Frank Jenko

Ionut-Gabriel Farcas, Benjamin Peherstorfer, Tobias Neckel et al.

Multi-fidelity Monte Carlo methods leverage low-fidelity and surrogate models for variance reduction to make tractable uncertainty quantification even when numerically simulating the physical systems of interest with high-fidelity models is computationally expensive. This work proposes a context-aware multi-fidelity Monte Carlo method that optimally balances the costs of training low-fidelity models with the costs of Monte Carlo sampling. It generalizes the previously developed context-aware bi-fidelity Monte Carlo method to hierarchies of multiple models and to more general types of low-fidelity models. When training low-fidelity models, the proposed approach takes into account the context in which the learned low-fidelity models will be used, namely for variance reduction in Monte Carlo estimation, which allows it to find optimal trade-offs between training and sampling to minimize upper bounds of the mean-squared errors of the estimators for given computational budgets. This is in stark contrast to traditional surrogate modeling and model reduction techniques that construct low-fidelity models with the primary goal of approximating well the high-fidelity model outputs and typically ignore the context in which the learned models will be used in upstream tasks. The proposed context-aware multi-fidelity Monte Carlo method applies to hierarchies of a wide range of types of low-fidelity models such as sparse-grid and deep-network models. Numerical experiments with the gyrokinetic simulation code \textsc{Gene} show speedups of up to two orders of magnitude compared to standard estimators when quantifying uncertainties in small-scale fluctuations in confined plasma in fusion reactors. This corresponds to a runtime reduction from 72 days to about four hours on one node of the Lonestar6 supercomputer at the Texas Advanced Computing Center.

Robin Greif, Frank Jenko, Nils Thuerey

Turbulence in fluids, gases, and plasmas remains an open problem of both practical and fundamental importance. Its irreducible complexity usually cannot be tackled computationally in a brute-force style. Here, we combine Large Eddy Simulation (LES) techniques with Machine Learning (ML) to retain only the largest dynamics explicitly, while small-scale dynamics are described by an ML-based sub-grid-scale model. Applying this novel approach to self-driven plasma turbulence allows us to remove large parts of the inertial range, reducing the computational effort by about three orders of magnitude, while retaining the statistical physical properties of the turbulent system.

Maximilian Mueller, Robin Greif, Frank Jenko et al.

We investigate uncertainty estimation and multimodality via the non-deterministic predictions of Bayesian neural networks (BNNs) in fluid simulations. To this end, we deploy BNNs in three challenging experimental test-cases of increasing complexity: We show that BNNs, when used as surrogate models for steady-state fluid flow predictions, provide accurate physical predictions together with sensible estimates of uncertainty. Further, we experiment with perturbed temporal sequences from Navier-Stokes simulations and evaluate the capabilities of BNNs to capture multimodal evolutions. While our findings indicate that this is problematic for large perturbations, our results show that the networks learn to correctly predict high uncertainties in such situations. Finally, we study BNNs in the context of solver interactions with turbulent plasma flows. We find that BNN-based corrector networks can stabilize coarse-grained simulations and successfully create multimodal trajectories.

Jeremy J. Williams, Jordy Trilaksono, Stefan Costea et al.

Particle-in-Cell (PIC) Monte Carlo (MC) simulations are central to plasma physics but face increasing challenges on heterogeneous HPC systems due to excessive data movement, synchronization overheads, and inefficient utilization of multiple accelerators. In this work, we present a portable, multi-GPU hybrid MPI+OpenMP implementation of BIT1 that enables scalable execution on both Nvidia and AMD accelerators through OpenMP target tasks with explicit dependencies to overlap computation and communication across devices. Portability is achieved through persistent device-resident memory, an optimized contiguous one-dimensional data layout, and a transition from unified to pinned host memory to improve large data-transfer efficiency, together with GPU Direct Memory Access (DMA) and runtime interoperability for direct device-pointer access. Standardized and scalable I/O is provided using openPMD and ADIOS2, supporting high-performance file I/O, in-memory data streaming, and in-situ analysis and visualization. Performance results on pre-exascale and exascale systems, including Frontier (OLCF-5) for up to 16,000 GPUs, demonstrate significant improvements in run time, scalability, and resource utilization for large-scale PIC MC simulations.

Ionut-Gabriel Farcas, Don Lawrence Carl Agapito Fernando, Alejandro Banon Navarro et al.

Constructing reduced models for turbulent transport is essential for accelerating profile predictions and enabling many-query tasks such as uncertainty quantification, parameter scans, and design optimization. This paper presents machine-learning-driven reduced models for Electron Temperature Gradient (ETG) turbulence in the Wendelstein 7-X (W7-X) stellarator. Each model predicts the ETG heat flux as a function of three plasma parameters: the normalized electron temperature radial gradient ($ω_{T_e}$), the ratio of normalized electron temperature and density radial gradients ($η_e$), and the electron-to-ion temperature ratio ($τ$). We first construct models across seven radial locations using regression and an active machine-learning-based procedure. This process initializes models using low-cardinality sparse-grid training data and then iteratively refines their training sets by selecting the most informative points from a pre-existing simulation database. We evaluate the prediction capabilities of our models using out-of-sample datasets with over $393$ points per location, and $95\%$ prediction intervals are estimated via bootstrapping to assess prediction uncertainty. We then investigate the construction of generalized reduced models, including a generic, position-independent model, and assess their heat flux prediction capabilities at three additional locations. Our models demonstrate robust performance and predictive accuracy comparable to the original reference simulations, even when applied beyond the training domain.

Luca Pennati, Erik M. Åsgrim, Jeremy J. Williams et al.

Plasma simulations are among the most computationally demanding scientific workloads, combining high-dimensional kinetic evolution, particle-mesh coupling, field solves, and data-intensive communication. As general-purpose processor scaling slows, post-Moore technologies are being explored to address bottlenecks in data movement, memory access, and power consumption. This paper provides a community perspective on the role of these technologies in plasma simulation, assessing three major classes: reconfigurable and data-path accelerators, non-von Neumann architectures, and quantum computing. Each is evaluated, in a co-design approach, against representative plasma workloads spanning particle-in-cell, continuum Vlasov, gyrokinetic, fluid/MHD, hybrid, and warm dense matter methods. We find that no single technology can replace existing HPC platforms. Instead, three tiers of opportunity emerge: FPGA-class and data-path accelerators offer near-term kernel offload and workflow-level data services, non-von Neumann architectures represent medium-term directions for operator-level acceleration, and quantum computing, although the least mature, is potentially the most disruptive for warm dense matter and inertial confinement fusion microphysics. We outline best practices for selective adoption and identify focused demonstrators, benchmarking, and modular software ecosystems as immediate community priorities.

Constantin Gahr, Ionut-Gabriel Farcas, Frank Jenko

This paper investigates non-intrusive Scientific Machine Learning (SciML) Reduced-Order Models (ROMs) for plasma turbulence simulations. In particular, we focus on Operator Inference (OpInf) to build low-cost physics-based ROMs from data for such simulations. As a representative example, we consider the (classical) Hasegawa-Wakatani (HW) equations used for modeling two-dimensional electrostatic drift-wave turbulence. For a comprehensive perspective of the potential of OpInf to construct predictive ROMs, we consider three setups for the HW equations by varying a key parameter, namely the adiabaticity coefficient. These setups lead to the formation of complex and nonlinear dynamics, which makes the construction of predictive ROMs of any kind challenging. We generate the training datasets by performing direct numerical simulations of the HW equations and recording the computed state data and outputs the over a time horizon of $100$ time units in the turbulent phase. We then use these datasets to construct OpInf ROMs for predictions over $400$ additional time units, that is, $400\%$ more than the training horizon. Our results show that the OpInf ROMs capture important statistical features of the turbulent dynamics and generalize beyond the training time horizon while reducing the computational effort of the high-fidelity simulation by up to five orders of magnitude. In the broader context of fusion research, this shows that non-intrusive SciML ROMs have the potential to drastically accelerate numerical studies, which can ultimately enable tasks such as the design of optimized fusion devices.

Wei Zhu, Bao Wang, Richard Barnard et al.

We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.