Related papers: Explainable Artificial Intelligence for Financial …

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

In recent years, Deep Neural Networks (DNN) based methods have achieved remarkable performance in a wide range of tasks and have been among the most powerful and widely used techniques in computer vision. However, DNN-based methods are both…

In this work, we generalize the reaction-diffusion equation in statistical physics, Schr\"odinger equation in quantum mechanics, Helmholtz equation in paraxial optics into the neural partial differential equations (NPDE), which can be…

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

This paper is concerned about a learning algorithm for a probabilistic model of spiking neural networks (SNNs). Jimenez Rezende & Gerstner (2014) proposed a stochastic variational inference algorithm to train SNNs with hidden neurons. The…

Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…

The ever-increasing demand for higher data rates in communication systems intensifies the need for advanced non-linear equalizers capable of higher performance. Recently artificial neural networks (ANNs) were introduced as a viable…

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…

Solving ill-posed inverse problems necessitates effective regularization strategies to stabilize the inversion process against measurement noise. While classical methods like Tikhonov regularization require heuristic parameter tuning, and…

Accurately characterizing non-linear functional manifolds with singularities is a fundamental challenge in scientific computing. While Multi-Layer Perceptrons (MLPs) dominate, their spectral bias hinders resolving high-curvature features…

The paper presents a Bayesian framework for the calibration of financial models using neural stochastic differential equations (neural SDEs), for which we also formulate a global universal approximation theorem based on Barron-type…

The self-attention mechanism (SAM) is widely used in various fields of artificial intelligence and has successfully boosted the performance of different models. However, current explanations of this mechanism are mainly based on intuitions…

Spiking Neural Networks (SNNs) have garnered attention over recent years due to their increased energy efficiency and advantages in terms of operational complexity compared to traditional Artificial Neural Networks (ANNs). Two important…

Although deep reinforcement learning has been shown to be effective, the model's black-box nature presents barriers to direct policy interpretation. To address this problem, we propose a neuro-symbolic approach called neural DNF-MT for…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

We present a Statistical Mechanics (SM) model of deep neural networks, connecting the energy-based and the feed forward networks (FFN) approach. We infer that FFN can be understood as performing three basic steps: encoding, representation…

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…

Deep neural networks (DNNs) have recently been applied and used in many advanced and diverse tasks, such as medical diagnosis, automatic driving, etc. Due to the lack of transparency of the deep models, DNNs are often criticized for their…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…