Related papers: AMITE: A Novel Polynomial Expansion for Analyzing …

We propose a method combining boundary integral equations and neural networks (BINet) to solve partial differential equations (PDEs) in both bounded and unbounded domains. Unlike existing solutions that directly operate over original PDEs,…

This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any H\"{o}lder smooth…

Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…

Due to the over-fitting problem caused by imbalance samples, there is still room to improve the performance of data-driven automatic modulation classification (AMC) in noisy scenarios. By fully considering the signal characteristics, an AMC…

In this paper we consider Deep Neural Networks (DNNs) with a smooth activation function as surrogates for high-dimensional functions that are somewhat smooth but costly to evaluate. We consider the standard (non-periodic) DNNs as well as…

Mathematical formulas serve as the means of communication between humans and nature, encapsulating the operational laws governing natural phenomena. The concise formulation of these laws is a crucial objective in scientific research and an…

This paper introduces AMMORE, a new dataset of 53,000 math open-response question-answer pairs from Rori, a learning platform used by students in several African countries and conducts two experiments to evaluate the use of large language…

Sharpness-aware and gradient-alignment methods have been shown to improve generalization, however each family of methods targets a single geometric property of the loss landscape, while ignoring the other. In this paper, we show that this…

As artificial intelligence increasingly drives critical decisions, the ability to genuinely explain how neural networks make predictions is essential for trust. Yet, most current explanation methods offer post-hoc rationalizations rather…

There is an increasing need for effective active learning algorithms that are compatible with deep neural networks. This paper motivates and revisits a classic, Fisher-based active selection objective, and proposes BAIT, a practical,…

Mixed effects (ME) models inform a vast array of problems in the physical and social sciences, and are pervasive in meta-analysis. We consider ME models where the random effects component is linear. We then develop an efficient approach for…

Accurate approximation of complex nonlinear functions is a fundamental challenge across many scientific and engineering domains. Traditional neural network architectures, such as Multi-Layer Perceptrons (MLPs), often struggle to efficiently…

Deep Neural Networks (DNNs) have achieved remarkable success in a variety of tasks, especially when it comes to prediction accuracy. However, in complex real-world scenarios, particularly in safety-critical applications, high accuracy alone…

Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties, is unavoidable. Polynomial Chaos Expansion (PCE) is widely…

In modern statistics, interests shift from pursuing the uniformly minimum variance unbiased estimator to reducing mean squared error (MSE) or residual squared error. Shrinkage based estimation and regression methods offer better prediction…

In this paper we show how to augment classical methods for inverse problems with artificial neural networks. The neural network acts as a prior for the coefficient to be estimated from noisy data. Neural networks are global, smooth function…

Several works have proven that finetuning is an applicable approach for debiasing contextualized word embeddings. Similarly, discrete prompts with semantic meanings have shown to be effective in debiasing tasks. With unfixed mathematical…

In this paper, a new deep learning architecture for stereo disparity estimation is proposed. The proposed atrous multiscale network (AMNet) adopts an efficient feature extractor with depthwise-separable convolutions and an extended cost…

The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…

Irregular Multivariate Time Series (IMTS) are common in practice, yet their irregular sampling complicates effective modeling. Existing approaches typically either (i) design specialized architectures that limit the reuse of proven…