Related papers: Learning dissipative Hamiltonian dynamics with rep…
This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet,…
In nonparametric classification and regression problems, regularized kernel methods, in particular support vector machines, attract much attention in theoretical and in applied statistics. In an abstract sense, regularized kernel methods…
A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which…
We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) $\mathscr{H}$ over infinite, discrete and countable sets $V$. In this setting we analyze in detail the distributions of the corresponding Dirac…
The Helmholtz decomposition splits a sufficiently smooth vector field into a gradient field and a divergence-free rotation field. Existing decomposition methods impose constraints on the behavior of vector fields at infinity and require…
In this paper, we investigate the asymptotic error distributions of symplectic methods for stochastic Hamiltonian systems and further provide Hamiltonian-specific analysis that clarifies the superiority of symplectic methods. Our…
Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system…
We consider multi-agent stochastic optimization problems over reproducing kernel Hilbert spaces (RKHS). In this setting, a network of interconnected agents aims to learn decision functions, i.e., nonlinear statistical models, that are…
We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size…
In this work, we introduce kernels with random Fourier features in the meta-learning framework to leverage their strong few-shot learning ability. We propose meta variational random features (MetaVRF) to learn adaptive kernels for the…
Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
We introduce a new approach to learning in hierarchical latent-variable generative models called the "distributed distributional code Helmholtz machine", which emphasises flexibility and accuracy in the inferential process. In common with…
We consider the problem of learning Stochastic Differential Equations of the form $dX_t = f(X_t)dt+\sigma(X_t)dW_t $ from one sample trajectory. This problem is more challenging than learning deterministic dynamical systems because one…
Statistical-physics calculations in machine learning and theoretical neuroscience often involve lengthy derivations that obscure physical interpretation. Here, we give concise, non-replica derivations of several key results and highlight…
We introduce Constr-DRKM, a deep kernel method for the unsupervised learning of disentangled data representations. We propose augmenting the original deep restricted kernel machine formulation for kernel PCA by orthogonality constraints on…
We develop a unified geometric framework for mechanical systems that combine conservative and dissipative dynamics by formulating them on contact manifolds. Within this setting, we identify the Reeb vector field as the intrinsic generator…
Biclustering algorithms partition data and covariates simultaneously, providing new insights in several domains, such as analyzing gene expression to discover new biological functions. This paper develops a new model-free biclustering…
Hamiltonian systems with multiple timescales arise in molecular dynamics, classical mechanics, and theoretical physics. Long-time numerical integration of such systems requires resolving fast dynamics with very small time steps, which…