Related papers: Explainable Artificial Intelligence for Financial …

It has been believed that stochastic feedforward neural networks (SFNNs) have several advantages beyond deterministic deep neural networks (DNNs): they have more expressive power allowing multi-modal mappings and regularize better due to…

In the field of systems biology, differential equations are commonly used to model biological systems, but solving them for large-scale and complex systems can be computationally expensive. Recently, the integration of machine learning and…

An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by…

Achieving transparency in black-box deep learning algorithms is still an open challenge. High dimensional features and decisions given by deep neural networks (NN) require new algorithms and methods to expose its mechanisms. Current…

The lack of interpretability and transparency are preventing economists from using advanced tools like neural networks in their empirical research. In this paper, we propose a class of interpretable neural network models that can achieve…

We present a novel and mathematically transparent approach to function approximation and the training of large, high-dimensional neural networks, based on the approximate least-squares solution of associated Fredholm integral equations of…

Imagine experiencing a crash as the passenger of an autonomous vehicle. Wouldn't you want to know why it happened? Current end-to-end optimizable deep neural networks (DNNs) in 3D detection, multi-object tracking, and motion forecasting…

This paper explores the integration of Diophantine equations into neural network (NN) architectures to improve model interpretability, stability, and efficiency. By encoding and decoding neural network parameters as integer solutions to…

Recurrent neural networks (RNNs) are powerful and effective for processing sequential data. However, RNNs are usually considered "black box" models whose internal structure and learned parameters are not interpretable. In this paper, we…

In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the process of finding model parameters through experimental data,…

Deep neural networks (DNNs) have demonstrated superior performance over classical machine learning to support many features in safety-critical systems. Although DNNs are now widely used in such systems (e.g., self driving cars), there is…

We develop an unsupervised physics-informed neural network to solve saddle-point equations (SPEs) governing direct above-threshold ionization (ATI) within the strong-field approximation. This setting provides a well-understood testbed in…

Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators…

Forecasting stock market direction is always an amazing but challenging problem in finance. Although many popular shallow computational methods (such as Backpropagation Network and Support Vector Machine) have extensively been proposed,…

Deep neural networks (DNNs) are known to perform well when deployed to test distributions that shares high similarity with the training distribution. Feeding DNNs with new data sequentially that were unseen in the training distribution has…

Deep Neural Networks (DNNs) do not inherently compute or exhibit empirically-justified task confidence. In mission critical applications, it is important to both understand associated DNN reasoning and its supporting evidence. In this…

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being…

Surface-from-gradients (SfG) aims to recover a three-dimensional (3D) surface from its gradients. Traditional methods encounter significant challenges in achieving high accuracy and handling high-resolution inputs, particularly facing the…

With the broader and highly successful usage of machine learning in industry and the sciences, there has been a growing demand for Explainable AI. Interpretability and explanation methods for gaining a better understanding about the problem…

Backward stochastic differential equation (BSDE) provides probabilistic solutions for a class of parabolic partial differential equations (PDEs). DeepBSDE and FBSNN are two deep learning approaches for solving high-dimensional PDEs through…