arXiv research

We propose a deep learning based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial differential equations. The Deep Ritz method is naturally nonlinear, naturally adaptive and has the potential to work in rather high dimensions. The framework is qui…

Paper uses deep Ritz method for solving stationary Schrödinger equation, proving convergence and feature emergence.

Paper studies deep learning for solving elliptic PDEs, proving optimal bounds and neural scaling laws.

Paper analyzes DRM for solving high-dimensional elliptic PDEs with generalization bounds.

Study analyzes error in neural network solving PDEs, providing convergence and error bounds.

This paper compares deeper and wider neural networks for optimal generalization error in Sobolev losses.

Paper develops IFTRR to solve sparse generalized eigenvalue problems efficiently.

In this paper, we propose the idea of radial scaling in frequency domain and activation functions with compact support to produce a multi-scale DNN (MscaleDNN), which will have the multi-scale capability in approximating high frequency and high dimensional functions and speeding up the solution of high dimensional PDEs…

NWoS solves high-dimensional Poisson equations using neural networks.

New neural network approach solves Poisson equations efficiently.

For a bounded domain $Ω$ with a piecewise smooth boundary in a complete Riemannian manifold $M$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. By making use of a fact that eigenfunctions form an orthonormal basis of $L^2(Ω)$ in place of the Rayleigh-Ritz formula, we obtain inequalities for …

We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the Cauchy-Schwarz inequality--is used to produce ``parameter-free'', ``projection-free'' vers…

Gradient descent achieves optimal learning for elliptic PDEs via Sobolev norms.

Fast and accurate methods for low-rank learning problems.

Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices, and so on. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes. Many issues remain, thou…

New algorithm updates eigenvectors of evolving graphs efficiently.

Bayesian methods enhance deep learning models by improving reliability and uncertainty.

Book introduces deep learning methods with math, theory, and applications.

Deep learning improves asset pricing and risk premium measurement.

Proposes a constraint for deep clustering to handle both simple and complex topologies.

Deep learning improves time series forecasting, outperforming other methods.

New method tackles convergence issues in approximating FBSDEs.

This paper provides an overview of deep semi-supervised learning methods.

Study develops efficient nested deep hedging method for derivatives pricing.

In recent years, deep learning methods applying unsupervised learning to train deep layers of neural networks have achieved remarkable results in numerous fields. In the past, many genetic algorithms based methods have been successfully applied to training neural networks. In this paper, we extend previous work and pro…

Hashing has been widely used for large-scale approximate nearest neighbor search because of its storage and search efficiency. Recent work has found that deep supervised hashing can significantly outperform non-deep supervised hashing in many applications. However, most existing deep supervised hashing methods adopt a …

Deep Penalty Method solves high-dimensional optimal stopping problems using deep learning.

Deep learning methods improve subsurface flow modeling efficiency.

New deep learning method solves stochastic control problems.

Survey of deep learning methods for forex and stock price prediction.

This paper introduces Deep Incremental Boosting, a new technique derived from AdaBoost, specifically adapted to work with Deep Learning methods, that reduces the required training time and improves generalisation. We draw inspiration from Transfer of Learning approaches to reduce the start-up time to training each incr…

Deep learning methods are widely regarded as indispensable when it comes to designing perception pipelines for autonomous agents such as robots, drones or automated vehicles. The main reasons, however, for deep learning not being used for autonomous agents at large scale already are safety concerns. Deep learning appro…

Unified theory linking Bayesian and ensemble methods in deep learning.

Improves deep learning robustness by considering task and model.

Bayesian Neural Networks help quantify uncertainty in deep learning predictions.

Deep density methods improve filtering in high-dimensional systems.

Deep learning methods are reviewed for preserving structure in neural networks.

Proposes a non-parametric method for deep discrete latent variable models.

Proposes a method to estimate drug sensitivity uncertainty using deep regression forests.

Survey of spectral, probabilistic, and deep metric learning methods.

The deep reinforcement learning method usually requires a large number of training images and executing actions to obtain sufficient results. When it is extended a real-task in the real environment with an actual robot, the method will be required more training images due to complexities or noises of the input images, …

Feature selection is central to contemporary high-dimensional data analysis. Grouping structure among features arises naturally in various scientific problems. Many methods have been proposed to incorporate the grouping structure information into feature selection. However, these methods are normally restricted to a li…

A new model DKMPP integrates covariates and uses an integration-free method for spatio-temporal point processes.

Develops deep jump learning for continuous treatment OPE.

URSABench benchmarks Bayesian methods for deep learning models.

This paper examines the applicability in realistic scenarios of two deep learning based solutions to the overlapping speaker separation problem. Firstly, we present experiments that show that these methods are applicable for a broad range of languages. Further experimentation indicates limited performance loss for untr…

This paper focuses on a comparative evaluation of the most common and modern methods for text classification, including the recent deep learning strategies and ensemble methods. The study is motivated by a challenging real data problem, characterized by high-dimensional and extremely sparse data, deriving from incoming…

Gradient descent methods for deep ReLU networks achieve optimal generalization rates.