Related papers: Identifying Physical Law of Hamiltonian Systems vi…
Recent advancements in quantum hardware and classical computing simulations have significantly enhanced the accessibility of quantum system data, leading to an increased demand for precise descriptions and predictions of these systems.…
Discovering physical laws directly from high-dimensional visual data is a long-standing human pursuit but remains a formidable challenge for machines, representing a fundamental goal of scientific intelligence. This task is inherently…
Accurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently. Here, for the Hamiltonian mechanics, we propose the Hamiltonian Neural…
Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum…
Data-driven prediction in quantum mechanics consists in providing an approximative description of the motion of any particles at any given time, from data that have been previously collected for a certain number of particles under the…
There has been increasing interest in methodologies that incorporate physics priors into neural network architectures to enhance their modeling capabilities. A family of these methodologies that has gained traction are Hamiltonian neural…
The first-principles-based effective Hamiltonian scheme provides one of the most accurate modeling technique for large-scale structures, especially for ferroelectrics. However, the parameterization of the effective Hamiltonian is…
We propose to interpret machine learning functions as physical observables, opening up the possibility to apply "standard" statistical-mechanical methods to outputs from neural networks. This includes histogram reweighting and finite-size…
Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…
Hamiltonian Learning is a process of recovering system Hamiltonian from measurements, which is a fundamental problem in quantum information processing. In this study, we investigate the problem of learning the symmetric Hamiltonian from its…
In recent years quantum simulation has made great strides culminating in experiments that operate in a regime that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum…
Learning the unknown Hamiltonian governing the dynamics of a quantum many-body system is a challenging task. In this manuscript, we propose a possible strategy based on repeated measurements on a single time-dependent state. We prove that…
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…
The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which…
The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…
Mathematical modeling of real-world physical systems requires the consistent combination of a multitude of physical laws and phenomenological models. This challenging task can be greatly simplified by hierarchically decomposing systems into…
Amidst the wide popularity of imitation learning algorithms in robotics, their properties regarding hyperparameter sensitivity, ease of training, data efficiency, and performance have not been well-studied in high-precision…
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…
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,…
Machine learning methods are widely used in the natural sciences to model and predict physical systems from observation data. Yet, they are often used as poorly understood "black boxes," disregarding existing mathematical structure and…