Related papers: Learning of Hamiltonian Dynamics with Reproducing …

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…

Hamiltonian systems describe a broad class of dynamical systems governed by Hamiltonian functions, which encode the total energy and dictate the evolution of the system. Data-driven approaches, such as symbolic regression and neural…

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…

Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in…

This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…

We prove the existence of a unitary transformation that enables two arbitrarily given Hamiltonians in the same Hilbert space to be transformed into one another. The result is straightforward yet, for example, it lays the foundation to…

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

Residual deep neural networks are formulated as interacting particle systems leading to a description through neural differential equations, and, in the case of large input data, through mean-field neural networks. The mean-field…

Due to its geometric properties, hyperbolic space can support high-fidelity embeddings of tree- and graph-structured data, upon which various hyperbolic networks have been developed. Existing hyperbolic networks encode geometric priors not…

Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to…

Discrete and continuous variables oftentimes require different treatments in many learning tasks. Identifying the Hamiltonian governing the evolution of a quantum system is a fundamental task in quantum learning theory. While previous works…

We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant…

Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…

Given a specific spectra of the single-particle reduced density matrices of three qubits, the singular symplectic reduction method is applied to the projective Hilbert space of tripartite pure states, under the local unitary group action.…

We give a systematic method for discretizing Hamiltonian partial differential equations (PDEs) with constant symplectic structure, while preserving their energy exactly. The same method, applied to PDEs with constant dissipative structure,…

Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the…

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…

We propose a Kolmogorov-Arnold Representation-based Hamiltonian Neural Network (KAR-HNN) that replaces the Multilayer Perceptrons (MLPs) with univariate transformations. While Hamiltonian Neural Networks (HNNs) ensure energy conservation by…

With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the…