Related papers: Recursive evaluation and iterative contraction of …
This paper applies the Recursive Projection Method (RPM) to the problem of finding the effective mechanical response of a periodic heterogeneous solid. Previous works apply the Fast Fourier Transform (FFT) in combination with various…
The performance of nuclear reactors and other nuclear systems depends on a precise understanding of the neutron interaction cross sections for materials used in these systems. These cross sections exhibit resonant structure whose shape is…
Deep clustering - joint representation learning and latent space clustering - is a well studied problem especially in computer vision and text processing under the deep learning framework. While the representation learning is generally…
Precise reconstruction of top quark properties is a challenging task at the Large Hadron Collider due to combinatorial backgrounds and missing information. We introduce a physics-informed neural network architecture called the Covariant…
The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body…
Accurately estimating the pose of an object is a crucial task in computer vision and robotics. There are two main deep learning approaches for this: geometric representation regression and iterative refinement. However, these methods have…
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…
In previous work, we introduced a method for modeling a configuration of objects in 2D and 3D images using a mathematical "medial/skeletal linking structure." In this paper, we show how these structures allow us to capture positional…
In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we…
In this article, we extend the conventional framework of convolutional-Restricted-Boltzmann-Machine to learn highly abstract features among abitrary number of time related input maps by constructing a layer of multiplicative units, which…
In human cognition, the binding problem describes the open question of how the brain flexibly integrates diverse information into cohesive object representations. Analogously, in machine learning, there is a pursuit for models capable of…
In this paper I present a conjecture for a recursive algorithm that finds each permutation of combining two sets of objects (AKA the Shuffle Product). This algorithm provides an efficient way to navigate this problem, as each atomic…
Atomic electron tomography (AET) enables the determination of 3D atomic structures by acquiring a sequence of 2D tomographic projection measurements of a particle and then computationally solving for its underlying 3D representation.…
We demonstrate a machine learning based approach which can learn the time-dependent electronic excitation dynamics of small molecules subjected to ion irradiation. Ensembles of recurrent neural networks are trained on data generated by…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…
Robotics is shifting from rigid, articulated systems to more sophisticated and heterogeneous mechanical structures. Soft robots, for example, have continuously deformable elements capable of large deformations. The flourishing of control…
In quantum physics, even simple data with a well-defined structure at the wave function level can be characterized by extremely complex correlations between its constituent elements. The inherent non-locality of the quantum correlations…
The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take…
The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries…
Encoding the electronic structure of molecules using 2-electron reduced density matrices (2RDMs) as opposed to many-body wave functions has been a decades-long quest as the 2RDM contains sufficient information to compute the exact molecular…