (DNNs) with binary weights. In particular, we first cast the problem of training binary neural networks (BiNNs) as a bilevel optimization instance and subsequently construct…

Deep learning has shown that learned functions can dramatically outperform hand-designed functions on perceptual tasks. Analogously, this suggests that learned optimizers may similarly outperform current hand-designed optimizers, especially…

Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…

Fault-tolerant deep learning accelerator is the basis for highly reliable deep learning processing and critical to deploy deep learning in safety-critical applications such as avionics and robotics. Since deep learning is known to be…

We show that the influence of a subset of the training samples can be removed -- or "forgotten" -- from the weights of a network trained on large-scale image classification tasks, and we provide strong computable bounds on the amount of…

Deep learning is formulated as a discrete-time optimal control problem. This allows one to characterize necessary conditions for optimality and develop training algorithms that do not rely on gradients with respect to the trainable…

Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Recently, deep neural networks (DNNs) have shown advantages in accelerating optimization algorithms. One approach is to unfold finite number of iterations of conventional optimization algorithms and to learn parameters in the algorithms.…

Deep learning based models are used regularly in every applications nowadays. Generally we train a single model on a single task. However, we can train multiple tasks on a single model under multi-task learning settings. This provides us…

Designing composite materials as per the application requirements is fundamentally a challenging and time consuming task. Here we report the development of a deep neural network based computational framework capable of solving the forward…

Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…

Pan-sharpening is an important technique for remote sensing imaging systems to obtain high resolution multispectral images. Recently, deep learning has become the most popular tool for pan-sharpening. This paper develops a model-based deep…

This paper introduces Selective-Backprop, a technique that accelerates the training of deep neural networks (DNNs) by prioritizing examples with high loss at each iteration. Selective-Backprop uses the output of a training example's forward…

Artificial neural networks are functions depending on a finite number of parameters typically encoded as weights and biases. The identification of the parameters of the network from finite samples of input-output pairs is often referred to…

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…

We consider the discretization of elliptic boundary-value problems by variational physics-informed neural networks (VPINNs), in which test functions are continuous, piecewise linear functions on a triangulation of the domain. We define an a…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…