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The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…
State-space systems encompass a broad class of algorithms used for modeling and forecasting time series. For such systems to be effective, two objectives must be met: (i) accurate point forecasts of the time series must be produced, and…
In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based…
Operational forecasting centers are investing in decadal (1-10 year) forecast systems to support long-term decision making for a more climate-resilient society. One method that has previously been employed is the Dynamic Mode Decomposition…
Predicting the long-term behavior of chaotic systems remains a formidable challenge due to their extreme sensitivity to initial conditions and the inherent limitations of traditional data-driven modeling approaches. This paper introduces a…
This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…
Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation…
Numerical models of weather and climate critically depend on long-term stability of integrators for systems of hyperbolic conservation laws. While such stability is often obtained from (physical or numerical) dissipation terms, physical…
On this paper, we have proposed an approach to observe the time-centered difference scheme for dissipative mechanical systems from a Hamiltonian perspective and to introduce the idea of symplectic algorithm to dissipative systems. The…
Thermodynamically consistent models in continuum physics, i.e. models which satisfy the first and second laws of thermodynamics, may be expressed using the metriplectic formalism. In this work, we leverage the structures underlying this…
We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary…
Numerical modeling of different structural materials that have highly nonlinear behaviors has always been a challenging problem in engineering disciplines. Experimental data is commonly used to characterize this behavior. This study aims to…
As deep learning becomes more prevalent for prediction and control of real physical systems, it is important that these overparameterized models are consistent with physically plausible dynamics. This elicits a problem with how much…
The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…
Machine learning recently proved efficient in learning differential equations and dynamical systems from data. However, the data is commonly assumed to originate from a single never-changing system. In contrast, when modeling real-world…
In this paper an approach is proposed to represent a class of dissipative mechanical systems by corresponding infinite-dimensional Hamiltonian systems. This approach is based upon the following structure: for any non-conservative classical…
We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…
The concept of Deadbeat Robust Model Predictive Control (DRMPC) is to completely extinguish the effect of external disturbances within the first few steps of the prediction horizon. The benefit is that the remaining dynamics of the system…
Switching physical systems are ubiquitous in modern control applications, for instance, locomotion behavior of robots and animals, power converters with switches and diodes. The dynamics and switching conditions are often hard to obtain or…
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics like work, heat and entropy production to the level of individual trajectories of well-defined…