Related papers: A Physics-informed Sheaf Model
The lack of a well-defined equilibrium reference configuration has long hindered a comprehensive atomic-level understanding of liquid dynamics and properties. The Instantaneous Normal Mode (INM) approach, which involves diagonalizing the…
In silico design of new molecules and materials with desirable quantum properties by high-throughput screening is a major challenge due to the high dimensionality of chemical space. To facilitate its navigation, we present a unification of…
Self Consistent Normal Mode Analysis (SCNMA) is applied to heme c type cytochrome f to study temperature dependent protein motion. Classical Normal Mode Analysis (NMA) assumes harmonic behavior and the protein Mean Square Displacement (MSD)…
We propose a unified approach to nonlinear modal analysis in dissipative oscillatory systems. This approach eliminates conflicting definitions, covers both autonomous and time-dependent systems, and provides exact mathematical existence,…
The vibrational behavior of molecules serves as a crucial fingerprint of their structure, chemical state, and surrounding environment. Neutron vibrational spectroscopy provides comprehensive measurements of vibrational modes without…
Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the…
We present an equivariant neural network for predicting vibrational and phonon modes of molecules and periodic crystals, respectively. These predictions are made by evaluating the second derivative Hessian matrices of the learned energy…
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
Some exact interactions between vibrational modes in systems with discrete symmetry can be described by the theory of the bushes of nonlinear normal modes (NNMs) [G.M. Chechin, V.P. Sakhnenko. Physica D 117, 43 (1998)]. Each bush represents…
A novel machine learning approach is used to provide further insight into atomic nuclei and to detect orderly patterns amidst a vast data of large-scale calculations. The method utilizes a neural network that is trained on ab initio results…
Identifying the intrinsic coordinates or modes of the dynamical systems is essential to understand, analyze, and characterize the underlying dynamical behaviors of complex systems. For nonlinear dynamical systems, this presents a critical…
A simple way to get insights about the possible functional motions of a protein is to perform a normal mode analysis (NMA). Indeed, it has been shown that low-frequency modes thus obtained are often closely related to domain motions…
Normal mode analysis offers an efficient way of modeling the conformational flexibility of protein structures. Simple models defined by contact topology, known as elastic network models, have been used to model a variety of systems, but the…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
Sheaf Neural Networks (SNNs) represent a powerful generalization of Graph Neural Networks (GNNs) that significantly improve our ability to model complex relational data. While directionality has been shown to substantially boost performance…
This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…
We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying…
We introduce in a reduced complex space, a "new coherent sub-sheaf" of the sheaf $\omega\_{X}^{\bullet}$ which has the "universal pull-back property" for any holomorphic map, and which is in general bigger than the usual sheaf of…
Graph Neural Networks (GNNs) have become the de facto standard for learning on relational data. While traditional GNNs' message passing is well suited for vector-valued node features, there are cases in which node features are better…