We introduce a class of nonlocal Hamilton–Jacobi equations in which the classical gradient is replaced by a finite-horizon interaction operator, thereby embedding an intrinsic length scale directly into first-order nonlinear evolution. In contrast with integro-differential formulations where nonlocality appears as an a...
K. Enakoutsa· Mathematics and mechanics of...· 0 citations
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Graph neural networks and spectral embeddings aggregate local neighbourhoods and so miss the global metric properties—growth rate, hyperbolicity, boundary at infinity—that govern large-scale structure in hierarchical, networked, and negatively curved data. We propose a fr...
K. Enakoutsa· Neural Processing Letters· 0 citations
Neural operators can accelerate repeated nonlinear mechanics calculations, but their accuracy can deteriorate as operating conditions move beyond the training range. This work studies whether high-fidelity solutions acquired during use can be reused to adapt a neural operator and improve subsequent mechanics-based comm...
Prashant K. Jha, K. Enakoutsa, Ian Galloway et al.· 0 citations
We develop a geometric and variational framework for nonlocal continuum mechanics in which nonlocal interaction kernels are reinterpreted as probabilistic transition structures on the configuration space, placing the theory within the setting of statistical manifolds equipped with the Fisher–Rao metric. After normali...
K. Enakoutsa· Mathematics and mechanics of...· 0 citations
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