Related papers: Explainable Artificial Intelligence for Financial …
Efficient algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the curse of dimensionality. We extend the forward-backward stochastic neural networks…
Deep neural networks (DNNs) achieve remarkable performance on a wide range of tasks, yet their mathematical analysis remains fragmented: stability and generalization are typically studied in disparate frameworks and on a case-by-case basis.…
This study investigates different Scientific Machine Learning (SciML) approaches for the analysis of functionally graded (FG) porous beams and compares them under a new framework. The beam material properties are assumed to vary as an…
Application of neural network architectures for financial prediction has been actively studied in recent years. This paper presents a comparative study that investigates and compares feed-forward neural network (FNN) and adaptive neural…
Solving coupled systems of differential equations (DEs) is a central problem across scientific computing. While Physics Informed Neural Networks (PINNs) offer a promising, mesh-free approach, their standard architectures struggle with the…
We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…
This paper presents machine learning techniques and deep reinforcement learningbased algorithms for the efficient resolution of nonlinear partial differential equations and dynamic optimization problems arising in investment decisions and…
Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…
Artificial Intelligence has emerged as a useful aid in numerous clinical applications for diagnosis and treatment decisions. Deep neural networks have shown same or better performance than clinicians in many tasks owing to the rapid…
Despite the remarkable performance, Deep Neural Networks (DNNs) behave as black-boxes hindering user trust in Artificial Intelligence (AI) systems. Research on opening black-box DNN can be broadly categorized into post-hoc methods and…
We introduce a novel framework for uncertainty quantification of solution operators associated with stochastic partial differential equations (SPDEs). Although SPDEs play a central role in modeling complex physical systems under…
The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
To advance the transparency of learning machines such as Deep Neural Networks (DNNs), the field of Explainable AI (XAI) was established to provide interpretations of DNNs' predictions. While different explanation techniques exist, a popular…
Software defined networking (SDN) represents a promising networking architecture that combines central management and network programmability. SDN separates the control plane from the data plane and moves the network management to a central…
Deep Neural Network (DNN) splitting is one of the key enablers of edge Artificial Intelligence (AI), as it allows end users to pre-process data and offload part of the computational burden to nearby Edge Cloud Servers (ECSs). This opens new…
Deep neural networks (DNNs) have transformed fields such as computer vision and natural language processing by employing architectures aligned with domain-specific structural patterns. In algorithmic trading, however, there remains a lack…
We studied the use of deep neural networks (DNNs) in the numerical solution of the oscillatory Fredholm integral equation of the second kind. It is known that the solution of the equation exhibits certain oscillatory behaviors due to the…
In this article, we introduce and analyze a deep learning based approximation algorithm for SPDEs. Our approach employs neural networks to approximate the solutions of SPDEs along given realizations of the driving noise process. If applied…
We introduce a class of Sparse, Physics-based, and partially Interpretable Neural Networks (SPINN) for solving ordinary and partial differential equations (PDEs). By reinterpreting a traditional meshless representation of solutions of PDEs…