Reconstructing spatially resolved plasma dynamics from few sensors is essential for diagnostics, reduced-order modelling and control, yet remains difficult because the sparse measurements incompletely constrain multiscale, regime-dependent degrees of freedom. The Shallow Recurrent Decoder (SHRED) partially addresses spatial sparsity by using measurement histories; however, its fully connected decoder provides no explicit mechanism for resolving spatial structure across scales or explicit parametric dependency. We introduce the Recurrent Multiscale Affine-modulated Inference Network (ReMAIN), which preserves SHRED's recurrent temporal encoding but replaces its decoder with a U-Net whose feature hierarchy is conditioned by the recurrent state through feature-wise linear modulation. The temporal representation supplies both a dense prior and scale-specific modulation throughout the U-Net. A parametric extension jointly embeds the operating condition and sensor history, enabling reconstruction to adapt as the governing dynamics change with operating regime. ReMAIN is first benchmarked against SHRED on six one-dimensional nonlinear PDEs representing diverse dynamics. Across all benchmarks, it reduces reconstruction errors on unseen trajectories and more faithfully resolves sharp transitions, localized extrema and fine-scale variations. The parameter-conditioned model is then demonstrated on a collisionless E×B plasma subject to perpendicular axial electric and radial magnetic fields, with the electric-field strength serving as the operating parameter. ReMAIN reconstructs the high-dimensional, multiscale plasma state and recovers its regime-dependent spatiotemporal dynamics at electric-field strengths withheld from training. Together, ReMAIN improves sparse-sensor full-state reconstruction and, through parameter conditioning, generalizes across plasma operating regimes.
Figures & tables
Figure 1: Schematic of the Recurrent Multiscale Affine-modulated Inference Network (ReMAIN) architecture.
Figure 2: Schematic architecture of the parameter-conditioned ReMAIN.
PDE
Spatial discretization
Time integrator
Solver Δt
Sampling stride [time steps]
Sampling interval [time unit]
CGL
Fourier spectral
ETDRK4 [ 23 ]
0.01
10
0.10
KdV–KS
Fourier pseudospectral; 2/3 de-aliasing
ETDRK4 [ 23 ]
0.05
5
0.25
Forced Burgers
Fourier pseudospectral; 2/3 de-aliasing
ETDRK4 [ 23 ]
0.005
20
0.10
Compressible Navier–Stokes
Finite volume; Rusanov flux
SSP-RK3
0.001
30
0.03
FitzHugh–Nagumo
Fourier spectral Laplacian
Classical RK4
0.02
10
0.20
Driven sine–Gordon
Fourier spectral Laplacian
Classical RK4
0.01
10
0.10
Table 1: Spatial discretization, time-integration scheme, solver time step, and temporal sampling parameters used for the six PDE benchmarks.
Figure 3: Test relative- L2 error distributions for SHRED and ReMAIN across the PDE benchmarks. Boxes show the interquartile range (25th–75th percentiles) of the relative L2 error across test snapshots; the black horizontal line denotes the median and the white diamond is the mean. The vertical lines extend to the most extreme non-outlier values lying no more than 1.5 times the box height below the lower quartile or above the upper quartile, and white circles indicate outliers beyond this range.
Figure 4: Comparison of SHRED and ReMAIN reconstructions for representative held-out test snapshots of the KdV–KS system. The green markers indicate sensor locations. Values above each subplot indicate the relative L2 reconstruction errors of SHRED and ReMAIN for the displayed snapshot.
Figure 5: Comparison of SHRED and ReMAIN reconstructions for representative held-out test snapshots of the driven Forced Burgers system. Values above each subplot indicate the relative L2 reconstruction errors of SHRED and ReMAIN for the displayed snapshot.
Figure 6: Comparison of SHRED and ReMAIN reconstructions for representative held-out test snapshots of the driven Compressible Navier-Stokes system. Values above each subplot indicate the relative L2 reconstruction errors of SHRED and ReMAIN for the displayed snapshot.
Figure 7: Comparison of SHRED and ReMAIN reconstructions for representative held-out test snapshots of the driven FitzHugh-Nagumo system. Values above each subplot indicate the relative L2 reconstruction errors of SHRED and ReMAIN for the displayed snapshot.
Figure 8: Comparison of SHRED and ReMAIN reconstructions for representative held-out test snapshots of the driven Sine-Gordon system. Values above each subplot indicate the relative L2 reconstruction errors of SHRED and ReMAIN for the displayed snapshot.
Figure 9: Comparison of SHRED and ReMAIN reconstructions for representative held-out test snapshots of the driven Complex Ginzburg–Landau system. Values above each subplot indicate the relative L2 reconstruction errors of SHRED and ReMAIN for the displayed snapshot.
Figure 10: Comparison of SHRED and ReMAIN reconstructions of spatiotemporal evolution for a sample test trajectory across the six PDE benchmarks; (a) KdV–KS, (b) Forced Burgers, (c) Compressible Navier-Stokes, (d) FitzHugh-Nagumo, (e) Sine-Gordon, and (f) Ginzburg–Landau equation.
Figure 11: Difference between SHRED and ReMAIN reconstructions and the ground truth for the sample test trajectories shown in Fig. 10 across the six PDE benchmarks; (a) KdV–KS, (b) Forced Burgers, (c) Compressible Navier–Stokes, (d) FitzHugh–Nagumo, (e) Sine–Gordon, and (f) Ginzburg–Landau equation.
Figure 12: Spatial distribution of the ten fixed sensor locations over the radial–azimuthal Jey field; green markers indicate the sensor positions.
Figure 13: Mean relative L2 , azimuthal spectral, and second-order structure-function errors of parametric ReMAIN reconstructions for the plasma test case. The error metrics are averaged over all snapshots for each test operating parameter, and the error bars show the corresponding population standard deviation across snapshots.
Figure 14: Mean azimuthal power spectra of truth and parametric ReMAIN across test operating parameters. Note both axes are shown on logarithmic scales.
Figure 15: Comparison of ground truth and parametric ReMAIN temporal evolution at three randomly selected spatial locations for each test operating parameter; each signal is independently normalized using the corresponding ground-truth range.
Figure 16: Comparison of parametric ReMAIN and ground-truth snapshots for sample test snapshots at E0E=1.25,1.75,2.25, and 2.75 .
Figure 17: Comparison of parametric ReMAIN and ground-truth snapshots for sample test snapshots at E0E=3.25,3.75,4.25, and 4.75 .
Inferring the evolution of high-dimensional and multi-modal (e.g., spatio-temporal) physical fields from irregular sparse measurements in real time is a fundamental challenge in science and engineering. Existing approaches, including diffusion-based generative models and functional tensor methods, typically operate in offline settings, depend on full temporal observations, or incur substantial inference cost. We propose StreamPhy, an end-to-end framework that enables efficient and accurate streaming inference of full-field physical dynamics from incoming irregular sparse measurements. The framework integrates a data-adaptive observation encoder that is robust to arbitrary observation patterns, a structured state-space model that supports memory-efficient online updates across irregular time intervals, and an expressive Functional Tensor Feature-wise Linear Modulation (FT-FiLM) decoder for continuous-field generation. We prove that FT-FiLM is more expressive than the functional Tucker model, admitting a richer function class for handling complex dynamics. Experiments on three representative physical systems under challenging sampling patterns show that StreamPhy consistently outperforms state-of-the-art baselines, with at least 48% improvement in accuracy and up to 20--100X faster inference than diffusion-based methods.
Panqi Chen, Yifan Sun, Shikai Fang +2
College of Information Science and Electronic Engineering, Zhejiang University · School of EECS,Oregon State University
Energy-based models (EBMs) provide a powerful and flexible way of learning a joint probability distribution over data by constructing an energy surface. This energy surface enables insight extraction and conditional sampling. We apply EBMs to laboratory plasma physics, a domain characterized by highly nonlinear phenomena. These phenomena are studied using plasma diagnostics, which are often difficult to analyze and subject to hardware degradation. In addition, the possible configuration space of a plasma device is sufficiently large that it cannot be efficiently searched using conventional analysis techniques. EBMs address these issues. At the Large Plasma Device (LAPD), a CNN- and attention-based EBM is trained on a set of randomly generated machine conditions and their corresponding diagnostic time series. We demonstrate diagnostic reconstruction using this EBM on real data and show that additional diagnostics improves reconstruction error and generation quality. The energy surface is directly evaluated for an ill-posed inverse problem: inferring probe position from a time-series measurement. This inference illuminates symmetries in the data, potentially leading to a method of inquiry to supplement conventional data analysis. Trends in diagnostic signals are inferred via conditional sampling over machine inputs. In addition, this multimodal EBM is able to unconditionally reproduce all distributional modes, suggesting future potential in anomaly detection on the LAPD. Fundamentally, this work demonstrates the flexibility and efficacy of EBM-based generative modeling of laboratory plasma data, and showcases multiple practical uses of just a single trained EBM in the physical sciences.
Phil Travis, Troy Carter
Ergodic LLC, USA · Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA
Plasma shape control in tokamaks requires a real-time controller that tracks dynamically changing shape targets while tolerating diagnostic failures. Classical approaches decompose the problem into equilibrium reconstruction followed by a linear controller, and assume a fixed, fully operational sensor set. We present a reinforcement learning agent that addresses both limitations simultaneously. The agent is trained in NSFsim, a high-fidelity tokamak simulator configured for DIII-D, on a curated dataset of 120 experimental plasma shapes. The shape targets are resampled as random step changes every 0.25 s, exposing the agent to diverse transitions across the full shape envelope. At test time the agent zero-shot tracks dynamic shape sequences; on a held-out static configuration in simulation it achieves a mean shape error of 2.01 cm, and dynamic trajectory following is demonstrated qualitatively in simulation and on the physical device. Diagnostic dropout randomly masks 30% of magnetic sensors per episode, yielding a single policy robust to arbitrary sensor subsets without backup controllers or mode-switching logic. An asymmetric actor-critic architecture with privileged equilibrium information improves value estimation under partial observability; an auxiliary shape reconstruction head on the actor enables end-to-end shape reconstruction from raw diagnostics and serves as an interpretability tool for policy analysis. The policy transfers to experimental DIII-D shots, where it directly commands the coil actuators on two dynamic shape maneuvers, and to the independent GSevolve simulator.
D. Sorokin, M. Stokolesov, A. Granovskiy +7
Next Step Fusion, Bertrange, L-8070, Luxembourg · Center for Energy Research, University of California San Diego, CA 92093, USA