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In industrial machine learning pipelines, data often arrive in parts. Particularly in the case of deep neural networks, it may be too expensive to train the model from scratch each time, so one would rather use a previously learned model…

We develop a probabilistic framework for deep learning based on the Deep Rendering Mixture Model (DRMM), a new generative probabilistic model that explicitly capture variations in data due to latent task nuisance variables. We demonstrate…

We consider a distributed learning setting where each agent/learner holds a specific parametric model and data source. The goal is to integrate information across a set of learners to enhance the prediction accuracy of a given learner. A…

In this work we address the practical challenges of training machine learning models on privacy-sensitive datasets by introducing a modular approach that minimizes changes to training algorithms, provides a variety of configuration…

Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum…

Deep neural networks have excelled on a wide range of problems, from vision to language and game playing. Neural networks very gradually incorporate information into weights as they process data, requiring very low learning rates. If the…

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…

As the size and richness of available datasets grow larger, the opportunities for solving increasingly challenging problems with algorithms learning directly from data grow at the same pace. Consequently, the capability of learning…

Highly oscillatory differential equations, commonly encountered in multi-scale problems, are often too complex to solve analytically. However, several numerical methods have been developed to approximate their solutions. Although these…

Deep learning has revolutionized many industries by enabling models to automatically learn complex patterns from raw data, reducing dependence on manual feature engineering. However, deep learning algorithms are sensitive to input data, and…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

This paper addresses the problem of modeling and estimating dynamic multi-valued mappings. While most mathematical models provide a unique solution for a given input, real-world applications often lack deterministic solutions. In such…

A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension…

In this paper, we show an approach to build deep learning algorithms for recognizing signals in distributed fiber optic monitoring and security systems for long perimeters. Synthesizing such detection algorithms poses a non-trivial research…

Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an…

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how…

Pre-trained representation is one of the key elements in the success of modern deep learning. However, existing works on continual learning methods have mostly focused on learning models incrementally from scratch. In this paper, we explore…

A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…

Model-based methods and deep neural networks have both been tremendously successful paradigms in machine learning. In model-based methods, problem domain knowledge can be built into the constraints of the model, typically at the expense of…

In this paper, we reveal that metric learning would suffer from serious inseparable problem if without informative sample mining. Since the inseparable samples are often mixed with hard samples, current informative sample mining strategies…