Related papers: A forward scheme with machine learning for forward…
The Forward-Forward (FF) Algorithm has been recently proposed to alleviate the issues of backpropagation (BP) commonly used to train deep neural networks. However, its current formulation exhibits limitations such as the generation of…
Most deep learning models are based on deep neural networks with multiple layers between input and output. The parameters defining these layers are initialized using random values and are "learned" from data, typically using stochastic…
The forward-backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward-backward envelope (FBE).…
We propose a new method for the numerical solution of the forward-backward stochastic differential equations (FBSDE) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. Using Girsanov's…
This paper is dedicated to solving high-dimensional coupled FBSDEs with non-Lipschitz diffusion coefficients numerically. Under mild conditions, we provided a posterior estimate of the numerical solution that holds for any time duration.…
We propose the predictive forward-forward (PFF) algorithm for conducting credit assignment in neural systems. Specifically, we design a novel, dynamic recurrent neural system that learns a directed generative circuit jointly and…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
We propose an accurate data-driven numerical scheme to solve Stochastic Differential Equations (SDEs), by taking large time steps. The SDE discretization is built up by means of a polynomial chaos expansion method, on the basis of…
Diffusion models with continuous stochastic differential equations (SDEs) have shown superior performances in image generation. It can serve as a deep generative prior to solving the inverse problem in magnetic resonance (MR)…
In this paper, we study the mean reflected backward stochastic differential equations with jump (BSDEJs). We extend the work of Briand and Hibon on the propagation of chaos for mean reflected BSDEs \cite{briand2021particles} to the jump…
We propose a numerical method for the computation of the forward-backward stochastic differential equations (FBSDE) appearing in the Feynman-Kac representation of the value function in stochastic optimal control problems. By the use of the…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
We introduce a discrete time reflected scheme to solve doubly reflected Backward Stochastic Differential Equations with jumps (in short DRBSDEs), driven by a Brownian motion and an independent compensated Poisson process. As in…
In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward…
Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters…
Artificial intelligence (AI) for fluid mechanics has become attractive topic. High-fidelity data is one of most critical issues for the successful applications of AI in fluid mechanics, however, it is expensively obtained or even…
In this work we consider a stochastic differential equation (SDEs) with jump. We prove the existence and the uniqueness of solution of this equation in the strong sense under global Lipschitz condition. Generally, exact solutions of SDEs…
In this paper, we study the existence and uniqueness of solution to a system of nonlinear fully coupled forward-backward doubly stochastic differential equations with Poisson jumps. Our work is established in infinite dimensional separable…
We introduce a new approach in distributed deep learning, utilizing Geoffrey Hinton's Forward-Forward (FF) algorithm to speed up the training of neural networks in distributed computing environments. Unlike traditional methods that rely on…
Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…