Related papers: A backward differential deep learning-based algori…
Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with…
Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may…
Neural ordinary differential equations (NODEs) treat computation of intermediate feature vectors as trajectories of ordinary differential equation parameterized by a neural network. In this paper, we propose a novel model, delay…
This work studies quantum algorithms to solve high-dimensional stochastic differential equations (SDEs) $\mathrm{d} \mathbf{X}_t = A(t) \mathbf{X}_t \mathrm{d} t + B(t) \mathrm{d} \mathbf{W}_t$. Aiming for a speed-up in the dimension $N$ of…
Neural SDEs combine many of the best qualities of both RNNs and SDEs: memory efficient training, high-capacity function approximation, and strong priors on model space. This makes them a natural choice for modelling many types of temporal…
In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the…
Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…
The backpropagation algorithm remains the dominant and most successful method for training deep neural networks (DNNs). At the same time, training DNNs at scale comes at a significant computational cost and therefore a high carbon…
We recently proposed the STiDi-BP algorithm, which avoids backward recursive gradient computation, for training multi-layer spiking neural networks (SNNs) with single-spike-based temporal coding. The algorithm employs a linear approximation…
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…
Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…
We introduce a novel meshless simulation method for the McKean-Vlasov Stochastic Differential Equation (MV-SDE) utilizing deep learning, applicable to both self-interaction and interaction scenarios. Traditionally, numerical methods for…
In this paper we present a novel sampling-based numerical scheme designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations (FBSDEs). By means of a nonlinear…
The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations…
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…
Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the…
This paper proposes the Nerual Energy Descent (NED) via neural network evolution equations for a wide class of deep learning problems. We show that deep learning can be reformulated as the evolution of network parameters in an evolution…
We introduce a predictor-corrector discretisation scheme for the numerical integration of a class of stochastic differential equations and prove that it converges with weak order 1.0. The key feature of the new scheme is that it builds up…
Deep learning-based partial differential equation(PDE) solvers have received much attention in the past few years. Methods of this category can solve a wide range of PDEs with high accuracy, typically by transforming the problems into…
This article deals with the numerical resolution of backward stochastic differential equations. Firstly, we consider a rather general case where the filtration is generated by a Brownian motion and a Poisson random measure. We provide a…