The paper introduces a mesh‑free, self‑supervised neural operator—called the Normalizing Flow Invertible Solution Transformer (NFIST)—for stochastic mean‑field control (MFC). By reformulating the controlled Fokker–Planck dynamics as a deterministic continuity equation via a probability‑flow ODE and an invertible normalizing‑flow transformer, the authors enable closed‑form score evaluation with linear cost per particle. The resulting operator learns from task prompts (distribution parameters or particle clouds) and can solve unseen MFC tasks in a single forward pass, achieving zero‑shot generalization across applications such as stochastic optimal control, Schrödinger bridges, systemic‑risk control, and obstacle‑avoiding path planning.
By Suyi Gao, Mo Zhou, Rongjie Lai
arXiv:2608. 08608v1 Announce Type: cross Abstract: Fourier neural operators (FNOs) provide efficient nonlocal spectral learning, but varying geometries and independently chosen discretizations remain difficult to accommodate.
By Roberto Nuca, Giovanni Testa, Luca Galimberti, Matteo Parsani
arXiv:2609.35938v1 Announce Type: new
Abstract: This paper proposes an interpretable neural operator framework, the Kernel Operator Network (KernelOnet), which incorporates kernel functions explicitl...
By Yuan Guo, Hanshu Chen, Qiang Xi, Timon Rabczuk, Zhuojia Fu
arXiv:2601. 04120v2 Announce Type: replace-cross Abstract: Optimal control of obstacle problems arises in a wide range of applications and is computationally challenging due to its nonsmoothness, nonlinearity, and bilevel structure.
By Yongcun Song, Shangzhi Zeng, Jin Zhang, Lvgang Zhang
arXiv:2609.36216v1 Announce Type: new
Abstract: Neural operators are typically trained in a supervised fashion, which requires a dataset to be generated with a classical solver. Training them physics...
By Shizheng Wen, Siddhartha Mishra, Marius Zeinhofer
Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning.