Related papers: Learning dissipative Hamiltonian dynamics with rep…
Hamiltonian mechanics is one of the cornerstones of natural sciences. Recently there has been significant interest in learning Hamiltonian systems in a free-form way directly from trajectory data. Previous methods have tackled the problem…
While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
We present an approach to construct appropriate and efficient emulators for Hamiltonian flow maps. Intended future applications are long-term tracing of fast charged particles in accelerators and magnetic plasma confinement configurations.…
We study symplectic deformations of Gabor frames using the covariance properties of the Heisenberg operators. This allows us to recover in a very simple way known results. We thereafter propose a general deformation scheme by Hamiltonian…
Although support vector machines (SVMs) are theoretically well understood, their underlying optimization problem becomes very expensive, if, for example, hundreds of thousands of samples and a non-linear kernel are considered. Several…
We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…
Learned image compression methods have shown superior rate-distortion performance and remarkable potential compared to traditional compression methods. Most existing learned approaches use stacked convolution or window-based self-attention…
This paper reports a development in the proper symplectic decomposition (PSD) for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD), PSD is designed to build a symplectic subspace to…
Determining the Hamiltonian of a quantum system is essential for understanding its dynamics and validating its behavior. Hamiltonian learning provides a data-driven approach to reconstruct the generator of the dynamics from measurements on…
This expository article presents the approach to statistical machine learning based on reproducing kernel Hilbert spaces. The basic framework is introduced for scalar-valued learning and then extended to operator learning. Finally, learning…
Data-driven modeling is playing an increasing role in robotics and control, yet standard learning methods typically ignore the geometric structure of nonholonomic systems. As a consequence, the learned dynamics may violate the nonholonomic…
We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number…
We discuss Hamiltonian and Liouvillian learning for analog quantum simulation from non-equilibrium quench dynamics in the limit of weakly dissipative many-body systems. We present and compare various methods and strategies to learn the…
This paper builds on the theoretical foundations for dynamic mode decomposition (DMD) of control-affine dynamical systems by leveraging the theory of vector-valued reproducing kernel Hilbert spaces (RKHSs). Specifically, control Liouville…
Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models…
In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
We propose a novel approach for pixel classification in hyperspectral images, leveraging on both the spatial and spectral information in the data. The introduced method relies on a recently proposed framework for learning on distributions…