arXiv:2606.27140v1 Announce Type: new Abstract: We develop the fTNN, a deterministic tensor neural network subspace method for problems involving the fractional Laplacian on bounded domains, taking the fractional Poisson equation and time-dependent fractional advection-diffusion equation as typical representatives. The work employs a geometry-adapted integration split featuring a spatially dependent near-field radius, which decomposes the fractional Laplacian into three contributions: a singular near field, a regular interior far field, and an analytical exterior far field. Then the singular r
This research is part of ongoing efforts to apply advanced computational methods like neural networks to complex scientific and engineering problems, continuously advancing the capabilities of AI.
Advanced numerical solvers are critical infrastructure for scientific discovery and engineering, enabling more accurate and efficient simulations across various domains.
This development offers a potentially more efficient and accurate method for solving fractional partial differential equations, which appear in diverse fields from physics to finance.
- · Computational scientists
- · Engineers in materials science
- · Financial modelers
- · AI researchers
- · Traditional numerical methods with high computational cost
Improved simulation accuracy and speed for systems involving fractional calculus.
Accelerated research and development in fields relying on these simulations, potentially leading to new material discoveries or better climate models.
Enhanced AI capabilities for scientific discovery, enabling data-driven solutions to previously intractable problems.
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Read at arXiv cs.LG