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Register a new userNeural network surrogate of QuaLiKiz using JET experimental data to populate training space
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Authors
Aaron Ho
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Within integrated tokamak plasma modelling, turbulent transport codes are typically the computational bottleneck limiting their routine use outside of post-discharge analysis. Neural network (NN) surrogates have been used to accelerate these calculations while retaining the desired accuracy of the physics-based models. This paper extends a previous NN model, known as QLKNN-hyper-10D, by incorporating the impact of impurities, plasma rotation and magnetic equilibrium effects. This is achieved by adding a light impurity fractional density ($n_{imp,light} / n_e$) and its normalized gradient, the normalized pressure gradient ($alpha$), the toroidal Mach number ($M_{tor}$) and the normalized toroidal flow velocity gradient. The input space was sampled based on experimental data from the JET tokamak to avoid the curse of dimensionality. The resulting networks, named QLKNN-jetexp-15D, show good agreement with the original QuaLiKiz model, both by comparing individual transport quantity predictions as well as comparing its impact within the integrated model, JINTRAC. The profile-averaged RMS of the integrated modelling simulations is <10% for each of the 5 scenarios tested. This is non-trivial given the potential numerical instabilities present within the highly nonlinear system of equations governing plasma transport, especially considering the novel addition of momentum flux predictions to the model proposed here. An evaluation of all 25 NN output quantities at one radial location takes $sim$0.1 ms, $10^4$ times faster than the original QuaLiKiz model. Within the JINTRAC integrated modelling tests performed in this study, using QLKNN-jetexp-15D resulted in a speed increase of only 60 - 100 as other physics modules outside of turbulent transport become the bottleneck.
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In order to predict and analyze turbulent transport in tokamaks, it is important to model transport that arises from microinstabilities. For this task, quasilinear codes have been developed that seek to calculate particle, angular momentum, and heat fluxes both quickly and accurately. In this tutorial, we present a derivation of one such code known as QuaLiKiz, a quasilinear gyrokinetic transport code. The goal of this derivation is to provide a self-contained and complete description of the underlying physics and mathematics of QuaLiKiz from first principles. This work serves both as a comprehensive overview of QuaLiKiz specifically as well as an illustration for deriving quasilinear models in general.
In recent years, there have been a surge in applications of neural networks (NNs) in physical sciences. Although various algorithmic advances have been proposed, there are, thus far, limited number of studies that assess the interpretability of neural networks. This has contributed to the hasty characterization of most NN methods as black boxes and hindering wider acceptance of more powerful machine learning algorithms for physics. In an effort to address such issues in fluid flow modeling, we use a probabilistic neural network (PNN) that provide confidence intervals for its predictions in a computationally effective manner. The model is first assessed considering the estimation of proper orthogonal decomposition (POD) coefficients from local sensor measurements of solution of the shallow water equation. We find that the present model outperforms a well-known linear method with regard to estimation. This model is then applied to the estimation of the temporal evolution of POD coefficients with considering the wake of a NACA0012 airfoil with a Gurney flap and the NOAA sea surface temperature. The present model can accurately estimate the POD coefficients over time in addition to providing confidence intervals thereby quantifying the uncertainty in the output given a particular training data set.
Simulations of high energy density physics are expensive in terms of computational resources. In particular, the computation of opacities of plasmas, which are needed to accurately compute radiation transport in the non-local thermal equilibrium (NLTE) regime, are expensive to the point of easily requiring multiple times the sum-total compute time of all other components of the simulation. As such, there is great interest in finding ways to accelerate NLTE computations. Previous work has demonstrated that a combination of fully-connected autoencoders and a deep jointly-informed neural network (DJINN) can successfully replace the standard NLTE calculations for the opacity of krypton. This work expands this idea to multiple elements in demonstrating that individual surrogate models can be also be generated for other elements with the focus being on creating autoencoders that can accurately encode and decode the absorptivity and emissivity spectra. Furthermore, this work shows that multiple elements across a large range of atomic numbers can be combined into a single autoencoder when using a convolutional autoencoder while maintaining accuracy that is comparable to individual fully-connected autoencoders. Lastly, it is demonstrated that DJINN can effectively learn the latent space of a convolutional autoencoder that can encode multiple elements allowing the combination to effectively function as a surrogate model.
The study of chemical reactions in aqueous media is very important for its implications in several fields of science, from biology to industrial processes. Modelling these reactions is however difficult when water directly participates in the reaction. Since it requires a fully quantum mechanical description of the system, $textit{ab-initio}$ molecular dynamics is the ideal candidate to shed light on these processes. However, its scope is limited by a high computational cost. A popular alternative is to perform molecular dynamics simulations powered by machine learning potentials, trained on an extensive set of quantum mechanical calculations. Doing so reliably for reactive processes is difficult because it requires including very many intermediate and transition state configurations. In this study, we used an active learning procedure accelerated by enhanced sampling to harvest such structures and to build a neural-network potential to study the urea decomposition process in water. This allowed us to obtain the free energy profiles of this important reaction in a wide range of temperatures, to discover a number of novel metastable states and to improve the accuracy of the kinetic rates calculations. Furthermore, we found that the formation of the zwitterionic intermediate has the same probability of occurring via an acidic or a basic pathway, which could be the cause of the insensitivity of reaction rates to the pH solution.
An encoder-decoder neural network has been used to examine the possibility for acceleration of a partial integro-differential equation, the Fokker-Planck-Landau collision operator. This is part of the governing equation in the massively parallel particle-in-cell code, XGC, which is used to study turbulence in fusion energy devices. The neural network emphasizes physics-inspired learning, where it is taught to respect physical conservation constraints of the collision operator by including them in the training loss, along with the L2 loss. In particular, network architectures used for the computer vision task of semantic segmentation have been used for training. A penalization method is used to enforce the soft constraints of the system and integrate error in the conservation properties into the loss function. During training, quantities representing the density, momentum, and energy for all species of the system is calculated at each configuration vertex, mirroring the procedure in XGC. This simple training has produced a median relative loss, across configuration space, on the order of 10E-04, which is low enough if the error is of random nature, but not if it is of drift nature in timesteps. The run time for the Picard iterative solver of the operator scales as order n squared, where n is the number of plasma species. As the XGC1 code begins to attack problems including a larger number of species, the collision operator will become expensive computationally, making the neural network solver even more important, since the training only scales as n. A wide enough range of collisionality is considered in the training data to ensure the full domain of collision physics is captured. An advanced technique to decrease the losses further will be discussed, which will be subject of a subsequent report. Eventual work will include expansion of the network to include multiple plasma species.
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