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Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for…
The nonequilibrium Green's function formalism provides a versatile and powerful framework for numerical studies of nonequilibrium phenomena in correlated many-body systems. For calculations starting from an equilibrium initial state, a…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory…
High-order Discontinuous Galerkin (DG) methods offer excellent accuracy for turbulent flow simulations, especially when implemented on GPU-oriented architectures that favor very high polynomial orders. On modern GPUs, high-order polynomial…
We study the use of truncated normal-ordered three-nucleon interactions in ab initio nuclear structure calculations starting from chiral two- plus three-nucleon Hamiltonians evolved consistently with the similarity renormalization group…
Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical…
Reduced numerical precision is a common technique to reduce computational cost in many Deep Neural Networks (DNNs). While it has been observed that DNNs are resilient to small errors and noise, no general result exists that is capable of…
The Keldysh formalism for nonequilibrium Green's functions is a powerful theoretical framework for the description of the electronic structure, spectroscopy, and dynamics of strongly correlated systems. However, the underlying Kadanoff-Baym…
With recent advancing of Internet of Things (IoTs), it becomes very attractive to implement the deep convolutional neural networks (DCNNs) onto embedded/portable systems. Presently, executing the software-based DCNNs requires…
Stochastic computing (SC) has emerged as an efficient low-power alternative for deploying neural networks (NNs) in resource-limited scenarios, such as the Internet of Things (IoT). By encoding values as serial bitstreams, SC significantly…
This work introduces various approaches to include connected three-body terms in unitary many-body theories, focusing a representative example on the driven similarity renormalization group (DSRG). Starting from the least approximate method…
The problem of tensor completion has applications in healthcare, computer vision, and other domains. However, past approaches to tensor completion have faced a tension in that they either have polynomial-time computation but require…
The evaluation of elastodynamic Green's functions across numerous source-receiver locations, frequencies, and material properties, particularly in the context of parametric studies or boundary element computations, is computationally…
We study lower bounds on the worst-case error of numerical integration in tensor product spaces. As reference we use the $N$-th minimal error of linear rules that use $N$ function values. The information complexity is the minimal number $N$…
In this article we study intrusive uncertainty quantification schemes for systems of conservation laws with uncertainty. Standard intrusive methods lead to oscillatory solutions which sometimes even cause the loss of hyperbolicity. We…
The computational cost of ab initio nuclear structure calculations is rendered particularly acute by the presence of (at least) three-nucleon interactions. This feature becomes especially critical now that many-body methods aim at extending…
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…
The rapid development of ab initio nuclear structure methods towards doubly open-shell nuclei, heavy nuclei and greater accuracy occurs at the price of evermore increased computational costs, especially RAM and CPU time. While most of the…
The simulation of open many-body quantum systems is challenging, requiring methods to both handle exponentially large Hilbert spaces and represent the influence of (infinite) particle and energy reservoirs. These two requirements are at…