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A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
This paper proposes a new approach to perform small-signal stability analysis based on linearization of implicit multilinear models. Multilinear models describe the system dynamics by multilinear functions of state, input, and algebraic…
We demonstrate how to map out the phase diagram of a two dimensional quantum many body system with no prior physical knowledge by applying deep \textit{anomaly detection} to ground states from infinite projected entangled pair state…
Reverse engineering of gene regulatory networks presents one of the big challenges in systems biology. Gene regulatory networks are usually inferred from a set of single-gene over-expressions and/or knockout experiments. Functional…
Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…
We propose and show the efficacy of a new method to address generic inverse problems. Inverse modeling is the task whereby one seeks to determine the control parameters of a natural system that produce a given set of observed measurements.…
Mesoscopic bio-systems typically evolve towards functionally important target states, such as cell-cycle checkpoints or decision boundaries for the release of specific behaviors. For the data-driven inference of the underlying directional…
Systems of differential equations with polynomial right-hand sides are very common in applications. On the other hand, their mathematical analysis is very challenging in general, due to the possibility of complex dynamics: multiple basins…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
By transforming identification and control for nonlinear system into optimization problems, a novel optimization method named state transition algorithm (STA) is introduced to solve the problems. In the proposed STA, a solution to a…
The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…
The Macaulay2 package GraphicalModels contains algorithms for the algebraic study of graphical models associated to undirected, directed and mixed graphs, and associated collections of conditional independence statements. Among the…
This paper studies a basic model of a dynamical distribution network, where the network topology is given by a directed graph with storage variables corresponding to the vertices and flow inputs corresponding to the edges. We aim at…
Network reconstruction of dynamical continuous-time (CT) systems is motivated by applications in many fields. Due to experimental limitations, especially in biology, data could be sampled at low frequencies, leading to significant…
State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…
Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the…
Finite element simulations are run by package design engineers to model design structures. The process is irreversible meaning every minute structural adjustment requires a fresh input parameter run. In this paper, the problem of modeling…
In the context of dynamical systems, nonlinearity measures quantify the strength of nonlinearity by means of the distance of their input-output behaviour to a set of linear input-output mappings. In this paper, we establish a framework to…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
A theoretical framework that supports automated construction of dynamic prime models purely from experimental time series data has been invented and developed, which can automatically generate (construct) data-driven models of any time…