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title SCPN Control: Neuro-Symbolic Stochastic Petri Net Controllers with First-Principles Gyrokinetic Transport for Real-Time Tokamak Plasma Control
tags
Python
Rust
plasma physics
tokamak control
gyrokinetics
spiking neural networks
Petri nets
neuro-symbolic AI
authors
name orcid affiliation corresponding
Miroslav Šotek
0009-0009-3560-0851
1
true
affiliations
name index
ANULUM CH & LI
1
date 17 March 2026
bibliography paper.bib

Summary

scpn-control is an open-source neuro-symbolic control engine for tokamak plasma control combining Stochastic Petri Net (SPN) compilation into spiking neural network (SNN) controllers, a five-tier gyrokinetic transport system including a nonlinear $\delta f$ solver, and an 8-layer Kuramoto-Sakaguchi phase dynamics engine.

The electromagnetic gyrokinetic and Lyapunov-monitor surfaces are repository research-prototype evidence, not facility-control guarantees. The finite-beta KBM/MTM branch logic has regression coverage, but nonlinear electromagnetic extension evidence and external-code or facility validation remain open. The Lyapunov guard is an advisory sliding-window monitor: it can approve during warm-up and until the configured consecutive-violation threshold is exceeded, so it is not a standalone fail-closed safety interlock.

The package provides: a Grad-Shafranov equilibrium solver (fixed and free boundary, JAX-differentiable), a 1.5D Crank-Nicolson transport solver with multi-ion physics, a native linear gyrokinetic eigenvalue solver with electromagnetic extension, a native TGLF-equivalent quasilinear model (SAT0/SAT1/SAT2 saturation rules), a nonlinear $\delta f$ gyrokinetic solver in flux-tube geometry with JAX GPU acceleration measured in a bounded local GPU benchmark (62$\times$ in that recorded context), interfaces to five external GK codes (TGLF, GENE, GS2, CGYRO, QuaLiKiz) whose quantitative external-code claims remain blocked until real artefacts are admitted, a hybrid surrogate+GK validation layer with out-of-distribution detection and online retraining, ten controllers (PID, MPC, $H_\infty$, $\mu$-synthesis, NMPC, SNN, safe RL, sliding-mode, gain-scheduled, fault-tolerant), disruption prediction with SPI mitigation, and a companion Rust backend (5 crates, PyO3 bindings) with a reproducible benchmark reporting a ~5 µs P50 native integrated control cycle on the CI runner (2.85 µs on the local workstation).

The nonlinear gyrokinetic solver implements the Cyclone Base Case configuration [@dimits2000], Rosenbluth-Hinton zonal-flow damping, kinetic electrons, and Sugama collisions. After the v0.19.0 physics audit, its late-time nonlinear heat-flux normalisation is treated as an open validation target: the latest 2000-step adiabatic run had not reached saturated $\chi_i$, and the linear local-dispersion path overpredicts the published GENE growth rate. The manuscript therefore does not claim quantitative nonlinear CBC agreement until a longer, reverified convergence campaign is complete.

The codebase comprises a Python package and 5 Rust crates with broad Python module tests, a 99% local package-coverage gate, and a multi-workflow CI matrix.

Statement of Need

Real-time plasma control in magnetic confinement fusion requires low-latency decision paths, bounded and traceable transport-physics evidence, and robust safety guarantees. Existing open-source tools address subsets of this problem: TORAX [@torax2024] provides JAX-differentiable transport with TGLF coupling, TCV-RL [@degrave2022] applies deep RL to tokamak control, FreeGS [@freegs] solves free-boundary equilibria, and FUSE [@fuse2024] offers integrated design-to-operations modelling. No single package combines compilable control logic (SPNs), neuromorphic execution (SNNs), first-principles gyrokinetic transport from quasilinear through nonlinear, and multi-layer phase dynamics in one coherent stack.

scpn-control fills this gap with four distinguishing capabilities:

  1. Five-tier gyrokinetic transport — spanning critical-gradient models ($\sim\mu$s), a QLKNN-style neural-transport facade with a compact MLP loader and analytic critical-gradient fallback, a native linear GK eigenvalue solver ($\sim$0.3 s per flux surface) [@dimits2000; @miller1998], a native TGLF-equivalent model with SAT0/SAT1/SAT2 spectral saturation [@staebler2007; @staebler2017; @maeyama2015], and a nonlinear $\delta f$ gyrokinetic solver with dealiased E$\times$B bracket, ballooning connection boundary conditions, Rosenbluth-Hinton zonal flow physics [@rosenbluth1998], Sugama collision operator [@sugama2006], and optional kinetic electrons via semi-implicit backward-Euler treatment. JAX GPU acceleration is reported as a bounded local benchmark result (62$\times$ in the recorded GPU context), not as a facility or production timing claim. The current public neural-transport claim report is analytic_fallback; quantitative QLKNN/QuaLiKiz claims remain blocked unless trained weights and strict reference artefacts are supplied.

  2. Cyclone Base Case validation harness — the repository includes CBC scenarios, grid scans, kinetic-electron lanes, and published-code interface adapters. Quantitative nonlinear agreement is not yet claimed: the current audited result is an unsaturated adiabatic heat-flux trace after 2000 steps, and the linear local-dispersion path overpredicts the GENE reference growth rate. The remaining publication gate is a longer reverified convergence campaign plus native GK comparison against real TGLF/GENE-class binaries on identical inputs.

  3. SPN-to-SNN compilation — translates control graphs into leaky integrate-and-fire neuron pools with stochastic bitstream encoding [@murata1989; @maass1997], enforcing pre/post-condition contracts on every observation and action. The pure-NumPy LIF+NEF engine requires no external dependencies.

  4. 8-layer plasma phase dynamics — a Kuramoto-Sakaguchi multi-layer UPDE engine [@kuramoto1975; @sotek2026knm] encoding experimentally grounded interactions (drift-wave/zonal-flow, NTM/bootstrap-current, ELM/pedestal), with GK-driven adaptive $K_{nm}$ coupling and Lyapunov stability monitoring. The monitor is a research-prototype advisory guard with warm-up and consecutive-window fail-open intervals, not a replacement for an independent facility safety interlock.

Implementation

The Python package is organised into four layers:

  • Core (scpn_control.core): Grad-Shafranov solver (Picard iteration with multigrid or SOR), 1.5D Crank-Nicolson transport, GEQDSK/IMAS I/O, IPB98(y,2) scaling [@ipb1999], neural equilibrium accelerator, uncertainty quantification, and the gyrokinetic transport stack:
    • Native linear GK: Miller flux-tube geometry [@miller1998], per-species Gauss-Legendre velocity grid, local dispersion relation with Newton root-finding, mixing-length quasilinear fluxes. Electromagnetic extension adds KBM [@tang1980] and microtearing [@drake1977] modes as repository research-prototype evidence pending nonlinear EM and external-code revalidation.
    • Native TGLF-equivalent: SAT0/SAT1/SAT2 spectral saturation [@staebler2007; @staebler2017], E$\times$B shear quench [@waltz1997], trapped-particle damping [@connor1974], multi-scale ITG-ETG coupling [@maeyama2015]. No external binary required.
    • Nonlinear $\delta f$: 5D Vlasov in flux-tube geometry, dealiased E$\times$B bracket (Orszag 2/3 rule), 4th-order parallel streaming with ballooning connection BC, Rosenbluth-Hinton zonal Krook damping [@rosenbluth1998], Sugama collision operator [@sugama2006] with particle/momentum/energy conservation, optional kinetic electrons (semi-implicit backward-Euler for electron parallel streaming), RK4 with CFL-adaptive dt, JAX-accelerated variant with the recorded bounded local GPU speedup described above.
    • External GK: TGLF [@staebler2007], GENE [@jenko2000], GS2 [@kotschenreuther1995], CGYRO [@candy2003], QuaLiKiz [@bourdelle2007] via subprocess with automatic input deck generation and output parsing.
    • Hybrid: OOD detection (Mahalanobis + ensemble + range), spot-check scheduling, multiplicative/additive correction with EMA smoothing, online surrogate retraining with validation holdout and rollback.
  • Phase (scpn_control.phase): Kuramoto-Sakaguchi stepper, UPDE multi-layer solver, adaptive $K_{nm}$ engine with GK→UPDE bridge, Lyapunov guard, WebSocket real-time monitor.
  • SCPN (scpn_control.scpn): SPN structure, compiler, contract system, artifact serialisation, FPGA HDL project export evidence.
  • Control (scpn_control.control): $H_\infty$ (Riccati DARE), $\mu$-synthesis (D-scaling upper bound; bounded static $\mu$-analysis, not validated full DK synthesis), NMPC (SQP), gain-scheduled PID, shape controller, safe RL (CPO-formulated Lagrangian constraints with control barrier functions, Ames 2017), sliding-mode vertical stability, scenario scheduler, fault-tolerant control, digital twin, flight simulator, Gymnasium environment, JAX-traceable runtime, ITER CODAC/EPICS interface, federated disruption prediction.

The Rust backend (scpn-control-rs, 5 crates, ndarray 0.16, rand 0.9) provides PyO3 bindings for performance-critical paths. Its reproducible benchmark reports a ~5 µs P50 native integrated control cycle on the CI runner (2.85 µs locally); production runtime claims remain subject to runtime-admission evidence.

Validation

The solver is validated against:

  • Cyclone Base Case [@dimits2000]: CBC input construction, nonlinear $\delta f$ evolution, JAX acceleration, kinetic-electron support, Sugama collisions, and grid-scan machinery are implemented. The latest audited 2000-step adiabatic run did not reach saturated $\chi_i$, so the former saturated-heat-flux agreement claims are withdrawn pending a longer convergence campaign. The current linear local-dispersion result overpredicts the GENE reference growth rate; it is retained as a model limitation, not a quantitative validation claim.
  • Dimits shift [@dimits2000]: the repository contains subcritical and supercritical scan machinery and zonal-flow damping, but the full Dimits-gap claim remains a revalidation target after the kinetic-electron and Gauss-Laguerre quadrature changes.
  • Sugama collision operator: pitch-angle scattering with energy-dependent collision rate ($\nu(v) \propto v^{-3}$) and conservation corrections. Verified: $\int C[f],dv < 3\times10^{-8}$ (particles), $\int v_\parallel C[f],dv < 10^{-23}$ (momentum), $\int E,C[f],dv < 2\times10^{-8}$ (energy). At low collisionality ($\nu = 0.01$), Sugama and Krook agree on the low-collisionality collision response in the verified operator tests; saturated nonlinear $\chi_i$ remains part of the CBC revalidation target.
  • SPARC/ITER equilibria: RMSE-gated against CFS SPARCPublic GEQDSK files and ITER design parameters.
  • DIII-D disruption shots: 17 synthetic fixture shots covering H-mode, VDE, beta-limit, locked-mode, density-limit, tearing, and snowflake configurations.
  • IMAS round-trip: real omas ODS for equilibrium and core_profiles IDS.
  • IPB98(y,2): ITPA 20-tokamak H-mode confinement database [@ipb1999].

The test suite comprises Python module tests and Rust workspace tests across CI jobs (Python 3.10–3.14 on Linux/Windows/macOS, Rust stable, JAX parity, CodeQL security analysis, OpenSSF Scorecard). The local and CI coverage configuration currently enforces a 100% package-coverage gate while publishing XML coverage artefacts. The project holds an OpenSSF CII Best Practices badge. All physics equations cite their source papers; ~80 citations spanning Porcelli (1996), Sauter (1999), Rosenbluth-Putvinski (1997), Stix (1972), Bosch-Hale (1992), Doyle (1989), Rawlings (2017), Stangeby (2000), Hirshman (1983), and others. Twelve cross-module integration tests verify consistency across physics chains (bootstrap→NTM, EPED→Troyon, L-H→EPED, runaway→SPI).

Limitations: external GK interfaces are mock-tested (no real Fortran binaries in CI); DIII-D shots use synthetic data, not real MDSplus archives; the neural equilibrium has not been cross-validated against P-EFIT on identical equilibria.

Acknowledgements

We thank the CFS SPARCPublic team for SPARC equilibrium data, the ITPA H-mode confinement database contributors, and the GACODE, GENE, GS2, and QuaLiKiz development teams for their publicly documented input/output formats.

References