Related papers: Symplectic Neural Networks Based on Dynamical Syst…

We introduce the process of symplectic reduction along a submanifold as a uniform approach to taking quotients in symplectic geometry. This construction holds in the categories of smooth manifolds, complex analytic spaces, and complex…

The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.

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…

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…

We compare the performances of symplectic and non-symplectic integrators for the computation of normal geodesics and conjugate points in sub-Riemannian geometry at the example of the Martinet case. For this case study we consider first the…

In this paper we developed a hierarchical network model, called Hierarchical Prediction Network (HPNet), to understand how spatiotemporal memories might be learned and encoded in the recurrent circuits in the visual cortical hierarchy for…

Dependable numerical results from long-time simulations require stable numerical integration schemes. For Hamiltonian systems, this is achieved with symplectic integrators, which conserve the symplectic condition and exactly solve for the…

Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…

Simplicial complexes can be viewed as high dimensional generalizations of graphs that explicitly encode multi-way ordered relations between vertices at different resolutions, all at once. This concept is central towards detection of higher…

Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…

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…

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated…

We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is…

In this paper, we present SIMAP, a novel layer integrated into deep learning models, aimed at enhancing the interpretability of the output. The SIMAP layer is an enhanced version of Simplicial-Map Neural Networks (SMNNs), an explainable…

Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…

We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework…

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…

We introduce an approach for imposing physically informed inductive biases in learned simulation models. We combine graph networks with a differentiable ordinary differential equation integrator as a mechanism for predicting future states,…

We present a morphological-symmetry-equivariant heterogeneous graph neural network, namely MS-HGNN, for robotic dynamics learning, that integrates robotic kinematic structures and morphological symmetries into a single graph network. These…

Deep learning architectures based on convolutional neural networks tend to rely on continuous, smooth features. While this characteristics provides significant robustness and proves useful in many real-world tasks, it is strikingly…