Minisymposium

Operator networks have emerged as promising machine learning tools for reduced order modeling of a wide range of physical systems described by partial differential equations (PDEs). This work describes a new architecture for operator networks that approximates the Green's operator to a linear PDE. Such a ‘Neural Green’s Operator’ (NGO) acts as a surrogate for the PDE solution operator: it maps the PDE’s input functions (e.g. forcings, boundary conditions, material parameters) to its solution. We apply NGOs to relevant canonical PDEs and ask the question whether the NGO architecture would lead to significant computational benefits and conclude the discussion with numerical examples.

The US goal (March, 2022) to deliver a Fusion Pilot Plant [1] has underscored urgency for accelerating the fusion energy development timeline. This will rely heavily on validated scientific and engineering advances driven by HPC together with advanced statistical methods featuring artificial intelligence/deep learning/machine learning (AI/DL/ML) that must properly embrace verification, validation, and uncertainty quantification (VVUQ). Especially time-urgent is the need to predict and avoid large­ scale “major disruptions” in tokamak systems. This keynote highlights the deployment of recurrent and convolutional neural networks in Princeton's Deep Learning Code -- "FRNN" – that enabled the first adaptable predictive DL model for carrying out efficient "transfer learning" while delivering validated predictions of disruptive events across prominent tokamak devices [2]. Moreover, the AI/DL capability can provide not only the “disruption score,” as an indicator of the probability of an imminent disruption but also a “sensitivity score” in real-time to indicate the underlying reasons for the predicted disruption [3]. A real-time prediction and control capability has recently been significantly advanced with a novel surrogate model/HPC simulator ("SGTC") [4] -- a first-principles-based prediction and control surrogate necessary for projections to future experimental devices (e.g., ITER, FPP's) for which no "ground truth" observational data exist.

Quantum computing promises to deliver large gains in computational power that can potentially benefit a number of Fusion Energy Science (FES) application areas. We will review our recent efforts [1] to develop and extend quantum algorithms to perform both classical and quantum FES-relevant calculations, as well as to perform calculations on present-day quantum hardware platforms. We have developed and explored quantum algorithms that can compute nonlinear and non-Hamiltonian dynamics by simulating the Koopman-von Neumann and Liouville equations; perform eigenvalue estimation for generalized eigenvalue problems common in plasma physics and MHD theory; simulate nonlinear wave-wave interactions; and explore the chaotic dynamics of both quantum and classical systems. We have implemented toy models of these algorithms on state-of-the-art quantum computing architectures to test the fidelity of emerging quantum hardware capabilities including Grover’s search, nonlinear three-wave interactions, and the chaotic dynamics of the quantum sawtooth map, a simple model for wave-particle interactions. The fidelity of the experimental results match noise models that include decay and dephasing processes and highlights key differences between state-of-the-art approaches to quantum computing hardware platforms.

[1] I. Joseph, Y. Shi, M. D. Porter, et al., Phys. Plasmas 30, 010501 (2023).

Controlled fusion offers the promise of sustainable and safe energy production on Earth. In magnetic fusion devices, the power gain increases nonlinearly with the energy confinement time. The quality of the plasma energy confinement thus largely determines the size and therefore the cost of a fusion reactor. Unfortunately, small-scale turbulence limits the quality of confinement in most fusion devices. Hence modelling of turbulent transport is mandatory to find routes towards improved confinement regimes. Numerical simulations are based on a kinetic description of the plasma that can only be performed on most powerful supercomputers. The gyrokinetic GYSELA code runs efficiently on several hundred thousand CPU cores. With a consumption of 150 million CPU hours per year, the code makes massive use of petascale computing capacities and manipulates Petabytes of data. However, there are still many challenges to overcome in order to achieve a full description of electron dynamics that will require exascale simulations. In this context, scientific machine learning could play an important role to optimize the storage and the number of CPU hours consumed. We will present here our on-going work on integrating in-situ diagnostics using Artificial Intelligence techniques for data compression and automatic detection of anomalies or rare events.