MS175 - Nonlocality and Machine Learning

Organized by: O. Burkovska (Oak Ridge National Laboratory, United States), C. Glusa (SANDIA National Laboratories, United States) and Y. Yu (Lehigh University, United States)
Keywords: coarse-graining, kernel identification, physics-informed machine learning, scientific machine learning, uncertainty quantification, Nonlocal modeling
Nonlocal models have become essential tools for capturing complex physical phenomena involving long-range interactions, memory effects, and multiscale structures. By extending the classical framework of local partial differential equations to incorporate finite-range and integral interactions, nonlocal formulations are well-suited for problems in fracture mechanics, anomalous diffusion, porous media, and heterogeneous materials. These models offer increased accuracy and provide natural frameworks for coarse-graining and upscaling, especially in systems with embedded length scales or evolving microstructures. Nonlocality also plays a central role in coarse-graining and reduced-order modeling, where eliminating fine-scale degrees of freedom give rise to nonlocal closure relations. These nonlocal closures, which incorporate memory and spatial interactions, account for unresolved dynamics and enable more accurate, interpretable surrogate models across scales. Concurrently, the rapid advancement of machine learning (ML) and artificial intelligence (AI) has reshaped how models are constructed, calibrated, and deployed across the sciences. Recent advances suggest that there is a natural synergy between nonlocality and ML: nonlocal operators can be learned from data using kernel methods or neural networks; neural operators naturally encode nonlocal mappings and structure. Moreover, nonlocality arises not only in physical systems but also in modern learning algorithms, through nonlocal gradients, attention mechanisms, and architectures such as graph neural networks and transformers, highlighting deep parallels between physical and algorithmic nonlocality. This minisymposium invites contributions at the interface between nonlocal modeling and machine learning/AI, that address diverse scientific and engineering problems. We believe that the following areas will be especially important for future research developments: • Neural operators • Learning nonlocal operators and kernels from data • Nonlocal modeling for damage, diffusion, and materials with microstructure • Data-driven homogenization and coarse-graining • Machine learning and nonlocal gradients • Data-driven nonlocal constitutive models • Machine learning for diffusion problems • Heterogeneities and nonlocality • Probabilistic modeling of nonlocal interactions • Uncertainty quantification for nonlocal and ML-augmented models