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Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

We propose and illustrate an approach to coarse-graining the dynamics of evolving networks (networks whose connectivity changes dynamically). The approach is based on the equation-free framework: short bursts of detailed network evolution…

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these…

Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function…

A theoretical framework which unifies the conventional Mori-Zwanzig formalism and the approximate Koopman learning is presented. In this framework, the Mori-Zwanzig formalism, developed in statistical mechanics to tackle the hard problem of…

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…

Significant efforts have been devoted in the last decade towards improving the predictivity of coarse-grained models in molecular dynamics simulations and providing a rigorous justification of their use, through a combination of theoretical…

Model reduction methods aim to describe complex dynamic phenomena using only relevant dynamical variables, decreasing computational cost, and potentially highlighting key dynamical mechanisms. In the absence of special dynamical features…

We develop a new formulation of deep learning based on the Mori-Zwanzig (MZ) formalism of irreversible statistical mechanics. The new formulation is built upon the well-known duality between deep neural networks and discrete dynamical…

Phenotypical variability in the absence of genetic variation often reflects complex energetic landscapes associated with underlying gene regulatory networks (GRNs). In this view, different phenotypes are associated with alternative states…

Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…

Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

Coarse-graining is a molecular modeling technique in which an atomistic system is represented in a simplified fashion that retains the most significant system features that contribute to a target output, while removing the degrees of…

Understanding, predicting and controlling laminar-turbulent boundary-layer transition is crucial for the next generation aircraft design. However, in real flight experiments, or wind tunnel tests, often only sparse sensor measurements can…

We consider a Graph Neural Network (GNN) non-Markovian modeling framework to identify coarse-grained dynamical systems on graphs. Our main idea is to systematically determine the GNN architecture by inspecting how the leading term of the…

In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…

Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller class of variables. While extensive literature has been…

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…

We introduce a method for determining the functional form of the stochastic and dissipative interactions in a dissipative particle dynamics (DPD) model from projected phase space trajectories. The DPD model is viewed as a coarse graining of…