arXiv:2606. 02582v1 Announce Type: cross Abstract: In this paper, we study the efficient numerical solution of Darcy equations in strongly heterogeneous media with high-contrast permeability and propose a hybrid framework that combines learning with multiscale numerical methods.
arXiv:2609.08034v1 Announce Type: new Abstract: Localized dimensionality reduction improves the scalability of operator learning for high-dimensional partial differential equations (PDEs), but indepe...
arXiv:2606. 30495v1 Announce Type: cross Abstract: Solving heterogeneous Helmholtz equations at high wavenumbers remains challenging because the discretized operator is indefinite, pollution degrades phase accuracy, and scalar coarse-grid correction can discard the local phase and propagation-direction information carried by oscillatory errors.
arXiv:2607. 28456v1 Announce Type: cross Abstract: Solving large, sparse linear systems is a core task in scientific computing, and efficient iterative solvers rely critically on effective and robust preconditioning.
arXiv:2607. 07718v1 Announce Type: cross Abstract: Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations.
The paper introduces a physics-informed neural network (PINN) framework for modeling fluid flow in dual‑network porous media, specifically addressing double porosity/permeability (DPP) systems. The framework embeds governing equations and boundary conditions into the loss function with adaptive weighting, employs dynamic collocation point selection, and uses shared trunk architectures to efficiently capture coupled pore‑network behavior. It is mesh‑free, accurately handles discontinuities across layered domains, and supports robust inverse analysis for parameter identification, with a systematic convergence study validating its stability and accuracy.
arXiv:2607. 12570v1 Announce Type: cross Abstract: Multiscale problems are notoriously difficult to tackle using traditional numerical methods, as accurately resolving fine-scale features often requires prohibitively fine discretizations.
arXiv:2603. 11250v2 Announce Type: replace-cross Abstract: Accurate modeling of gas flow through porous media is critical for many technological applications, including reservoir performance prediction, carbon capture and sequestration, and fuel cells and batteries.
arXiv:2608. 11572v1 Announce Type: new Abstract: Coarse-grid numerical solvers can substantially reduce the computational cost of time-dependent PDE simulation, but under-resolution often degrades both the trajectory and the spatial fidelity of the solution.
The paper introduces LatentDDM, a neural operator framework that first pretrains on small subdomains and then adapts to new settings by training only a lightweight composition module. Experiments on steady Darcy flow and unsteady airfoil flow show that this approach reduces error by 36‑56% on larger domains and improves 20‑step rollouts, outperforming capacity‑matched full‑domain models. The study highlights co‑designed local pretraining and composition‑level transfer as a promising design principle for physical foundation models.
arXiv:2601. 20496v2 Announce Type: replace-cross Abstract: Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications.
arXiv:2609.22349v1 Announce Type: cross Abstract: Transient pressure diffusion in heterogeneous porous media becomes difficult to resolve efficiently when permeability is discontinuous and spans seve...
arXiv:2412.04596v3 Announce Type: replace Abstract: We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations (PDEs). The appro...