Related papers: Data-driven Discovery of Closure Models
Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…
Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…
Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…
In this paper, a computationally efficient data-driven hybrid automaton model is proposed to capture unknown complex dynamical system behaviors using multiple neural networks. The sampled data of the system is divided by valid partitions…
We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…
This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…
End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…
Many engineered as well as naturally occurring dynamical systems do not have an accurate mathematical model to describe their dynamic behavior. However, in many applications, it is possible to probe the system with external inputs and…
This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order,…
This paper develops a data-driven safe control framework for nonlinear discrete-time systems with parametric uncertainty and additive disturbances. The proposed approach constructs a data-consistent closed-loop representation that enables…
This work concerns control-oriented and structure-preserving learning of low-dimensional approximations of high-dimensional physical systems, with a focus on mechanical systems. We investigate the integration of neural autoencoders in model…
Resolvent analysis identifies the most responsive forcings and most receptive states of a dynamical system, in an input--output sense, based on its governing equations. Interest in the method has continued to grow during the past decade due…
We propose a latent score-based generative AI framework for learning stochastic, non-local closure models and constitutive laws in nonlinear dynamical systems of computational mechanics. This work addresses a key challenge of modeling…
Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop…
Discovering dynamical models to describe underlying dynamical behavior is essential to draw decisive conclusions and engineering studies, e.g., optimizing a process. Experimental data availability notwithstanding has increased…
Recent advances in learning dynamical systems from data have shown significant promise. However, many existing methods assume access to the full state of the system -- an assumption that is rarely satisfied in practice, where systems are…
In this contribution, we discuss the modeling and model reduction framework known as the Loewner framework. This is a data-driven approach, applicable to large-scale systems, which was originally developed for applications to linear…
Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…
We consider data-driven reduced-order models of partial differential equations with shift equivariance. Shift-equivariant systems typically admit traveling solutions, and the main idea of our approach is to represent the solution in a…