Related papers: Computing invariant sets of random differential eq…
Polynomial chaos expansions (PCE) allow us to propagate uncertainties in the coefficients of differential equations to the statistics of their solutions. Their main advantage is that they replace stochastic equations by systems of…
We are concerned with random ordinary differential equations (RODEs). Our main question of interest is how uncertainties in system parameters propagate through the possibly highly nonlinear dynamical system and affect the system's…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
In this contribution, we discuss the construction of Polynomial Chaos surrogates for Monte Carlo radiation transport applications via non-intrusive spectral projection. This contribution focuses on improvements with respect to the approach…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
Incorporating probabilistic terms in mathematical models is crucial for capturing and quantifying uncertainties in real-world systems, especially when the solution is not unique or exhibits sudden qualitative changes as parameters vary.…
Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…
Studying 2 degree-of-freedom (DOF) Hamiltonian dynamical systems often involves the computation of stable & unstable manifolds of periodic orbits, due to the homoclinic & heteroclinic connections they can generate. Such study is generally…
Polynomial chaos expansion (PCE) is a classical and widely used surrogate modeling technique in physical simulation and uncertainty quantification. By taking a linear combination of a set of basis polynomials - orthonormal with respect to…
Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…
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,…
Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…
Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…
Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple strategies for evaluating PCE coefficients. In contrast,…
We present a computational method for studying transverse homoclinic orbits for periodic solutions of delay differential equations, a phenomenon that we refer to as the \emph{Poincar\'{e} scenario}. The strategy is geometric in nature, and…
The application of polynomial chaos expansions (PCEs) to the propagation of uncertainties in stochastic dynamical models is well-known to face challenging issues. The accuracy of PCEs degenerates quickly in time. Thus maintaining a…
In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and…
Long-horizon motion forecasting for multiple autonomous robots is challenging due to non-linear agent interactions, compounding prediction errors, and continuous-time evolution of dynamics. Learned dynamics of such a system can be useful in…