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Neural operators improve conventional neural networks by expanding their capabilities of functional mappings between different function spaces to solve partial differential equations (PDEs). One of the most notable methods is the Fourier…

We develop an unsupervised deep learning method to solve the barrier options under the Bergomi model. The neural networks serve as the approximate option surfaces and are trained to satisfy the PDE as well as the boundary conditions. Two…

Neural networks with sufficiently smooth activation functions can approximate values and derivatives of any smooth function, and they are differentiable themselves. We improve the approximation capability of neural networks by utilizing the…

Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…

We propose Partially Interpretable Estimators (PIE) which attribute a prediction to individual features via an interpretable model, while a (possibly) small part of the PIE prediction is attributed to the interaction of features via a…

Various phenomena in biology, physics, and engineering are modeled by differential equations. These differential equations including partial differential equations and ordinary differential equations can be converted and represented as…

Fourier Neural Operator (FNO) is a powerful and popular operator learning method. However, FNO is mainly used in forward prediction, yet a great many applications rely on solving inverse problems. In this paper, we propose an invertible…

There exist many problem domains where the interpretability of neural network models is essential for deployment. Here we introduce a recurrent architecture composed of input-switched affine transformations - in other words an RNN without…

It is critical yet challenging for deep learning models to properly characterize uncertainty that is pervasive in real-world environments. Although a lot of efforts have been made, such as heteroscedastic neural networks (HNNs), little work…

The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the FFT is limited to equispaced (rectangular) grids,…

Deep neural networks (DNN) are versatile parametric models utilised successfully in a diverse number of tasks and domains. However, they have limitations---particularly from their lack of robustness and over-sensitivity to out of…

Spiking neural networks (SNN) have recently emerged as alternatives to traditional neural networks, owing to energy efficiency benefits and capacity to better capture biological neuronal mechanisms. However, the classic backpropagation…

The success of artificial intelligence (AI), and deep learning models in particular, has led to their widespread adoption across various industries due to their ability to process huge amounts of data and learn complex patterns. However,…

By decoupling substrate resources, network virtualization (NV) is a promising solution for meeting diverse demands and ensuring differentiated quality of service (QoS). In particular, virtual network embedding (VNE) is a critical enabling…

There have been several attempts to use deep learning based on brain fMRI signals to classify cognitive impairment diseases. However, deep learning is a hidden black box model that makes it difficult to interpret the process of…

The Schr\"odinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates…

The aim of this work is to propose an extension of the deep solver by Han, Jentzen, E (2018) to the case of forward backward stochastic differential equations (FBSDEs) with jumps. As in the aforementioned solver, starting from a discretized…

A novel approach for supervised classification is presented which sits at the intersection of machine learning and dynamical systems theory. At variance with other methodologies that employ ordinary differential equations for classification…

In this paper, we establish that for a wide class of controlled stochastic differential equations (SDEs) with stiff coefficients, the value functions of corresponding zero-sum games can be represented by a deep artificial neural network…

Deep Neural Networks have often been called the black box because of the complex, deep architecture and non-transparency presented by the inner layers. There is a lack of trust to use Artificial Intelligence in critical and high-precision…