The paper introduces equation recast, a method that transforms parametric operator learning into learning a single canonical operator. By analytically deriving parameter-induced variations from the governing equations and incorporating them as effective sources, the approach enables zero‑shot predictions across new parameter regimes and supports extrapolation in multi‑parameter, nonlinear, and singular PDE settings. It also integrates sparse heterogeneous datasets, uses loss of convergence as an internal warning, and demonstrates unification of electron‑temperature data from multiple tokamak geometries in high‑fidelity nuclear fusion simulations.
arXiv:2509. 05510v3 Announce Type: replace-cross Abstract: Continued progress in inertial confinement fusion (ICF) requires solving inverse problems relating experimental observations to simulation input parameters, followed by design optimization.
arXiv:2606. 15512v1 Announce Type: new Abstract: Real-time reconstruction of magnetohydrodynamic equilibria is essential for plasma shaping, stability assessment and feedback control in magnetic confinement fusion.
The paper introduces Neptune, a method that uses independent coordinate neural networks to infer parameter fields in multi-physics PDEs from sparse measurements. Neptune can accurately estimate parameters with nonlinear, spatiotemporal variations, outperforming existing techniques by reducing estimation errors by up to two orders of magnitude and improving dynamic response predictions by a factor of ten. It also demonstrates strong physical extrapolation, enabling reliable predictions beyond the training data.
The paper demonstrates that a neural solver trained on a single condition can generate a reusable response space via its output Jacobian, enabling efficient cross‑condition solution transfer. By introducing Linearized Subspace Transfer (LST) and Active Transfer Modeling (ATM), the authors recover target solutions through residual minimization and selectively acquire additional response spaces based on coverage indicators. Experiments on six PDE systems show that this approach reduces error and offline construction cost compared to physics‑informed baselines, achieving significant accuracy gains and rapid target adaptation.
arXiv:2602. 09303v2 Announce Type: replace Abstract: We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference.
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv:2608. 04778v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) incorporate governing equations into neural-network training and can approximate PDE solutions without requiring large observational datasets.
arXiv:2608.24049v1 Announce Type: new Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...
arXiv:2508. 09156v3 Announce Type: replace-cross Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.
arXiv:2606. 07550v1 Announce Type: cross Abstract: Offline reinforcement learning (RL) offers a promising route for developing plasma controllers from historical tokamak data, since online trial-and-error on real devices is costly and risky.
arXiv:2606. 29440v1 Announce Type: new Abstract: Repeatedly solving parametric PDEs is essential for uncertainty quantification, design optimization and inverse problems, but conventional neural operators require expensive non-convex training.
arXiv:2608.22026v1 Announce Type: new Abstract: Accurate simulation of the long-time evolution of systems governed by partial differential equations (PDEs) is central to scientific computing. Among e...