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Binding kinetic parameters can be correlated with drug efficacy, which led to the development of various computational methods for predicting binding kinetic rates and gaining insight into protein-drug binding paths and mechanisms in recent…

Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…

This tutorial paper provides an introduction to recently developed tools for machine learning, especially learning dynamical systems (system identification), with stability and robustness constraints. The main ideas are drawn from…

The atomistic characterization of the transition state is a fundamental step to improve the understanding of the folding mechanism and the function of proteins. From a computational point of view, the identification of the conformations…

In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

Determining the different conformational states of a protein and the transition paths between them is key to fully understanding the relationship between biomolecular structure and function. This can be accomplished by sampling protein…

Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of…

The modeling of dynamical systems is a pervasive concern for not only describing but also predicting and controlling natural phenomena and engineered systems. Current data-driven approaches often assume prior knowledge of the relevant state…

A method is proposed to identify target states that optimize a metastability index amongst a set of trial states and use these target states as milestones (or core sets) to build Markov State Models (MSMs). If the optimized metastability…

Molecular systems often remain trapped for long times around some local minimum of the potential energy function, before switching to another one -- a behavior known as metastability. Simulating transition paths linking one metastable state…

Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory…

Stability is a basic requirement when studying the behavior of dynamical systems. However, stabilizing dynamical systems via reinforcement learning is challenging because only little data can be collected over short time horizons before…

Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…

The article is aimed to address a mutually boosting use of asymptotic analysis and machine learning, for fast stiffness design of configurations infilled with smoothly-varying graded microstructures. The discussion is conducted in the…

Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…

Phase diagrams are an invaluable tool for material synthesis and provide information on the phases of the material at any given thermodynamic condition. Conventional phase diagram generation involves experimentation to provide an initial…

Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state…

Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…