Related papers: Data-driven discoveries of B\"acklund transforms a…

Understanding transformations under electron beam irradiation requires mapping the structural phases and their evolution in real time. To date, this has mostly been a manual endeavor comprising of difficult frame-by-frame analysis that is…

B\"acklund transformations (BTs) are traditionally regarded as a tool for integrating nonlinear partial differential equations (PDEs). Their use has been recently extended, however, to problems such as the construction of recursion…

Bilevel programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision…

The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…

Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel model reduction methods, coupled with detection of abnormal modes with plasma…

Despite deep learning's success in chemistry, its impact is hindered by a lack of interpretability and an inability to resolve activity cliffs, where minor structural nuances trigger drastic property shifts. Current representation learning,…

Deep neural networks are able to learn multi-layered representation via back propagation (BP). Although the gradient boosting decision tree (GBDT) is effective for modeling tabular data, it is non-differentiable with respect to its input,…

Inspired by Gauss-Newton-like methods, we study the benefit of leveraging the structure of deep learning objectives, namely, the composition of a convex loss function and of a nonlinear network, in order to derive better direction oracles…

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…

Deep learning has demonstrated the power of detailed modeling of complex high-order (multivariate) interactions in data. For some learning tasks there is power in learning models that are not only Deep but also Broad. By Broad, we mean…

Incorporating the Hamiltonian structure of physical dynamics into deep learning models provides a powerful way to improve the interpretability and prediction accuracy. While previous works are mostly limited to the Euclidean spaces, their…

The feasibility of deep neural networks (DNNs) to address data stream problems still requires intensive study because of the static and offline nature of conventional deep learning approaches. A deep continual learning algorithm, namely…

In this work, we propose learnable Bernoulli dropout (LBD), a new model-agnostic dropout scheme that considers the dropout rates as parameters jointly optimized with other model parameters. By probabilistic modeling of Bernoulli dropout,…

Data-efficient image classification is a challenging task that aims to solve image classification using small training data. Neural network-based deep learning methods are effective for image classification, but they typically require…

Recent advances in scanning transmission electron and scanning probe microscopies have opened exciting opportunities in probing the materials structural parameters and various functional properties in real space with angstrom-level…

Machine learning can extract information from neural recordings, e.g., surface EEG, ECoG and {\mu}ECoG, and therefore plays an important role in many research and clinical applications. Deep learning with artificial neural networks has…

Designing learning systems which are invariant to certain data transformations is critical in machine learning. Practitioners can typically enforce a desired invariance on the trained model through the choice of a network architecture, e.g.…

Automatic modulation classification is of crucial importance in wireless communication networks. Deep learning based automatic modulation classification schemes have attracted extensive attention due to the superior accuracy. However, the…

We construct integrable discrete nonautonomous quad-equations as B\"acklund auto-transformations for known Volterra and Toda type semidiscrete equations, some of which are also nonautonomous. Additional examples of this kind are found by…

The backpropagation algorithm remains the dominant and most successful method for training deep neural networks (DNNs). At the same time, training DNNs at scale comes at a significant computational cost and therefore a high carbon…