Related papers: A composable machine-learning approach for steady-…

Maximum likelihood estimation (MLE) is a well-known estimation method used in many robotic and computer vision applications. Under Gaussian assumption, the MLE converts to a nonlinear least squares (NLS) problem. Efficient solutions to NLS…

We propose a class of convex relaxations to solve the sensor network localization problem, based on a maximum likelihood (ML) formulation. This class, as well as the tightness of the relaxations, depends on the noise probability density…

The large time and length scales and, not least, the vast number of particles involved in industrial-scale simulations inflate the computational costs of the Discrete Element Method (DEM) excessively. Coarse grain models can help to lower…

Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…

This paper investigates the approximation of functions with finite smoothness defined on domains with a Cartesian product structure. The recently proposed tensor product multilevel method (TPML) combines Smolyak's sparse grid method with a…

Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with…

This paper aims to extend the BML method proposed in Wang et al. [22] to make it applicable to more general coupled nonlinear FBSDEs. We interpret BML from the fixed-point iteration perspective and show that optimizing BML is equivalent to…

We develop in this paper a multi-grade deep learning method for solving nonlinear partial differential equations (PDEs). Deep neural networks (DNNs) have received super performance in solving PDEs in addition to their outstanding success in…

Despite their ubiquity throughout science and engineering, only a handful of partial differential equations (PDEs) have analytical, or closed-form solutions. This motivates a vast amount of classical work on numerical simulation of PDEs and…

In this work, we perform a comprehensive study of the machine learning (ML) methods for the purpose of characterising the quantum set of correlations. As our main focus is on assessing the usefulness and effectiveness of the ML approach, we…

Deep Metric Learning (DML) aims to learn embedding functions that map semantically similar inputs to proximate points in a metric space while separating dissimilar ones. Existing methods, such as pairwise losses, are hindered by complex…

In this work we apply the Deep Galerkin Method (DGM) described in Sirignano and Spiliopoulos (2018) to solve a number of partial differential equations that arise in quantitative finance applications including option pricing, optimal…

Identifying parameters in partial differential equations (PDEs) represents a very broad class of applied inverse problems. In recent years, several unsupervised learning approaches using (deep) neural networks have been developed to solve…

The existing work on the distributed training of machine learning (ML) models has consistently overlooked the distribution of the achieved learning quality, focusing instead on its average value. This leads to a poor dependability}of the…

A novel extension of the Probabilistic Learning on Manifolds (PLoM) is presented. It makes it possible to synthesize solutions to a wide range of nonlinear stochastic boundary value problems described by partial differential equations…

Supervised Machine Learning (SML) algorithms such as Gradient Boosting, Random Forest, and Neural Networks have become popular in recent years due to their increased predictive performance over traditional statistical methods. This is…

We address a new numerical scheme based on a class of machine learning methods, the so-called Extreme Learning Machines with both sigmoidal and radial-basis functions, for the computation of steady-state solutions and the construction of…

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage…