Related papers: Numerical Computation of Partial Differential Equa…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Although deep learning models are highly effective for various learning tasks, their high computational costs prohibit the deployment to scenarios where either memory or computational resources are limited. In this paper, we focus on…

Hybrid Language Models (HLMs) combine the low-latency efficiency of Small Language Models (SLMs) on edge devices with the high accuracy of Large Language Models (LLMs) on centralized servers. Unlike traditional end-to-end LLM inference,…

Extreme learning machine (ELM) as a neural network algorithm has shown its good performance, such as fast speed, simple structure etc, but also, weak robustness is an unavoidable defect in original ELM for blended data. We present a new…

We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural…

Many DNN-enabled vision applications constantly operate under severe energy constraints such as unmanned aerial vehicles, Augmented Reality headsets, and smartphones. Designing DNNs that can meet a stringent energy budget is becoming…

Efficient and accurate joint representation of a collection of images, that belong to the same class, is a major research challenge for practical image set classification. Existing methods either make prior assumptions about the data…

In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization…

This paper questions the effectiveness of a modern predictive uncertainty quantification approach, called \emph{evidential deep learning} (EDL), in which a single neural network model is trained to learn a meta distribution over the…

An alternative extreme learning machine -ELM- paradigm is presented exploiting random non-linearities -RN, named RN-ELM, instead of a conventional fixed node non-linearity. This method is implemented on a hybrid neural engine, with the…

Deep learning solutions of the salient object detection problem have achieved great results in recent years. The majority of these models are based on encoders and decoders, with a different multi-feature combination. In this paper, we show…

The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of…

A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient approximation of parameter-to-solution maps, rivaling…

Numerical simulation is dominant in solving partial difference equations (PDEs), but balancing fine-grained grids with low computational costs is challenging. Recently, solving PDEs with neural networks (NNs) has gained interest, yet…

We present Epidemic Learning (EL), a simple yet powerful decentralized learning (DL) algorithm that leverages changing communication topologies to achieve faster model convergence compared to conventional DL approaches. At each round of EL,…

We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential…

A novel multi-level method for partial differential equations with uncertain parameters is proposed. The principle behind the method is that the error between grid levels in multi-level methods has a spatial structure that is by good…