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Spatio-temporal process models are often used for modeling dynamic physical and biological phenomena that evolve across space and time. These phenomena may exhibit environmental heterogeneity and complex interactions that are difficult to…
We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
Topologically ordered phase has emerged as one of most exciting concepts that not only broadens our understanding of phases of matter, but also has been found to have potential application in fault-tolerant quantum computation. The direct…
This work proposes an algorithmic framework to learn time-varying graphs from online data. The generality offered by the framework renders it model-independent, i.e., it can be theoretically analyzed in its abstract formulation and then…
Stochastic Approximation (SA) is a classical algorithm that has had since the early days a huge impact on signal processing, and nowadays on machine learning, due to the necessity to deal with a large amount of data observed with…
We introduce a novel framework for uncertainty quantification of solution operators associated with stochastic partial differential equations (SPDEs). Although SPDEs play a central role in modeling complex physical systems under…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
Gaussian Mixture Models (GMMs) are one of the most potent parametric density models used extensively in many applications. Flexibly-tied factorization of the covariance matrices in GMMs is a powerful approach for coping with the challenges…
A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the…
We describe spatio-temporal random processes using linear mixed models. We show how many commonly used models can be viewed as special cases of this general framework and pay close attention to models with separable or product-sum…
We develop new unbiased estimators of a number of quantities defined for functions of conditional moments, like conditional expectations and variances, of functions of two independent random variables given the first variable, including…
In the paper, we propose a higher-order geometry-preserving numerical method for stochastic differential equations (SDEs) evolving on the Lie groups SO(n) and SE(n). Most existing Lie group integrators rely on Magnus expansion of the…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant…
We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…
The "folding algorithm"\cite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the…
Various processes can be modelled as quasi-reaction systems of stochastic differential equations, such as cell differentiation and disease spreading. Since the underlying data of particle interactions, such as reactions between proteins or…
Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model,…
We propose a quantum algorithm for sampling from a solution of stochastic differential equations (SDEs). Using differentiable quantum circuits (DQCs) with a feature map encoding of latent variables, we represent the quantile function for an…