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Particle based optimization algorithms have recently been developed as sampling methods that iteratively update a set of particles to approximate a target distribution. In particular Stein variational gradient descent has gained attention…

Here we present a quantum algorithm for clustering data based on a variational quantum circuit. The algorithm allows to classify data into many clusters, and can easily be implemented in few-qubit Noisy Intermediate-Scale Quantum (NISQ)…

Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…

Algorithmic discrepancy theory seeks efficient algorithms to find those two-colorings of a set that minimize a given measure of coloring imbalance in the set, its {\it discrepancy}. The {\it Euclidean discrepancy} problem and the problem of…

Circuit design for quantum machine learning remains a formidable challenge. Inspired by the applications of tensor networks across different fields and their novel presence in the classical machine learning context, one proposed method to…

Nonlinear stochastic modeling is useful for describing complex engineering systems. Meanwhile, neuromorphic (brain-inspired) computing paradigms are developing to tackle tasks that are challenging and resource intensive on digital…

Causality graphs are routinely estimated in social sciences, natural sciences, and engineering due to their capacity to efficiently represent the spatiotemporal structure of multivariate data sets in a format amenable for human…

Quantum machine learning algorithms aim to take advantage of quantum computing to improve classical machine learning algorithms. In this paper, we have applied a quantum machine learning algorithm, the variational quantum classifier for the…

We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…

Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching…

Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and…

The use of complex networks for time series analysis has recently shown to be useful as a tool for detecting dynamic state changes for a wide variety of applications. In this work, we implement the commonly used ordinal partition network to…

We apply physics-informed neural networks (PINNs) to first-order two-scale periodic asymptotic homogenization of the property tensor in a generic elliptic equation. The problem of lack of differentiability of property tensors at the sharp…

Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…

A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…

We introduce highly efficient online nonlinear regression algorithms that are suitable for real life applications. We process the data in a truly online manner such that no storage is needed, i.e., the data is discarded after being used.…

A variational framework for structural topology optimization is developed, integrating quantum and classical latent encoding strategies within a coordinate-based neural decoding architecture. In this approach, a low-dimensional latent…

Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…

We present a new method to perform variation after projection in many-body systems on quantum computers that does not require performing explicit projection. The technique employs the notion of ``oracle'', generally used in quantum search…

The logistic network design is an abstract optimization problem that, under the assumption of minimal cost, seeks the optimal configuration of the supply chain's infrastructures and facilities based on customer demand. Key economic…