Related papers: Learning Linear Representations of Nonlinear Dynam…
In this paper, We study the problem of learning a controllable representation for high-dimensional observations of dynamical systems. Specifically, we consider a situation where there are multiple sets of observations of dynamical systems…
In this proceeding, we will briefly review our recent progress on implementing deep learning to relativistic hydrodynamics. We will demonstrate that a successfully designed and trained deep neural network, called {\tt stacked U-net}, can…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to…
In this paper, we present a new data-driven method for learning stable models of nonlinear systems. Our model lifts the original state space to a higher-dimensional linear manifold using Koopman embeddings. Interestingly, we prove that…
Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…
The growing interest in creating a parametric representation of liquid sloshing inside a container stems from its practical applications in modern engineering systems. The resonant excitation, on the other hand, can cause unstable and…
Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In…
How can we effectively encode evolving information over dynamic graphs into low-dimensional representations? In this paper, we propose DyRep, an inductive deep representation learning framework that learns a set of functions to efficiently…
Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…
Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…
While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learned representations meaningful. For this, the typical approach is to regularize the learned…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
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 study the learning ability of linear recurrent neural networks with Gradient Descent. We prove the first theoretical guarantee on linear RNNs to learn any stable linear dynamic system using any a large type of loss functions. For an…
Deep learning has been widely used within learning algorithms for robotics. One disadvantage of deep networks is that these networks are black-box representations. Therefore, the learned approximations ignore the existing knowledge of…
Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods…
Deep learning using neural networks has revolutionized machine learning and put artificial intelligence into everyday life. In order to introduce self-learning to dynamic systems other than neural networks, we extend the Brandt-Lin learning…
Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…
We investigate the use of deep neural networks to control complex nonlinear dynamical systems, specifically the movement of a rigid body immersed in a fluid. We solve the Navier Stokes equations with two way coupling, which gives rise to…