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We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and…
The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…
Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…
We introduce a tensor-channel equivariant graph neural network for direct prediction of molecular polarizability tensors. Building on the efficient PaiNN architecture, we augment the hidden representation with explicit symmetric rank-2…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…
We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level…
In large-scale quantum-chemical calculations the electron-repulsion integral (ERI) tensor rapidly becomes the bottleneck in terms of memory and disk space. When an external finite magnetic field is employed, this problem becomes even more…
If a tensor with various symmetries is properly unfolded, then the resulting matrix inherits those symmetries. As tensor computations become increasingly important it is imperative that we develop efficient structure preserving methods for…
We present a new class of tensor network states that are specifically designed to capture the electron correlation of a molecule of arbitrary structure. In this ansatz, the electronic wave function is represented by a Complete-Graph Tensor…
We develop a quartic-scaling implementation of coupled-cluster singles and doubles based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our…
Quantum interference (QI) in molecular transport junctions can lead to dramatic reductions of the electron transmission at certain energies. In a recent work [Markussen et al., Nano Lett. 2010, 10, 4260] we showed how the presence of such…
We introduce two new approximation methods for the numerical evaluation of the long-range Coulomb potential and the approximation of the resulting high dimensional Two-Electron Integrals tensor (TEI) with long-range interactions arising in…
Knowledge graph embedding aims to predict the missing relations between entities in knowledge graphs. Tensor-decomposition-based models, such as ComplEx, provide a good trade-off between efficiency and expressiveness, that is crucial…
Modern E(3)-Equivariant networks may be used to predict rotationally equivariant properties, including tensorial quantities. Three such quantities: the dielectric, piezoelectric, and elasticity tensors, are computationally expensive to…
Pairwise Fisher graphs capture local covariance information, but they cannot distinguish an irreducible multi-observable radiation pattern from a collection of ordinary pairwise correlations. We show that this missing structure is naturally…
We introduce a novel equivariant graph neural network (GNN) architecture designed to predict the tensorial response properties of molecules. Unlike traditional frameworks that focus on regressing scalar quantities and derive tensorial…
A universal interatomic potential for an arbitrary set of chemical elements is urgently needed in computational materials science. Graph convolution neural network (GCN) has rich expressive power, but previously was mainly employed to…
Tensor networks have been an important concept and technique in many research areas, such as quantum computation and machine learning. We study the exponential complexity of contracting tensor networks on two special graph structures:…
Graph classification is a significant problem in many scientific domains. It addresses tasks such as the classification of proteins and chemical compounds into categories according to their functions, or chemical and structural properties.…
Message passing neural networks have become a method of choice for learning on graphs, in particular the prediction of chemical properties and the acceleration of molecular dynamics studies. While they readily scale to large training data…