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Traditional end-to-end deep learning models often enhance feature representation and overall performance by increasing the depth and complexity of the network during training. However, this approach inevitably introduces issues of parameter…

Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem…

A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional…

Deep Learning (DL) applications are gaining momentum in the realm of Artificial Intelligence, particularly after GPUs have demonstrated remarkable skills for accelerating their challenging computational requirements. Within this context,…

Learning with neural networks relies on the complexity of the representable functions, but more importantly, the particular assignment of typical parameters to functions of different complexity. Taking the number of activation regions as a…

Modern convolutional neural networks (CNNs) have massive identical convolution blocks, and, hence, recursive sharing of parameters across these blocks has been proposed to reduce the amount of parameters. However, naive sharing of…

Today's deep learning models are primarily trained on CPUs and GPUs. Although these models tend to have low error, they consume high power and utilize large amount of memory owing to double precision floating point learning parameters.…

Graph neural network architectures are advantageous for predicting core-electron binding energies which depend on local bond environment effects, as the number of message passing layers defines the topological (bond) radius of the model's…

Recurrent neural networks (RNN) are powerful tools to explain how attractors may emerge from noisy, high-dimensional dynamics. We study here how to learn the ~N^(2) pairwise interactions in a RNN with N neurons to embed L manifolds of…

Learning probability models from data is at the heart of many machine learning endeavors, but is notoriously difficult due to the curse of dimensionality. We introduce a new framework for learning \emph{normalized} energy (log probability)…

Parameter estimation for dynamical systems remains challenging due to non-convexity and sensitivity to initial parameter guesses. Recent deep learning approaches enable accurate and fast parameter estimation but do not exploit transferable…

We incorporate in the Kohn-Sham self consistent equation a trained neural-network projection from the charge density distribution to the Hartree-exchange-correlation potential $n \rightarrow V_{\rm Hxc}$ for possible numerical approach to…

We consider the problem of training input-output recurrent neural networks (RNN) for sequence labeling tasks. We propose a novel spectral approach for learning the network parameters. It is based on decomposition of the cross-moment tensor…

The thesis is aimed to solve the template-free protein folding problem by tackling two important components: efficient sampling in vast conformation space, and design of knowledge-based potentials with high accuracy. We have proposed the…

We investigate the generalization ability of a simple perceptron trained in the off-line and on-line supervised modes. Examples are extracted from the teacher who is a non-monotonic perceptron. For this system, difficulties of training can…

The ability to understand and engineer molecular structures relies on having accurate descriptions of the energy as a function of atomic coordinates. Here we outline a new paradigm for deriving energy functions of hyperdimensional molecular…

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the…

Due to the lack of phase information, determining the physical parameters of multilayer thin films from measured neutron and X-ray reflectivity curves is, on a fundamental level, an underdetermined inverse problem. This so-called phase…

The expansion of artificial intelligence (AI) applications has driven substantial investment in computational infrastructure, especially by cloud computing providers. Quantifying the energy footprint of this infrastructure requires models…

Brenier proved that under certain conditions on a source and a target probability measure there exists a strictly convex function such that its gradient is a transport map from the source to the target distribution. This function is called…