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Molecular dynamics (MD) simulations have been widely applied to study macromolecules including proteins. However, high-dimensionality of the datasets produced by simulations makes it difficult for thorough analysis, and further hinders a…

The success of enhanced sampling molecular simulations that accelerate along collective variables (CVs) is predicated on the availability of variables coincident with the slow collective motions governing the long-time conformational…

Monte Carlo simulations are widely used to simulate complex molecular systems, but standard approaches suffer from metastability. Lately, the use of non-local proposal updates in a collective-variable (CV) space has been proposed in several…

This work introduces a novel methodology to derive physical scalings for input features from data. The approach developed in this article relies on the maximization of mutual information to derive optimal nonlinear combinations of input…

Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a…

Designing an appropriate set of collective variables is crucial to the success of several enhanced sampling methods. Here we focus on how to obtain such variables from information limited to the metastable states. We characterize these…

Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…

Instrumental variables (IVs) provide a powerful strategy for identifying causal effects in the presence of unobservable confounders. Within the nonparametric setting (NPIV), recent methods have been based on nonlinear generalizations of…

We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…

Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between…

Enhanced sampling simulations make the computational study of rare events feasible. A large family of such methods crucially depends on the definition of some collective variables (CVs) that could provide a low-dimensional representation of…

Analyzing data from dynamical systems often begins with creating a reconstruction of the trajectory based on one or more variables, but not all variables are suitable for reconstructing the trajectory. The concept of nonlinear observability…

Biological and artificial systems encode information through several complex nonlinear operations, making their exact study a formidable challenge. These internal mechanisms often take place across multiple timescales and process external…

Inferring biophysical parameters and hidden state variables from partial and noisy observations is a fundamental challenge in computational neuroscience. This problem is particularly difficult for fast - slow spiking and bursting models,…

This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has…

We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…

The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…

Nonlinear materials are often difficult to model with classical state model theory because they have a complex and sometimes inaccurate physical and mathematical description or we simply do not know how to describe such materials in terms…