Kanad Sen | Searcharxiv

arXiv2026

Scale-Aware Learning of Chaotic Dynamics on Unstructured Meshes via Binned Spectral Losses

Surrogate modeling for high-dimensional nonlinear dynamical systems that exhibit chaos requires mechanisms that preserve not only pointwise accuracy but also the scale-dependent structure of physical fields. Bandwise spectral power losses, such as the binned spectral loss function, provide such supervision on structured grids, where Fourier modes define a standard frequency decomposition. On irregular meshes, however, no canonical Fourier basis exists, and spectral representations must be constructed from graph operators induced by mesh connectivity and geometry. In this study, we extend the binned spectral power loss for application to unstructured-mesh surrogate modeling of nonlinear dynamical systems. This is obtained by replacing Fourier bands with graph-Laplacian frequency bands, and we provide scalable Chebyshev and multilevel approximations for improving long-horizon rollout fidelity. In its full-spectrum form, our approach uses graph Laplacian eigenspaces to provide a graph analogue of Fourier band-power matching, but incurs the high cost of spectral decomposition. As a scalable approximation, we replace exact band projectors with sparse Chebyshev polynomial graph filters, avoiding explicit eigendecomposition. When utilizing multilevel graph architectures, we introduce Graph Laplacian Energy Alignment for Meshes (GLEAM), which applies retained-subspace scale-aware supervision across graph hierarchies so that coarse and fine representations are regularized during autoregressive rollout. Our results show that the proposed spectral losses improve long-horizon rollout fidelity and preserve statistical invariants for the forecasting of turbulent flows on unstructured meshes, compared to deterministic baselines.

cs.LG↗

arXiv2024

Graph Residual based Method for Molecular Property Prediction

Machine learning-driven methods for property prediction have been of deep interest. However, much work remains to be done to improve the generalization ability, accuracy, and inference time for critical applications. The traditional machine learning models predict properties based on the features extracted from the molecules, which are often not easily available. In this work, a novel Deep Learning method, the Edge Conditioned Residual Graph Neural Network (ECRGNN), has been applied, allowing us to predict properties directly only the Graph-based structures of the molecules. SMILES (Simplified Molecular Input Line Entry System) representation of the molecules has been used in the present study as input data format, which has been further converted into a graph database, which constitutes the training data. This manuscript highlights a detailed description of the novel GRU-based methodology, ECRGNN, to map the inputs that have been used. Emphasis is placed on highlighting both the regressive property and the classification efficacy of the same. A detailed description of the Variational Autoencoder (VAE) and the end-to-end learning method used for multi-class multi-label property prediction has been provided as well. The results have been compared with standard benchmark datasets as well as some newly developed datasets. All performance metrics that have been used have been clearly defined, and their reason for choice.

q-bio.QM↗