arXiv:2603. 29237v2 Announce Type: replace Abstract: Enforcing prescribed global integral constraints in mesh-free neural PDE solvers is challenging in high-dimensional domains.
By Zhangyong Liang, Huanhuan Gao
arXiv:2607. 15291v1 Announce Type: cross Abstract: We develop a physics-informed neural network (PINN) framework for nonlocal partial differential equations arising in dynamic density functional theory (DDFT).
By Dimitrios Gourzoulidis, Soumaya Elkantassi, Serafim Kalliadasis
arXiv:2607. 20378v1 Announce Type: new Abstract: Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability.
By Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee, Aida Pakniyat, Dara Rahmati, Saeid Gorgin
arXiv:2606. 08343v1 Announce Type: new Abstract: We introduce GENERIC-FNO, the first neural operator to embed the full GENERIC (metriplectic) structure of nonequilibrium thermodynamics -- reversible, energy-conserving dynamics and irreversible, entropy-producing dynamics coupled through the degeneracy conditions -- directly in function space.
By Jason Sulskis, Sathya Ravi
arXiv:2606. 19562v1 Announce Type: new Abstract: This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations.
By Gabriel F. Barros, R\^omulo M. Silva, Alvaro L. G. A. Coutinho
arXiv:2607. 25624v1 Announce Type: new Abstract: Positive quadratic networks admit the low-rank representation f_U(x)=x^top UU^top x, where Uinmathbb{R}^{dtimes r} is identifiable only up to right orthogonal multiplication, representing a rank-r PSD matrix Q=UU^top.
By Pengcheng Cheng