Related papers: Unsupervised Deep Learning Algorithm for PDE-based…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
In insurance mathematics optimal control problems over an infinite time horizon arise when computing risk measures. Their solutions correspond to solutions of deterministic semilinear (degenerate) elliptic partial differential equations. In…
In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods…
In this work, we propose a new deep learning-based scheme for solving high dimensional nonlinear backward stochastic differential equations (BSDEs). The idea is to reformulate the problem as a global optimization, where the local loss…
We investigate solving partial integro-differential equations (PIDEs) using unsupervised deep learning in this paper. To price options, assuming underlying processes follow Levy processes, we require to solve PIDEs. In supervised deep…
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…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
In recent years a large literature on deep learning based methods for the numerical solution partial differential equations has emerged; results for integro-differential equations on the other hand are scarce. In this paper we study deep…
A method for approximating sixth-order ordinary differential equations is proposed, which utilizes a deep learning feedforward artificial neural network, referred to as a neural solver. The efficacy of this unsupervised machine learning…
This paper focuses on proposing a deep learning initialized iterative method (Int-Deep) for low-dimensional nonlinear partial differential equations (PDEs). The corresponding framework consists of two phases. In the first phase, an…
We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…
We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion maps (DM) and deep learning. The PDE solver is formulated…
We introduce a deep neural network based method for solving a class of elliptic partial differential equations. We approximate the solution of the PDE with a deep neural network which is trained under the guidance of a probabilistic…
Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available. To emulate this encounter, in this study, we assume it is unknown how to solve the imaging problem of Computed…
Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…
Eigenvalue problems are critical to several fields of science and engineering. We present a novel unsupervised neural network for discovering eigenfunctions and eigenvalues for differential eigenvalue problems with solutions that…
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional…