Two-dimensional RMSD projections for reaction path visualization and validation

• URL: http://arxiv.org/abs/2512.07329v1
• Date: Mon, 08 Dec 2025 09:15:24 GMT
• Title: Two-dimensional RMSD projections for reaction path visualization and validation
• Authors: Rohit Goswami,
• Abstract summary: We present a method mapping trajectories onto a two-dimension surface defined by a permutation corrected root mean square deviation from the reactant and product configurations.<n>This representation highlights optimization trajectories, identifies endpoint basins, and diagnoses convergence concerns invisible in one-dimensional profiles.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Transition state or minimum energy path finding methods constitute a routine component of the computational chemistry toolkit. Standard analysis involves trajectories conventionally plotted in terms of the relative energy to the initial state against a cumulative displacement variable, or the image number. These dimensional reductions obscure structural rearrangements in high dimensions and may often be trajectory dependent. This precludes the ability to compare optimization trajectories of different methods beyond the number of calculations, time taken, and final saddle geometry. We present a method mapping trajectories onto a two-dimension surface defined by a permutation corrected root mean square deviation from the reactant and product configurations. Energy is represented as an interpolated color-mapped surface constructed from all optimization steps using radial basis functions. This representation highlights optimization trajectories, identifies endpoint basins, and diagnoses convergence concerns invisible in one-dimensional profiles. We validate the framework on a cycloaddition reaction, showing that a machine-learned potential saddle and density functional theory reference lie on comparable energy contours despite geometric displacements.

Related papers

• Global Symmetry and Orthogonal Transformations from Geometrical Moment $n$-tuples [0.304585143845864]
  This paper employs geometrical moments to identify symmetries and estimate transformations, including rotations and mirror transformations, for objects centered at the frame origin.<n>A comprehensive methodology is developed to obtain these functions in n-dimensional space, specifically moment ( n )-tuples.<n> Extensive validation tests are conducted on both 2D and 3D objects to ensure the robustness and reliability of the proposed approach.
  arXiv  Detail & Related papers  (2026-02-08T00:07:11Z)
• Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensions [0.9940728137241214]
  gradient flows of the Kullback--Leibler divergence evolve a distribution toward a target density known only up to a normalizing constant.<n>We introduce new gradient flows of the KL divergence with a remarkable combination of properties.<n>They admit accurate interacting-particle approximations in high dimensions, and the per-step cost scales linearly in both the number of particles and the dimension.
  arXiv  Detail & Related papers  (2026-02-05T02:38:56Z)
• Mapping phase diagrams of quantum spin systems through semidefinite-programming relaxations [1.4860310476969767]
  We show how relaxation methods can be used to generate the phase diagram for one- and two-dimensional quantum systems.<n>We reproduce the phase transitions for the one-dimensional transverse field Ising model and the two-dimensional frustrated bilayer Heisenberg model.
  arXiv  Detail & Related papers  (2025-07-03T19:26:56Z)
• Generalized Linear Mode Connectivity for Transformers [87.32299363530996]
  A striking phenomenon is linear mode connectivity (LMC), where independently trained models can be connected by low- or zero-loss paths.<n>Prior work has predominantly focused on neuron re-ordering through permutations, but such approaches are limited in scope.<n>We introduce a unified framework that captures four symmetry classes: permutations, semi-permutations, transformations, and general invertible maps.<n>This generalization enables, for the first time, the discovery of low- and zero-barrier linear paths between independently trained Vision Transformers and GPT-2 models.
  arXiv  Detail & Related papers  (2025-06-28T01:46:36Z)
• Bridging Geometric States via Geometric Diffusion Bridge [79.60212414973002]
  We introduce the Geometric Diffusion Bridge (GDB), a novel generative modeling framework that accurately bridges initial and target geometric states. GDB employs an equivariant diffusion bridge derived by a modified version of Doob's $h$-transform for connecting geometric states. We show that GDB surpasses existing state-of-the-art approaches, opening up a new pathway for accurately bridging geometric states.
  arXiv  Detail & Related papers  (2024-10-31T17:59:53Z)
• Retrieving space-dependent polarization transformations via near-optimal quantum process tomography [55.41644538483948]
  We investigate the application of genetic and machine learning approaches to tomographic problems. We find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time. We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes.
  arXiv  Detail & Related papers  (2022-10-27T11:37:14Z)
• Symmetric Volume Maps [26.715010694637243]
  We propose a method for mapping between volumes represented as tetrahedral volumetric meshes. Our formulation minimizes a distortion energy designed to extract maps symmetrically, without dependence on the ordering of the source and target domains. We demonstrate our method on a diverse geometric dataset, producing low-distortion matchings that align to the boundary.
  arXiv  Detail & Related papers  (2022-02-05T14:44:37Z)
• A Model for Multi-View Residual Covariances based on Perspective Deformation [88.21738020902411]
  We derive a model for the covariance of the visual residuals in multi-view SfM, odometry and SLAM setups. We validate our model with synthetic and real data and integrate it into photometric and feature-based Bundle Adjustment.
  arXiv  Detail & Related papers  (2022-02-01T21:21:56Z)
• Analytical Modelling of Exoplanet Transit Specroscopy with Dimensional Analysis and Symbolic Regression [68.8204255655161]
  The deep learning revolution has opened the door for deriving such analytical results directly with a computer algorithm fitting to the data. We successfully demonstrate the use of symbolic regression on synthetic data for the transit radii of generic hot Jupiter exoplanets. As a preprocessing step, we use dimensional analysis to identify the relevant dimensionless combinations of variables.
  arXiv  Detail & Related papers  (2021-12-22T00:52:56Z)
• Tensor Component Analysis for Interpreting the Latent Space of GANs [41.020230946351816]
  This paper addresses the problem of finding interpretable directions in the latent space of pre-trained Generative Adversarial Networks (GANs) Our scheme allows for both linear edits corresponding to the individual modes of the tensor, and non-linear ones that model the multiplicative interactions between them. We show experimentally that we can utilise the former to better separate style- from geometry-based transformations, and the latter to generate an extended set of possible transformations.
  arXiv  Detail & Related papers  (2021-11-23T09:14:39Z)
• Improving Metric Dimensionality Reduction with Distributed Topology [68.8204255655161]
  DIPOLE is a dimensionality-reduction post-processing step that corrects an initial embedding by minimizing a loss functional with both a local, metric term and a global, topological term. We observe that DIPOLE outperforms popular methods like UMAP, t-SNE, and Isomap on a number of popular datasets.
  arXiv  Detail & Related papers  (2021-06-14T17:19:44Z)
• Matrix factorisation and the interpretation of geodesic distance [6.445605125467574]
  Given a graph or similarity matrix, we consider the problem of recovering a notion of true distance between the nodes. We show that this can be accomplished in two steps: matrix factorisation, followed by nonlinear dimension reduction.
  arXiv  Detail & Related papers  (2021-06-02T16:11:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.