Related papers: A Riemannian Framework for Learning Reduced-order …

Neural networks are playing a crucial role in everyday life, with the most modern generative models able to achieve impressive results. Nonetheless, their functioning is still not very clear, and several strategies have been adopted to…

Natural gradient descent is a principled method for adapting the parameters of a statistical model on-line using an underlying Riemannian parameter space to redefine the direction of steepest descent. The algorithm is examined via methods…

Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we…

Data-centric methods have shown great potential in understanding and predicting spatiotemporal dynamics, enabling better design and control of the object system. However, deep learning models often lack interpretability, fail to obey…

Planning is a powerful approach to control problems with known environment dynamics. In unknown environments the agent needs to learn a model of the system dynamics to make planning applicable. This is particularly challenging when the…

We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and…

We introduce a deep residual recurrent neural network (DR-RNN) as an efficient model reduction technique for nonlinear dynamical systems. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…

Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the…

The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural…

In this paper, we consider the learning of a Reduced-Order Linear Parameter-Varying Model (ROLPVM) of a nonlinear dynamical system based on data. This is achieved by a two-step procedure. In the first step, we learn a projection to a lower…

Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…

We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems.The cornerstone of the proposed method is the maximum volume algorithm.…

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…

This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…

Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks.…

Neural networks with physics based inductive biases such as Lagrangian neural networks (LNN), and Hamiltonian neural networks (HNN) learn the dynamics of physical systems by encoding strong inductive biases. Alternatively, Neural ODEs with…