Related papers: A Physics-informed Sheaf Model
As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex systems where extensive structure is available, but must be drawn…
This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…
The normal distribution plays a central role in information theory - it is at the same time the best-case signal and worst-case noise distribution, has the greatest representational capacity of any distribution, and offers an equivalence…
Nearly all standard force fields employ the 'sum-of-spheres' approximation, which models intermolecular interactions purely in terms of interatomic distances. Nonetheless, atoms in molecules can have significantly non-spherical shapes,…
Recently, machine learning (ML) has been used to address the computational cost that has been limiting ab initio molecular dynamics (AIMD). Here, we present GNNFF, a graph neural network framework to directly predict atomic forces from…
Molecular dynamics (MD) simulations are a central tool in science and engineering enabling the study of dynamical behavior and the link between microscopic structure and macroscopic function. Their high computational cost, however, has…
We study the shear momentum diffusion and related modes of a strongly coupled $(2+1)$-dimensional conformal field theory at finite temperature and chemical potential, using a dual holographic description. We consider a space-time filling…
Neutrino oscillations encode fundamental information about neutrino masses and mixing parameters, offering a unique window into physics beyond the Standard Model. Estimating these parameters from oscillation probability maps is, however,…
Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on…
Interannual variability in the Southern Ocean is investigated via nonlinear Laplacian spectral analysis (NLSA), an objective eigendecomposition technique for nonlinear dynamical systems that can simultaneously recover multiple timescales…
Neural Sheaf Diffusion (NSD) generalizes diffusion-based Graph Neural Networks by replacing scalar graph Laplacians with sheaf Laplacians whose learned restriction maps define a task-adapted geometry. While the diffusion limit of NSD is…
A semi-analytical dynamical mean-field approximation (DMA) has been developed for large but finite $N$-unit active rotator (AR) networks subject to individual white noises. Assuming weak noises and the Gaussian distribution of state…
Molecular mechanics (MM) potentials have long been a workhorse of computational chemistry. Leveraging accuracy and speed, these functional forms find use in a wide variety of applications in biomolecular modeling and drug discovery, from…
Computational studies of chemical reactions in complex environments such as proteins, nanostructures, or on surfaces require accurate and efficient atomistic models applicable to the nanometer scale. In general, an accurate parametrization…
We demonstrate that gauge equivariant diffusion models can accurately model the physics of non-Abelian lattice gauge theory using the Metropolis-adjusted annealed Langevin algorithm (MAALA), as exemplified by computations in two-dimensional…
We suggest to utilize the rich information content about microstructural tissue properties entangled in asymmetric balanced steady-state free precession (bSSFP) profiles to estimate multiple diffusion metrics simultaneously by neural…
This research undertakes a comprehensive exploration of neutrino mass model grounded in $A_4$ discrete non-Abelian modular symmetry formulated within a linear seesaw framework that modifies the conventional type-I seesaw structure with a…
In this work, we propose a novel generative model for mapping inputs to structured, high-dimensional outputs using structured conditional normalizing flows and Gaussian process regression. The model is motivated by the need to characterize…
We study the relaxation of the Peano chain's deformations in the presence of gaussian noise. The D=2 spring network which models the chain's elasticity has no bulk, but only boundaries:its continuum version would be a flat and thin elastic…
Graph Neural Networks (GNNs) conventionally rely on standard Laplacian or adjacency matrices for structural message passing. In this work, we substitute the traditional Laplacian with a Doubly Stochastic graph Matrix (DSM), derived from the…