Related papers: Learning Neural Hamiltonian Dynamics: A Methodolog…

This article examines the impact of Hamiltonian dynamics on the interaction graph of Boolean networks. Three types of dynamics are considered: maximum height, Hamiltonian cycle, and an intermediate dynamic between these two. The study…

The principled design and discovery of biologically- and physically-informed models of neuronal dynamics has been advancing since the mid-twentieth century. Recent developments in artificial intelligence (AI) have accelerated this progress.…

Neural networks are complex functions of both their inputs and parameters. Much prior work in deep learning theory analyzes the distribution of network outputs at a fixed a set of inputs (e.g. a training dataset) over random initializations…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

We propose Symplectic Recurrent Neural Networks (SRNNs) as learning algorithms that capture the dynamics of physical systems from observed trajectories. An SRNN models the Hamiltonian function of the system by a neural network and…

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…

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…

Conventional artificial neural networks are powerful tools in science and industry, but they can fail when applied to nonlinear systems where order and chaos coexist. We use neural networks that incorporate the structures and symmetries of…

We develop inductive biases for the machine learning of complex physical systems based on the port-Hamiltonian formalism. To satisfy by construction the principles of thermodynamics in the learned physics (conservation of energy,…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…

This paper proposes a neural network hybrid modeling framework for dynamics learning to promote an interpretable, computationally efficient way of dynamics learning and system identification. First, a low-level model will be trained to…

Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under…

In this paper, we present neural networks learning mechanical systems that are both symplectic (for instance particle mechanics) and non-symplectic (for instance rotating rigid body). Mechanical systems have Hamiltonian evolution, which…

Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation…

The interpretation of deep learning as a dynamical system has gained a considerable attention in recent years as it provides a promising framework. It allows for the use of existing ideas from established fields of mathematics for studying…

When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…

Physics-informed deep learning models have emerged as powerful tools for learning dynamical systems. These models directly encode physical principles into network architectures. However, systematic benchmarking of these approaches across…

In this work, we introduce Dissipative SymODEN, a deep learning architecture which can infer the dynamics of a physical system with dissipation from observed state trajectories. To improve prediction accuracy while reducing network size,…

We present a method for learning generalized Hamiltonian decompositions of ordinary differential equations given a set of noisy time series measurements. Our method simultaneously learns a continuous time model and a scalar energy function…

Determining the Hamiltonian of a quantum system is essential for understanding its dynamics and validating its behavior. Hamiltonian learning provides a data-driven approach to reconstruct the generator of the dynamics from measurements on…