Related papers: Weak Form Generalized Hamiltonian Learning
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
This paper presents a sequence of two approaches for the data-driven control-oriented modeling of networked systems, i.e., the systems that involve many interacting dynamical components. First, a novel deep learning approach named the weak…
We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary…
Complex systems manifest a small number of instabilities and bifurcations that are canonical in nature, resulting in universal pattern forming characteristics as a function of some parametric dependence. Such parametric instabilities are…
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…
In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…
In the identification of differential equations from data, significant progresses have been made with the weak/integral formulation. In this paper, we explore the direction of finding more efficient and robust test functions adaptively…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
This paper presents a new method for learning dissipative Hamiltonian dynamics from a limited and noisy dataset. The method uses the Helmholtz decomposition to learn a vector field as the sum of a symplectic and a dissipative vector field.…
The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…
Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model…
Hamiltonian mechanics is an effective tool to represent many physical processes with concise yet well-generalized mathematical expressions. A well-modeled Hamiltonian makes it easy for researchers to analyze and forecast many related…
This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses…
Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a…
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…
In this paper we design and use two Deep Learning models to generate the ground and excited wavefunctions of different Hamiltonians suitable for the study the vibrations of molecular systems. The generated neural networks are trained with…
Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…
We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…