Related papers: Riemannian Denoising Model for Molecular Structure…

This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…

It is known that the trajectory of an endoreversibly driven system with minimal dissipation is a geodesic on the equilibrium state space. Thereby, the state space is equipped with the Riemannian metric given by the Hessian of the free…

This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the…

Rapid determination of molecular structures can greatly accelerate workflows across many chemical disciplines. However, elucidating structure using only one-dimensional (1D) NMR spectra, the most readily accessible data, remains an…

Accurately calculating energies and atomic forces with linear-scaling methods is a crucial approach to accelerating and improving molecular dynamics simulations. In this paper, we introduce HamGNN-DM, a machine learning model designed to…

This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…

The simulation of complex nonlinear engineering systems such as compressible fluid flows may be targeted to make more efficient and accurate the approximation of a specific (scalar) quantity of interest of the system. Putting aside modeling…

Machine Learning (ML) techniques are revolutionizing the way to perform efficient materials modeling. Nevertheless, not all the ML approaches allow for the understanding of microscopic mechanisms at play in different phenomena. To address…

Molecular dynamics (MD) has long been the de facto choice for simulating complex atomistic systems from first principles. Recently deep learning models become a popular way to accelerate MD. Notwithstanding, existing models depend on…

Bayesian optimization is a data-efficient technique which can be used for control parameter tuning, parametric policy adaptation, and structure design in robotics. Many of these problems require optimization of functions defined on…

Reduced density matrices (RDMs) are fundamental in quantum information processing, allowing the computation of local observables, such as energy and correlation functions, without the exponential complexity of fully characterizing quantum…

In this paper, we demonstrate a computationally efficient new approach based on deep learning (DL) techniques for analysis, design, and optimization of electromagnetic (EM) nanostructures. We use the strong correlation among features of a…

We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

As vast databases of chemical identities become increasingly available, the challenge shifts to how we effectively explore and leverage these resources to study molecular properties. This paper presents an active learning approach for…

Nowadays, the coupling of electronic structure and machine learning techniques serves as a powerful tool to predict chemical and physical properties of a broad range of systems. With the aim of improving the accuracy of predictions, a large…

In probabilistic modeling, parameter estimation is commonly formulated as a minimization problem on a parameter manifold. Optimization in such spaces requires geometry-aware methods that respect the underlying information structure. While…

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schr\"odinger equation is mapped onto a…

Using molecular simulation to aid in the analysis of neutron reflectometry measurements is commonplace. However, reflectometry is a tool to probe large-scale structures, and therefore the use of all-atom simulation may be irrelevant. This…

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this…

Machine learning (ML) can be used to construct surrogate models for the fast prediction of a property of interest. ML can thus be applied to chemical projects, where the usual experimentation or calculation techniques can take hours or days…