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We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical…
This paper introduces the TulipaProfileFitting.jl package, a tool developed in Julia for generating renewable energy profiles that fit a specified capacity factor. It addresses the limitations of naive methods in adjusting existing profiles…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
Fibre-reinforced hydrogels are promising materials for biomedical applications due to their strength, toughness, and tunability. However, it remains unclear how to design fibre-reinforced hydrogels for use in specific applications due to…
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in…
Transformer-based large language models (LLMs) have displayed remarkable creative prowess and emergence capabilities. Existing empirical studies have revealed a strong connection between these LLMs' impressive emergence abilities and their…
Tensor network methods provide an intuitive graphical language to describe quantum states, channels, open quantum systems and a class of numerical approximation methods that efficiently simulate certain many-body states in one spatial…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…
Tensor contraction (TC) is an important computational kernel widely used in numerous applications. It is a multi-dimensional generalization of matrix multiplication (GEMM). While Strassen's algorithm for GEMM is well studied in theory and…
The Information Dynamics Toolkit xl (IDTxl) is a comprehensive software package for efficient inference of networks and their node dynamics from multivariate time series data using information theory. IDTxl provides functionality to…
In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are…
We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. Firstly, we recall established techniques for how the partition function of a 2D…
The rapid growth of entanglement under unitary time evolution is the primary bottleneck for modern tensor-network techniques--such as Matrix Product States (MPS)--when computing time-dependent expectation values. This {entanglement barrier}…
Large Language Models (LLMs) have demonstrated extraordinary performance across a broad array of applications, from traditional language processing tasks to interpreting structured sequences like time-series data. Yet, their effectiveness…
Transactional data structure libraries (TDSL) combine the ease-of-programming of transactions with the high performance and scalability of custom-tailored concurrent data structures. They can be very efficient thanks to their ability to…
In the world of linear algebra computation, a well-established standard exists called BLAS(Basic Linear Algebra Subprograms). This standard has been crucial for the development of software using linear algebra operations. Its benefits…
Large language and vision models (LLVMs) have been driven by the generalization power of large language models (LLMs) and the advent of visual instruction tuning. Along with scaling them up directly, these models enable LLVMs to showcase…
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this…
LongMemory.jl is a package for time series long memory modelling in Julia. The package provides functions to generate long memory, estimate model parameters, and forecast. Generating methods include fractional differencing, stochastic error…
We introduce a variational algorithm to simulate quantum many-body states based on a tree tensor network ansatz which releases the isometry constraint usually imposed by the real-space renormalization coarse-graining: This additional…