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Forward regression is a classical and effective tool for variable screening in ultra-high dimensional linear models, but its standard projection-based implementation can be computationally costly and numerically unstable when predictors are…

This paper proposes a novel deep generative model, called BSDE-Gen, which combines the flexibility of backward stochastic differential equations (BSDEs) with the power of deep neural networks for generating high-dimensional complex target…

Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…

Reinforcement Learning (RL) has proven effective in solving complex decision-making tasks across various domains, but challenges remain in continuous-time settings, particularly when state dynamics are governed by stochastic differential…

In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional $\theta$-scheme, we reduce truncation errors by taking $\theta$ carefully for every subinterval…

Optimizing over the stationary distribution of stochastic differential equations (SDEs) is computationally challenging. A new forward propagation algorithm has been recently proposed for the online optimization of SDEs. The algorithm solves…

Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems…

The explosion of data in recent years has generated an increasing need for new analysis techniques in order to extract knowledge from massive datasets. Machine learning has proved particularly useful to perform this task. Fully automatized…

We propose a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, by making an analogy between the BSDE and reinforcement learning with the…

We present a deep recurrent neural network architecture to solve a class of stochastic optimal control problems described by fully nonlinear Hamilton Jacobi Bellmanpartial differential equations. Such PDEs arise when one considers…

In this paper, we consider a class of backward doubly stochastic differential equations (BDSDE for short) with general terminal value and general random generator. Those BDSDEs do not involve any forward diffusion processes. By using the…

This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…

In the first part of this paper we give a solution for the one-dimensional reflected backward stochastic differential equation (BSDE for short) when the noise is driven by a Brownian motion and an independent Poisson point process. The…

Data-driven methods are emerging as efficient alternatives to traditional numerical forecasting, offering fast inference and lower computational cost. Yet, for complex systems, long-term accuracy often deteriorates due to error…

The optimal stopping problem is one of the core problems in financial markets, with broad applications such as pricing American and Bermudan options. The deep BSDE method [Han, Jentzen and E, PNAS, 115(34):8505-8510, 2018] has shown great…

Forward gradient descent (FGD) has been proposed as a biologically more plausible alternative of gradient descent as it can be computed without backward pass. Considering the linear model with $d$ parameters, previous work has found that…

High-dimensional parabolic partial integro-differential equations (PIDEs) appear in many applications in insurance and finance. Existing numerical methods suffer from the curse of dimensionality or provide solutions only for a given…

In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only…

Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery)…

The application of deep learning to the area of communications systems has been a growing field of interest in recent years. Forward-forward (FF) learning is an efficient alternative to the backpropagation (BP) algorithm, which is the…