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DIFFER is part of andDIFFER huisstijl presentatie 1 juni 2017

Realtime capable first principle transport modelling for tokamak prediction and control

J. Citrin1, T. Aniel2, C. Bourdelle2, Y. Camenen3, V. Dagnelie1, H. Doerk4, F. Felici5, A. Ho1, D. Hogeweij1, K. van de Plassche1,6, G. Verdoolaege7,8, D. van Vugt6

1DIFFER - Dutch Institute for Fundamental Energy Research, Eindhoven, the Netherlands2CEA, IRFM, F-13108 Saint Paul Lez Durance, France

3CNRS, Aix-Marseille Univ., PIIM UMR7345, Marseille, France4Max Planck Institute for Plasma Physics, Boltzmannstr. 2, Garching, Germany

5Eindhoven University of Technology, Control Systems Technology Group, Eindhoven, The Netherlands6Science and Technology of Nuclear Fusion, Eindhoven University of Technology, Eindhoven, The Netherlands

7Department of Applied Physics, Ghent University, B-9000 Ghent, Belgium8Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels, Belgium

Acknowledgement to EUROfusion for Enabling Research grant

Integrated tokamak modelling demands tractable calculations of all components

Full prediction and optimization cannot be inferred from the isolated behaviour of the components

Heating

MHD stability

Turbulence

Plasma-wall-interaction

Fusion power

Heat exhaust

Magnetic equilibrium

Calculation of each physics component must be reduced to a tractable level

Jonathan Citrin IAEA Technical Meeting, Boston, 2017 2

Pathway towards unprecedented model tractability while remaining first-principle-based

Reduced quasilinear model. 102 CPU hours for 1s JET-scale profile evolution

Local nonlinear gyrokinetics108 CPUh for 1s JET-scale profile evolution

Bridging 12 orders of magnitude in calculation speed

Realtime capability.Neural network emulation

Faster than realtime!

• Neural network emulation of quasilinear transport models. Realtime capable. Powerful tool for experiment design and optimization

𝑇𝑇𝑒𝑒 q-profile

Heating powerTotal current

• “Golden standard” of local nonlinear gyrokinetics. Validation against experiments

• Reduced turbulence model for tractable profile evolution. Validation against NL and exp


QuaLiKiz assumptions

• Ballooned Gaussian eigenfunction ansatz

• Shifted circle (𝑠𝑠 − 𝛼𝛼) geometry

• Electrostatic only (nonlinear EM-stabilization effects to beadded to nonlinear saturation rule)

• Collisions only with Krook operator for trapped electrons

Quasilinear modelling a significant acceleration compared to nonlinear

Fast reduced transport model QuaLiKiz: quasilinear gyrokinetic ITG/TEM/ETG heat, particle, andmomentum turbulent core transport [Bourdelle PPCF 2016]

New release, QuaLiKiz 2.3.0. 10 CPUs per flux, × 106 faster than nonlinear [Citrin submitted to PPCF]


Validation on a JET ILW baseline dischargeJET 87412 (ILW baseline). 1s evolution, approx × 4𝜏𝜏𝐸𝐸

• Boundary condition at 𝜌𝜌 = 0.85

• Rotation important for confinement improvement in all channels

• Just one example of many validations: Tore Supra: Casati PhD ‘09, Villegas PRL ‘10. JET: Baiocchi NF ‘15, Breton EPS ’17. AUG: Linder EPS ‘17


1. Quasilinear model validated vs nonlinear simulations and experiments

2. Use quasilinear model to create datasets of turbulent flux calculations. Include all tokamak parameters of interest (e.g. based on experiments). Even for linear-GENE/GYRO/etc, feasible with 107 CPUh scale HPC projects (currently ‘routine’)

3. Define training sets from the database for neural network regression

4. Use the trained neural network as the ‘transport model’

Neural networks can provide a furtherspeedup in turbulence modelling

10 𝐶𝐶𝐶𝐶𝐶𝐶𝑠𝑠 per turbulent flux is fast, but we can go much further!

We apply (shallow) multilayer perceptron neural networks


“Very fast” tokamak simulator

• Offline trajectory optimization. Reinforcement learning

Realtime tokamak simulator

• Online trajectory optimizationfaster-than-real-time (model-based predictive control)

• Controller design

• Controller validation

• Discharge supervision and monitoring(e.g. disruption mitigation)

Neural network technique opens up wide applications for scenario prediction and control


Reminder of neural network nuts and bolts

8

Multilayer perceptron neural network (simple topology)

𝑔𝑔 𝑥𝑥 =2

1 + 𝑒𝑒−𝑥𝑥 − 1

x: Inputs: e.g. Ti/Te, q, �̂�𝑠, R/Ltiy: Output: e.g. ion heat flux𝑤𝑤1,2: free weights for optimization

With, e.g.

𝑥𝑥1

𝑥𝑥2

𝑥𝑥3

𝑥𝑥4

𝑦𝑦 = �𝑤𝑤𝑗𝑗2𝑔𝑔𝑗𝑗 �𝑤𝑤𝑖𝑖,𝑗𝑗1 𝑥𝑥𝑖𝑖𝑦𝑦

𝑤𝑤𝑗𝑗2𝑤𝑤𝑖𝑖,𝑗𝑗1 𝑔𝑔1

𝑔𝑔2

𝑔𝑔3

𝑔𝑔4

𝑔𝑔5

Optimize weights by minimizing: ∑𝑁𝑁 𝑡𝑡𝑁𝑁 − 𝑦𝑦𝑁𝑁 2 + 𝜆𝜆∑ 𝑤𝑤𝑖𝑖𝑗𝑗2

𝑡𝑡𝑁𝑁 are target values, known from, e.g. QuaLiKiz runs𝜆𝜆 is the regularization factor. Avoids overfitting

Provides an analytical formula with analytical derivatives. Critical for trajectory optimization applications and implicit timestep solvers


A proof-of-principle NN transport model is developed

Neural network fit for QuaLiKiz output. ITG regime(S.Breton MSc, J. Redondo MSc ; Citrin, Breton et al., Nucl. Fusion Lett. 2015)

4D input training set for ~50,000 fluxes. NN with 2 hidden layers of 30 nodes. L-BFGS optimization𝑞𝑞 = 1 − 5 ; �̂�𝑠 = 0.1 − 3 ; 𝑇𝑇𝑖𝑖

𝑇𝑇𝑒𝑒= 0.3 − 3 ; 𝑅𝑅

𝐿𝐿𝑇𝑇𝑖𝑖= 2 − 12

Parameter scans of NN ion heat conductivity vs original QuaLiKiz results

Note that regularization even allows reasonable extrapolation.

Extrapolation not recommended, but encouraging for robustness in sparse datasets


• Neural network successfully reproduces QuaLiKiz results × 106 faster! ~1ms for a flux

• Already works well on JET ITG dominated case in flux driven integrated modellingExtension to more input dimensions (for ITG/TEM/ETG) needed for generalization

CRONOS/QLKNN simulation of flat top in JET 73342 standard H-mode. Original QLK simulation in Baiocchi PPCF 2015. Boundary condition at 𝜌𝜌 = 0.88

Neural Network QuaLiKiz validatedby JET discharge modelling


RAPTOR control-oriented simulator now multi-channel for 𝑗𝑗,𝑇𝑇𝑒𝑒 ,𝑇𝑇𝑖𝑖 ,𝑛𝑛. Faster than realtime

F. Felici and RAPTOR team

Ion temperature and density evolution now added to RAPTOR

• First simultaneous 𝑇𝑇𝑖𝑖 and 𝑇𝑇𝑒𝑒 simulationwith RAPTOR and QuaLiKiz-NN

• 6 order of magnitude speedup compared to original QuaLiKiz

• ITER scenario modelling faster than realtime. Successful comparison to previous CRONOS/GLF23 modelling (1 week simulation) [Citrin NF ‘10]

ITER hybrid scenario 𝑇𝑇𝑖𝑖 + 𝑇𝑇𝑒𝑒CRONOS/GLF23 vs RAPTOR/QLKANN4D

∼ 20𝑠𝑠simulationwalltime

𝜌𝜌𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 = 0.5 timetrace


Onwards and upwards! A 9 input dimension database for QuaLiKiz neural network training

• Database compiled! 3 ⋅ 108 flux evaluations,1.5 MCPUh of QuaLiKiz runs @ NERSC

• Also separate database for ITG, TEM, ETG fluxes (may be easier to fit)

• Non-uniform spacings for each parameter (based on experience and tests), but still a hyper-rectangle. Conceptually simple.

MSc Karel van de Plassche


A 9 input dimension database forQuaLiKiz neural network training

9D database permanently online and accessible at dataslicer.qualikiz.com


9D neural network training undergoing

Example of heat flux NN outputTransition from ITG to ETG in𝑅𝑅/𝐿𝐿𝑇𝑇𝑒𝑒 scan. QLK points are discreteFlux > 50 [GB units] is extrapolation Lots to optimize in NN fitting:

• Network topology• Activation function• Optimization routine• Regularization (cost function)• Data filtering (e.g. find QLK outliers, set

upper limit on flux to improve thresholds)

Ongoing work for 9D (Karel van de Plassche, Nishith Chennakeshava)

Soon to test in RAPTOR heat+particle transport

𝑞𝑞𝑖𝑖 NN –-𝑞𝑞𝑒𝑒 NN ETG + ITG-TEM ⋅⋅⋅𝑞𝑞𝑒𝑒 NN –-

𝑅𝑅/𝐿𝐿𝑇𝑇𝑒𝑒


Adding 𝐸𝐸𝑥𝑥𝐸𝐸 flow shear as 10th input dimension for neural network fits

MSc Victor DagnelieWorking on new Waltz-rule-style 𝐸𝐸𝑥𝑥𝐸𝐸 suppression model includingparallel flow destabilisation.Based on database of linear-GENE scans, mostly around GA-STD case parameters for now (varying 𝑅𝑅

𝐿𝐿𝑇𝑇𝑖𝑖, 𝑞𝑞, �̂�𝑠, 𝜖𝜖)

To be included in post-processing to QLK database

and try 10D NN fits

𝛾𝛾𝐸𝐸 [𝑐𝑐𝑠𝑠/𝑎𝑎]


Constructing more complete NN transport model with ~25 input dimensions

• For all local input dimensions (~25D), including shaping, 𝛽𝛽, impurities, we must restrict to subspace containing natural experimental correlations

• Construct database for training sets based on wide range of experimental scenarios, and extrapolations to future devices

• New multi-machine profile database for neural network training set sampling. Subset (including sources) for integrated modelling validation

• Have started with JET. Database now complete.~2000 discharges, 7 time slices each. Automated Gaussian Processes (GP) fitting routines, consistency checks (PhD Aaron Ho).

• Next step GK runs (QLK + lin-GENE on representative subset of ~10%)

• GP fitting routines provide automatic error bars on gradients. Informs how to sample additional inputs for GK runs to ensure thresholds are hit


Automated routines for Gaussian Processfitting of JET profile measurements

Aaron Hothis conference


We are developing a database forstoring linear gyrokinetic runs

Goal: gyrokinetic database (GKDB) openly accessible to community for storing results of linear gyrokinetic runs from various codes (linear-GENE/GKW/GYRO, etc)

• Populate training sets for neural network regression

• Code-code benchmarks

• In SQL with direct queries performed from Python, Matlab, IDL

Yann Camenen, Thierry Aniel, Karel van de Plassche, Daan van Vugt


A 10 input dimension database forQuaLiKiz neural network training

SQL schema for GKDB


Workflow of GKDB data input

Now entering phase where early adopters can volunteer to use and test


Summary and outlook

• Reduced turbulence transport model QuaLikiz 2.3.0 release. Ongoing successful validations on JET and AUG discharges.

• 4D QLK neural network proof-of-principle. Validation of heat and particle transport in JET discharge. Implementation on realtime capable control-oriented simulator RAPTOR

• 9D (10 with 𝐸𝐸 × 𝐸𝐸) QLK database complete. NN fitting well underway. To be implemented and tested in RAPTOR

• New extensive JET profile database for sampling inputs for >20D GK runs. Automated Gaussian Process fit workflow. QuaLiKiz and quailinear-GENE runs and NN fits to come.

• GyroKineticDataBase (GKDB) project advancing for enhancing community wide linear benchmarks and defining neural network training sets for transport model emulation

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