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Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several…

In decision support systems, it is essential to get a candidate solution fast, even if it means resorting to an approximation. This constraint introduces a scalability requirement with regard to the kind of heuristics which can be used in…

Exploiting the efficiency and stability of Position-Based Dynamics (PBD), we introduce a novel crowd simulation method that runs at interactive rates for hundreds of thousands of agents. Our method enables the detailed modeling of per-agent…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

Predictive state representation~(PSR) uses a vector of action-observation sequence to represent the system dynamics and subsequently predicts the probability of future events. It is a concise knowledge representation that is well studied in…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…

Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects.…

We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…

The long time dynamics of polymeric materials has been extensively studied in the past through various experimental techniques and computer simulations. While computer simulations typically treat generic, simplified models, experiments deal…

Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow…

In this Letter, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced in [Sompolinsky et. al, 1988] in the context of random neural networks. It is known that increasing the disorder parameter…

The low-temperature driven or thermally activated motion of several condensed matter systems is often modeled by the dynamics of interfaces (co-dimension-1 elastic manifolds) subject to a random potential. Two characteristic quantitative…

We develop a generalized hyperdynamics method, which is able to simulate slow dynamics in atomistic general (both energy and entropy-dominated) systems. We show that a few functionals of the pair correlation function, involving two-body…

Point masses connected by springs, or mass-spring systems, are widely used in computer animation to approximate the behavior of deformable objects. One of the restrictions imposed by these models is that points that are not topologically…

The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these…

Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. The central challenge is to simulate turbulent flows in complex geometries, a compute-power intensive task due to the large…

This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…

The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…