Related papers: Approximating linear response of physical chaos
We consider the problem of impulse response estimation of stable linear single-input single-output systems. It is a well-studied problem where flexible non-parametric models recently offered a leap in performance compared to the classical…
We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…
In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems by time domain decomposition. The available algorithms enabling such decompositions present severe efficiency limitations and are an…
Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…
It is shown, using direct numerical simulations and laboratory experiments data, that distributed chaos is often tuned to large scale coherent motions in anisotropic inhomogeneous turbulence. The examples considered are: fully developed…
Background: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state…
Parametric linear systems are linear systems of equations in which some symbolic parameters, that is, symbols that are not considered to be candidates for elimination or solution in the course of analyzing the problem, appear in the…
In this paper, we consider a generalized multivariate regression problem where the responses are monotonic functions of linear transformations of predictors. We propose a semi-parametric algorithm based on the ordering of the responses…
Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome $Y$ to a large number of covariates $\mathbf {X}$, for example,…
The behavior of some stochastic chemical reaction networks is largely unaffected by slight inaccuracies in reaction rates. We formalize the robustness of state probabilities to reaction rate deviations, and describe a formal connection…
We present a high order parameter-robust numerical method for a system of (M>=2) coupled singularly perturbed parabolic reaction-diffusion problems. A small perturbation parameter {\epsilon} is multiplied with the second order spatial…
We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified…
In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…
We prove quantitative statistical stability results for a large class of small $C^{0}$ perturbations of circle diffeomorphisms with irrational rotation numbers. We show that if the rotation number is Diophantine the invariant measure varies…
Several regularization methods have been considered over the last decade for sparse high-dimensional linear regression models, but the most common ones use the least square (quadratic) or likelihood loss and hence are not robust against…
A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…
Hierarchy of one and many-parameter families of random trigonometric chaotic maps and one-parameter random elliptic chaotic maps of $\bf{cn}$ type with an invariant measure have been introduced. Using the invariant measure…
We propose a physics-constrained machine learning method-based on reservoir computing- to time-accurately predict extreme events and long-term velocity statistics in a model of turbulent shear flow. The method leverages the strengths of two…
The control of spatio-temporally chaos is challenging because of high dimensionality and unpredictability. Model-free reinforcement learning (RL) discovers optimal control policies by interacting with the system, typically requiring…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…