arXiv Machine Learning
Neural Operator Splitting for Fluid Dynamics in Complex Geometry
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Neural Operator Splitting for Fluid Dynamics in Complex Geometry
Solving dynamical systems in complex and diverse geometries remains challenging for both numerical solvers and learning-based surrogate models. We propose Neural Operator Splitting, a framework for le...
arXiv Machine Learning
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Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows
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arXiv Machine Learning
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Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations
arXiv:2605. 04853v2 Announce Type: replace Abstract: We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error.
arXiv Machine Learning
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ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching
arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.
arXiv Machine Learning
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LSR-Net: Learning the Forward Evolution Operator for Nonlinear Fluid Dynamics
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arXiv Machine Learning
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Discretization-independent operator learning for partial differential equations
arXiv:2507.07292v2 Announce Type: replace Abstract: We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for inpu...