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Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…

Enabling low precision implementations of deep learning models, without considerable performance degradation, is necessary in resource and latency constrained settings. Moreover, exploiting the differences in sensitivity to quantization…

Depth separation -- why a deeper network is more powerful than a shallower one -- has been a major problem in deep learning theory. Previous results often focus on representation power. For example, arXiv:1904.06984 constructed a function…

A state-of-the-art deep domain decomposition method (D3M) based on the variational principle is proposed for partial differential equations (PDEs). The solution of PDEs can be formulated as the solution of a constrained optimization…

This paper is concerned with the approximation of the solution of partial differential equations by means of artificial neural networks. Here a feedforward neural network is used to approximate the solution of the partial differential…

Hierarchical learning models, such as mixture models and Bayesian networks, are widely employed for unsupervised learning tasks, such as clustering analysis. They consist of observable and hidden variables, which represent the given data…

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…

Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…

Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…

The least squares method with deep neural networks as function parametrization has been applied to solve certain high-dimensional partial differential equations (PDEs) successfully; however, its convergence is slow and might not be…

Supervised deep learning performance is heavily tied to the availability of high-quality labels for training. Neural networks can gradually overfit corrupted labels if directly trained on noisy datasets, leading to severe performance…

Layer-wise learning, as an alternative to global back-propagation, is easy to interpret, analyze, and it is memory efficient. Recent studies demonstrate that layer-wise learning can achieve state-of-the-art performance in image…

We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their…

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…

This paper explores the use of deep neural networks for semiparametric estimation of economic models of maximizing behavior in production or discrete choice. We argue that certain deep networks are particularly well suited as a…

Deep neural networks achieve state-of-the-art and sometimes super-human performance across various domains. However, when learning tasks sequentially, the networks easily forget the knowledge of previous tasks, known as "catastrophic…

Autonomous robotic systems applied to new domains require an abundance of expensive, pixel-level dense labels to train robust semantic segmentation models under full supervision. This study proposes a model-agnostic Depth Edge Alignment…

An emerging class of trajectory optimization methods enforces collision avoidance by jointly optimizing the robot's configuration and a separating hyperplane. However, as linear separators only apply to convex sets, these methods require…

We present ConDiff, a novel dataset for scientific machine learning. ConDiff focuses on the parametric diffusion equation with space dependent coefficients, a fundamental problem in many applications of partial differential equations…

Despite significant recent advances in deep neural networks, training them remains a challenge due to the highly non-convex nature of the objective function. State-of-the-art methods rely on error backpropagation, which suffers from several…