Generative Diffusion Surrogates with Analytical Variance Schedule

Stochastic transport describes physical systems in which an initially structured distribution spreads under unresolved forcing, scattering, or heterogeneous media. Useful surrogates for such systems should be probabilistic, time-resolved, and able to represent non-Gaussian distributional structure. Generative diffusion models, which corrupt data with Gaussian noise and learn a reverse flow back to structured states, have these properties. Their noise schedules, however, are usually chosen heuristically: image and audio generation---the canonical use cases---provide no physical clock. In transport, by contrast, the variance, or mean-square displacement, is often known from macroscopic theory or empirical scaling even when the full distribution is not. Here we prescribe the forward noising rate as the time derivative of this variance, turning generative time into a calibrated transport clock. The variance path is enforced by construction, while the learned score field represents how non-Gaussian structure inherited from entrance data is smoothed along that path, requiring no intermediate-time physical transport data. For ballistic-to-diffusive transport in turbulent plasmas, the surrogate matches test-particle distributions, reproduces the laboratory-measured variance scale, and tracks the simulated kurtosis evolution without schedule tuning, enabling calibrated emulation and likelihood-based inference.

Physics Attention Transformer Surrogate for Rapid Vertical Instability Growth Rate Prediction: Alcator C-Mod to SPARC

In this work, we investigate rapid prediction of the dominant $n{=}0$ vertical instability growth rate in C-Mod and SPARC equilibria, where nonrigid free boundary response models are too slow for control cycle use. Using a Physics Attention Transformer trained on MEQ-FGE-L labels, we predict both the scalar growth rate and the associated two dimensional perturbed toroidal current density. We find mean absolute errors of 5.4~s$^{-1}$ on held out C-Mod equilibria and 12.7~s$^{-1}$ on synthetic SPARC cases, with spatial eigenfunction errors near 5\%. We also compared PAT with operator based ML models : FNO2D and DeepONet, where we found PAT predicts a much lower normalised growth rate error and improved spatial reconstruction. These results indicate that PAT can reproduce MEQ-FGE-L outputs at control relevant latency and could support future studies of growth rate headroom monitoring and proximity aware shape control.

AI Surrogate Modeling for Real-Time Tokamak Equilibrium Prediction: Benchmarking Neural Architectures and Validation on EXL-50U

Fast and reliable plasma equilibrium prediction is essential for real-time tokamak operation and control, but conventional Grad-Shafranov (GS) solvers are often too costly for real-time deployment. We develop an AI surrogate framework and benchmark five architectures (MLP, CNN, FNO, Transformer, and KAN) on a numerical GS database with 100,000 IID and 10,000 OOD samples. Under a unified protocol, we evaluate accuracy, inference efficiency, model scaling, and robustness. We also establish device-level validation on the EXL-50U tokamak by linking numerical GS solutions, surrogate predictions, and the standard Shape Editor reference to assess simulation-to-device consistency. The surrogates achieve errors of $10^{-3}$-$10^{-2}$ relative to GS solutions, while the GS-to-device discrepancy remains at $10^{-3}$. Transformer gives the best IID accuracy, whereas CNN offers the best balance of accuracy, robustness, and speed, reaching 0.7 ms TensorRT latency. On unseen plasma geometries and parameter regimes, CNN and FNO show the strongest extrapolation stability, with 4%-5% relative $L_2$ error, while models with weaker inductive biases degrade more substantially. Scaling data and model capacity improves interpolation but not necessarily extrapolation, revealing a trade-off between capacity and OOD generalization. Overall, this work provides a systematic, device-consistent benchmark for AI-based GS prediction and practical guidance for selecting reliable surrogates for real-time plasma control and fusion applications.

Data-Driven Reconstruction of Spatially Resolved Electron and Ion Energy Distributions from Macroscopic Plasma Quantities with Deep Neural Networks

Spatially resolved EEDFs/IEDFs provide essential kinetic information about low-temperature plasmas (LTPs) and play a central role in determining transport, chemical reaction rates, and plasma surface interactions. While kinetic simulations directly resolve these distributions, experimental measurements remain challenging and are often invasive, spatially limited, or require assumptions regarding the distribution shape such as a Maxwellian. However, several macroscopic plasma observables can be measured non-invasively using advanced diagnostic techniques, providing spatially resolved information about the plasma state. An important inverse problem is therefore whether readily measurable macroscopic plasma quantities contain sufficient information to reconstruct the underlying kinetic state. In this work, we investigate this problem by learning a nonlinear mapping from spatially resolved macroscopic plasma observables to the corresponding spatially resolved EEDFs/IEDFs using a deep learning framework. Paired datasets comprising 2D macroscopic observables and spatially resolved EDFs are generated using 2D-3V PIC-MCC simulations. Three representative learning paradigms, a U-Net, a FNO, and a MeshGraphNet, are employed in this study to learn this inverse mapping. The predicted EDFs reproduce both bulk plasma and sheath characteristics with good agreement to the PIC-MCC reference data, with the FNO providing the best overall performance. Beyond conventional metrics, physics-based validation demonstrates that the reconstructed EDFs accurately recover the corresponding density and temperature, and rate coefficients. These results demonstrate that macroscopic plasma observables encode sufficient information to infer important kinetic properties in LTPs, providing a potential foundation for surrogate kinetic modeling and next-generation plasma diagnostics.

SafeDivertor: Faithful Divertor Heat Flux Reconstruction from Macroscopic Plasma State Signals via Time-Frequency Prior Exploitation

Divertor heat-flux analysis is essential for understanding plasma-wall interactions and protecting plasma-facing components in magnetic-confinement fusion devices, while conventional infrared-based inversion is usually performed after discharge and requires heat-conduction modeling with device-specific material properties, divertor geometry, and boundary conditions. Rather than accelerating this conventional infrared-based inversion paradigm, we introduce a new online-oriented signal-based reconstruction paradigm that directly reconstructs time-resolved radial heat-flux profiles from multi-source macroscopic plasma-state signals available during discharge. To enable systematic study of this task, we construct \textbf{DivMPS2HF}, a multi-source discharge dataset that provides the data foundation and benchmark for signal-based divertor heat-flux reconstruction. We further propose \textbf{SafeDivertor}, a task-driven framework designed to address the key challenges of signal-based heat-flux reconstruction. It employs physical prior-aware initialization to provide radial-distribution guidance for target channels, input perturbation to reduce over-reliance on specific heterogeneous signals, spectral-aware reconstruction optimization to exploit time-frequency priors and preserve transient dynamics, and progressive training to stabilize the optimization of these complementary objectives. Experiments on DivMPS2HF demonstrate that SafeDivertor achieves the best overall performance among the evaluated time-series baselines across all five metrics, establishing a new performance benchmark for signal-based divertor heat-flux reconstruction. The source code will be released on https://github.com/Event-AHU/OpenFusion

Physics-Informed Neural Networks for Complex Eigenfrequency Identification and Mode Structure Reconstruction of the Ground-State ITG Branch

Physics-informed neural networks (PINNs) combine sparse observations with physical equations, providing an important approach for modeling complex plasma processes and inferring unknown physical quantities. The steep-gradient pedestal of high-confinement-mode tokamaks is closely linked to plasma confinement and edge transport. Analyzing ion-temperature-gradient (ITG) drift waves in this region requires jointly identifying complex eigenfrequencies and reconstructing two-dimensional complex-valued mode fields. Localized high-frequency oscillations, strong real-imaginary coupling, and nonlinear coupling between the mode field and eigenfrequency challenge PINN representation and joint optimization. To address these challenges, we propose a physics-informed neural framework combining Fourier feature encoding, complex-valued feature propagation, and three-stage training. Under sparse observations and physical constraints, it jointly solves for the complex eigenfrequency and mode field of a representative ground-state ITG branch. Experiments show that the framework accurately recovers the target complex eigenfrequency and two-dimensional complex-valued mode field and outperforms representative PINN baselines. It also provides a basis for analyzing higher-order and multiple-branch drift-wave modes.

Agentic Stage-One Stellarator Optimization: Autonomous Multi-Objective Search for Finite-Beta Equilibria

Stage-one stellarator design searches a high-dimensional family of three-dimensional plasma boundaries and fixed-boundary MHD equilibria for configurations that jointly meet requirements on confinement, field-line topology, force balance, stability proxies, and geometry. These specifications do not provide a general constructive map to a validated finite-beta equilibrium. High-quality targets are commonly developed through iterative numerical optimization whose outcome depends on the initial configuration, active Fourier resolution, objective priorities, and local solver budget. Coordinating this process is computationally costly and expert-intensive, limiting both design throughput and the production of consistently evaluated data. We present a proof of concept for \emph{agentic} stage-one optimization. A bounded language-model agent diagnoses the current equilibrium and selects the next local optimization experiment, while deterministic DESC execution owns prescribed profiles and flux, symmetry, metric evaluation, solver validity, and acceptance. On a common-budget subset from an expanding finite-beta campaign, the number of gate-valid configurations increases from five inputs to nineteen outputs; median Boozer QS RMS decreases from $2.39\times10^{-4}$ to $1.07\times10^{-4}$, and median maximum principal curvature decreases from $62.56$ to $33.00\,\mathrm{m}^{-1}$. A complementary long route achieves a $9.10\times$ QS reduction while repairing magnetic-well and curvature defects. The system also records every attempted local action as transition evidence, yielding 734 structured parent--action--outcome records in the reported experiments. These results show that agentic outer-loop control can sustain finite-beta, multi-objective search and turn repeated optimization into a scalable source of improved equilibria and reusable decision data.

Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs

Parameterized and coupled partial differential equations (PDEs) are central to modeling phenomena in science and engineering, yet neural operator methods that address both aspects remain limited. We extend Fourier neural operators (FNOs) with minimal architectural modifications along two directions. For parameterized dynamics, we propose a hypernetwork-based modulation that conditions the operator on physical parameters. For coupled systems, we conduct a systematic exploration of architectural choices, examining how operator components can be adapted to balance shared structure with cross-variable interactions while retaining the efficiency of standard FNOs. Evaluations on benchmark PDEs, including the one-dimensional capacitively coupled plasma equations and the Gray-Scott system, show that our methods achieve up to 55-72% lower errors than strong baselines, demonstrating the effectiveness of principled modulation and systematic design exploration.

Cycle-Consistent and Uncertainty-Aware Neural Surrogates for Tokamak Edge Plasmas

The boundary and divertor plasma govern how a tokamak exhausts power and particles, setting heat fluxes, target conditions, and the onset of detachment. Predicting these quantities is essential for operating current and future devices, but edge simulations that resolve them are too slow for parameter scans, optimization, or real-time control. Machine-learning surrogates offer a fast alternative, yet most are forward-only: they cannot recover input parameters from observations or assess the reliability of their predictions. We introduce a cycle-consistent neural surrogate for edge plasmas, combining a conditional U-Net forward model with an optimization-based inverse method built on the frozen forward network. The forward model maps five control parameters to two-dimensional plasma-state fields on the SOLPS-ITER mesh; the inverse method enforces consistency between forward and inverse predictions, a self-supervised quality check needing no ground-truth labels at inference. An ensemble of multilayer perceptrons also predicts electron temperature and density profiles at the outboard midplane and divertor targets, with uncertainty estimates that flag where more simulations are needed. The forward model achieves normalized root-mean-square errors below 2.6% and Pearson correlations above 0.95 for all fields. Cycle-consistency regularization raises the average cyclical $R^2$ from 0.59 to 0.99 without degrading forward accuracy and enables recovery of the core fueling rate; all five control parameters are recovered with Pearson $r\ge0.97$. A $k$-d tree warm start yields a database completion rate above 95%, versus roughly 30% outright failures when cold-started. With about $4\times10^6$ parameters, the model produces full 2D predictions in milliseconds, five to six orders of magnitude faster than SOLPS-ITER, enabling real-time control, parameter scans, uncertainty analysis, and digital twins.

Bidirectional Autoregressive Latent Diffusion for Forward and Inverse Magnetohydrodynamics

This work presents a new bidirectional autoregressive latent diffusion approach for predicting the evolution of multiple fields (mass density, pressure, velocity, and magnetic field components) for magnetohydrodynamics. We show that this bidirectional flow can be used as a self-supervised consistency metric for uncertainty and error estimation, which enables the model to estimate test-time uncertainty and error without access to ground truth, by comparing how closely flowing forwards and backwards in time returns to the same predicted fields. We also demonstrate this methods's potential to serve as a non-invasive plasma diagnostic, and show how adaptive feedback can be used to make the model more robust based on sparse diagnostics or limited views/measurements.

Towards Data-Efficient Cross-Device Generalization of Grad-Shafranov Equilibria via Transfer Learning Neural Operator

Real-time reconstruction of magnetohydrodynamic equilibria is essential for plasma shaping, stability assessment and feedback control in magnetic confinement fusion. However, Grad-Shafranov equilibrium calculations remain largely device-specific and iterative, limiting their use in latency-constrained control settings. Existing neural approaches can accelerate individual equilibrium predictions, but they do not generally provide reusable models across changing plasma boundaries or tokamak geometries. Here we show that equilibrium reconstruction can be recast as a cross-device operator learning problem. We develop a domain-specific neural operator framework that maps geometry and profile parameters directly to the poloidal flux field, replacing repeated solve-on-demand computation with amortized operator inference. Using the analytically tractable Solov'ev family as a controlled Grad-Shafranov testbed, we generate equilibria across eight geometrically distinct tokamak-like configurations and benchmark five neural operator architectures under four transfer-learning strategies. Single-geometry pretraining gives poor transfer to unseen devices, whereas multi-geometry pretraining enables data-efficient adaptation. The Wavelet Neural Operator gives the strongest cross-geometry performance, reaching mean relative L2 errors below 4% with 100 labelled target equilibria and below 2% with full fine-tuning. The predicted magnetic fields satisfy the divergence-free constraint to numerical precision, and four architectures achieve millisecond or sub-millisecond inference. These results identify neural operator pretraining as a route towards reusable, real-time equilibrium inference across fusion device configurations.

Provable imitation learning for control of instability in partially-observed Vlasov--Poisson equations

We consider the stabilization of Vlasov--Poisson plasma dynamics, a central control problem in nuclear fusion. Our focus is the gap between what an ideal controller would use and what experiments can actually observe: while optimal policy may rely on the full phase-space state, practical feedback is typically limited to sparse macroscopic diagnostics. We therefore study imitation learning methods that distill a fully observed expert policy into controllers operating only on macroscopic measurements. We show the stability guarantees of the learned policy, where the error floor depends on the minimal behavior cloning loss achievable under the observation constraints. We further characterize this minimal loss in terms of a notion of entropy that quantifies the complexity of the initial distribution. Our results demonstrates the theoretical feasibility of learning stabilizing feedback policies for kinetic plasma dynamics from macroscopic observations, and exhibits the adaptivity of the learning approach to low-complexity structures. Through extensive numerical experiments, we validate our theory and show that the learned policies can stabilize the system using only macroscopic observations, within a significantly longer time horizon than non-adaptive baseline controllers.