Related papers: Hamiltonian Neural Networks with Automatic Symmetr…

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem…

A new approach is introduced to classify faults in rotating machinery based on the total energy signature estimated from sensor measurements. The overall goal is to go beyond using black-box models and incorporate additional physical…

Symplectic integration of autonomous Hamiltonian systems is a well-known field of study in geometric numerical integration, but for non-autonomous systems the situation is less clear, since symplectic structure requires an even number of…

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…

Training deep neural networks (DNNs) can be difficult due to the occurrence of vanishing/exploding gradients during weight optimization. To avoid this problem, we propose a class of DNNs stemming from the time discretization of Hamiltonian…

The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…

Lagrangian Neural Networks (LNNs) present a principled and interpretable framework for learning the system dynamics by utilizing inductive biases. While traditional dynamics models struggle with compounding errors over long horizons, LNNs…

Integrable systems have provided various insights into physical phenomena and mathematics. The way of constructing many-body integrable systems is limited to few ansatzes for the Lax pair, except for highly inventive findings of conserved…

We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this,…

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.…

Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This…

This article presents an innovative approach to integrating port-Hamiltonian systems with neural network architectures, transitioning from deterministic to stochastic models. The study presents novel mathematical formulations and…

Stability and safety are critical properties for successful deployment of automatic control systems. As a motivating example, consider autonomous mobile robot navigation in a complex environment. A control design that generalizes to…

Recognizing symmetries in data allows for significant boosts in neural network training. In many cases, however, the underlying symmetry is present only in an idealized dataset, and is broken in the training data, due to effects such as…

Lagrangian Neural Networks (LNNs) can learn arbitrary Lagrangians from trajectory data, but their unusual optimization objective leads to significant training instabilities that limit their application to complex systems. We propose several…

Many dynamical systems -- from robots interacting with their surroundings to large-scale multiphysics systems -- involve a number of interacting subsystems. Toward the objective of learning composite models of such systems from data, we…

Machine learning is playing an increasing role in the physical sciences and significant progress has been made towards embedding domain knowledge into models. Less explored is its use to discover interpretable physical laws from data. We…

We introduce a generalizable framework for learning to identify effective Hamiltonians directly from experimental data in solid-state quantum systems. Our approach is based on a physics-informed neural network architecture that embeds…

The Hamiltonian Monte Carlo method generates samples by introducing a mechanical system that explores the target density. For distributions on manifolds it is not always simple to perform the mechanics as a result of the lack of global…

When sampling for Bayesian inference, one popular approach is to use Hamiltonian Monte Carlo (HMC) and specifically the No-U-Turn Sampler (NUTS) which automatically decides the end time of the Hamiltonian trajectory. However, HMC and NUTS…