Related papers: Machine learning moment closure models for the rad…

The current deep learning model is of a single-grade, that is, it learns a deep neural network by solving a single nonconvex optimization problem. When the layer number of the neural network is large, it is computationally challenging to…

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…

Under data distributions which may be heavy-tailed, many stochastic gradient-based learning algorithms are driven by feedback queried at points with almost no performance guarantees on their own. Here we explore a modified "anytime…

Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…

Training deep learning neural networks often requires massive amounts of computational ressources. We propose to sequentially monitor network predictions to trigger retraining only if the predictions are no longer valid. This can reduce…

We propose a method of moments (MoM) algorithm for training large-scale implicit generative models. Moment estimation in this setting encounters two problems: it is often difficult to define the millions of moments needed to learn the model…

This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws with a physically consistent penalty and first-moment…

Label noise may affect the generalization of classifiers, and the effective learning of main patterns from samples with noisy labels is an important challenge. Recent studies have shown that deep neural networks tend to prioritize the…

Recurrent neural networks are powerful models for sequential data, able to represent complex dependencies in the sequence that simpler models such as hidden Markov models cannot handle. Yet they are notoriously hard to train. Here we…

Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several…

Radiative transfer calculations are essential for modeling planetary atmospheres. However, standard methods are computationally demanding and impose accuracy-speed trade-offs. High computational costs force numerical simplifications in…

Deep learning is increasingly becoming a promising pathway to improving the accuracy of sub-grid scale (SGS) turbulence closure models for large eddy simulations (LES). We leverage the concept of differentiable turbulence, whereby an…

We investigate the application of artificial neural networks to stabilize proper orthogonal decomposition based reduced order models for quasi-stationary geophysical turbulent flows. An extreme learning machine concept is introduced for…

This paper studies the problem of learning causal structures from observational data. We reformulate the Structural Equation Model (SEM) with additive noises in a form parameterized by binary graph adjacency matrix and show that, if the…

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…

In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…

In this work, we study the transfer learning problem under high-dimensional generalized linear models (GLMs), which aim to improve the fit on target data by borrowing information from useful source data. Given which sources to transfer, we…

Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…

Research in machine learning has polarized into two general approaches for regression tasks: Transductive methods construct estimates directly from available data but are usually problem unspecific. Inductive methods can be much more…