AI-Driven Optimization for Direct-Drive ICF Implosions

Three-dimensional multicolored hydra simulation of shot 94017.

Three-dimensional hydra simulation of shot 94017, modeled from the beginning of the implosion including all large-scale drive nonuniformity sources. This simulation helps researchers understand how imperfections can distort the shape and reduce the performance of a fusion implosion.

Integrating Machine Learning Techniques for Enhanced Performance

Inertial confinement fusion (ICF) holds promise as a powerful energy source capable of producing bursts of energy measured in hundreds of megajoules. It has the potential to support both national security and the development of clean, sustainable energy. At Lawrence Livermore National Laboratory, scientists recently reached ignition using a laser-indirect-drive approach. Meanwhile, researchers here at LLE’s Omega Laser Facility are taking a different path studying laser direct drive, a method that could prove to be more energy efficient. Unlike laser indirect drive, which works by converting laser beams into x rays that heat and compress the target, laser direct drive applies the laser energy directly to the target itself. This direct interaction can achieve higher compression with less energy input, but it also makes it harder to keep the implosion symmetric—a key factor in triggering fusion.

Kristen Churnetski and Jack Woo in the OMEGA Control Room at the Laboratory for Laser Energetics. — Kristen Churnetski and Jack Woo in the OMEGA Control Room at the Laboratory for Laser Energetics on Monday, November 18, 2024.

This article explores how imperfections in the drive symmetry of laser direct drive implosions can lead to uneven compression of the fuel capsule, leaving behind residual kinetic energy. This leftover energy, which fails to contribute to compressing the fuel, ultimately limits the total energy output of the implosion [1]. LLE scientists Jack Woo and Kristen Churnetski, a doctoral student in mechanical engineering, are investigating deep-learning neural network models to create 3D reconstructions of the hot spots formed during implosions. Their work helps scientists better understand and correct the asymmetries that can limit the efficiency of fusion experiments on the OMEGA Laser System.

On the OMEGA Laser System, 60 high-power ultraviolet laser beams deliver up to 30 kJ of energy onto spherical targets. The goal is to drive a smooth, symmetric compression of a fusion capsule with layered fuel. As the laser strikes the outer surface of the target, the material ablates and the ablation blows material off (outward) creating the “rocket effect” that accelerates (or pushes) the remaining material inward. This forms a high-temperature, low-density central hot spot surrounded by a dense, colder shell of fuel. For ignition to occur, the pressure in the hot spot must soar to nearly 100 Gbar—approximately 100 billion times the atmosphere of Earth—and remain at this pressure for roughly 70 trillionths of a second. However, imperfections in the implosion often stand in the way, disrupting the symmetry needed to reach those extreme conditions [2,3,4].

There are several sources of asymmetry in laser-direct-drive implosions. First, the target is illuminated by only a finite number of laser beams. Each beam has a slightly different focal profile and pulse shape, and no beam is perfectly aimed at the exact center of the target. Combined, these factors produce nonuniformities known as low-mode asymmetries. Scientists describe these nonuniformities using spherical harmonics and focus on the lowest few modes, which tend to have the greatest impact on performance. Low-mode asymmetries reduce the effectiveness of the implosion by limiting how much the fuel can be compressed.

To picture the challenge, imagine squeezing a balloon. When pressure is applied evenly and from all sides, the balloon’s shape will remain uniform and intact, with no bulges or distortions. But with two hands, a person can only squeeze from opposite directions, causing air to bulge out from the sides. Something similar happens when low-mode asymmetries distort the compression of a fusion target. The material in regions with stronger drive pushes into areas where the laser energy is weaker, breaking the symmetry and causing degradation in fuel compression.

In an ideal implosion, the compression is perfectly spherical, and all motion within the fuel stops at the moment of peak compression. This means that the kinetic energy used to compress the fuel is fully converted into internal energy in the hot spot and surrounding fuel. When the implosion is asymmetric, however, the fuel continues moving, even at peak compression. This leftover motion drains energy from the system, a phenomenon known as residual kinetic energy. The greater the asymmetry, the more energy remains in motion rather than contribute to the pressure and temperature needed for fusion. As a result, the fusion yield drops, limiting the overall performance of the implosion [5,6].

Scientists can detect this lingering motion by analyzing the energy spectrum of the neutrons produced during fusion reactions between deuterium and tritium. In a perfectly symmetric implosion, the neutron spectrum forms a bell-shaped curve, and its width reflects the ion temperature of the fuel. In an asymmetric implosion, however, different parts of the shell move at different speeds, and the extra motion adds to the width of the spectrum. By measuring the neutron spectrum along different directions, researchers can infer the extent of residual fuel motion. Because both thermal motion and flow contribute to the broadening of the spectrum, the result is an “apparent” temperature that varies depending on where it is measured. The greater the difference between directions, the more residual motion is present in the fuel [7].

In addition to measuring apparent temperature differences, researchers also examine the shape of the x rays emitted by the hot plasma in the core. Variations in the x-ray image offer another clue to understanding how low-mode asymmetries shape the implosion from within [8,9,10].

Deep learning neural networks give us a way to learn complex data relationships in order to better understand the 3D nature of implosions.

Dr. Jack Woo
Scientist, Laboratory for Laser Energetics

Machine Learning Framework

Because low-mode asymmetries reduce compression and lower the chances of achieving ignition, researchers are now turning to AI to help understand asymmetry development and optimize implosion performance. These tools form a target optimization system made up of three core modules: a 3D reconstruction platform, a data analysis platform, and a 1D optimization platform.

To support this system, scientists use an artificial neural network, a type of AI that loosely replicates the work of neurons in the brain to process information [11]. A basic neural network consists of an input layer, a hidden layer of interconnected artificial neurons, and an output layer. Each neuron receives input data, applies a set of weights and a bias, and transforms the result using a nonlinear function. These outputs are passed forward through the network, gradually refining the data.

With enough neurons and the right structure, an artificial neural network can learn to model complex, continuous relationships between input and output variables. In the context of ICF, this means the network can predict how design choices affect implosion performance and help identify opportunities for improvement.

Three-Dimensional Reconstruction Platform

The first step in the optimization process uses a neural network to convert 2D x-ray images from ICF experiments into a 3D reconstruction of the implosion. The network’s layers distill high-dimensional spatial features, pulling out the 3D structure encoded in the 2D images. Before the network can perform these tasks, however, it must be trained by adjusting its internal weights and biases. In this case, training is done using data obtained from hydrodynamic code dec3d [5].

To build the training set, Woo and Churnetski generated a large database of synthetic x-ray images using 3D simulations. Once the network was trained on this dataset, it could be applied to real experimental data from the Omega Laser Facility. By combining information from multiple x-ray detectors, the model reconstructs the 3D shape of implosions, quantifies asymmetries, and helps explain how those asymmetries affect fusion performance. It can also estimate physics quantities such as x-ray emissivity and pressure in the region where fusion reactions occur.

As discussed earlier, residual kinetic energy is one way to access asymmetry in an implosion. To better understand the link between asymmetries and this leftover energy, researchers ran 3D simulations with a range of asymmetry levels. They found that higher asymmetries led to stronger internal flows and more residual energy, suggesting a direct connection between drive imperfections and energy loss.

Improving Implosion Symmetry

In the previous section, we described how we use the neural network model to infer implosion asymmetry. In this section, we discuss the ways to apply AI models to mitigate such asymmetries. Next, we show an example of this process using a series of implosions where the targets are filled with the fuel at room temperature (without forming a cryogenic fuel layer). This was done to simplify the target production and facility operations so many more targets can be shot during the experimental campaign. To demonstrate the techniques, we first deliberately introduced mode-1 and mode-2 shape distortions to the target followed by 3D hot-spot reconstructions after each shot, as described in the previous section. Then we applied appropriate laser-energy balance correction across all 60 of OMEGA’s beams to progressively achieve more-symmetric implosions within a shot day.

Optimization Platform

Building on the models used to identify and mitigate implosion asymmetries, researchers developed a strategy to improve the performance of cryogenic ICF implosions. This strategy involves two steps: first, minimize asymmetries through 3D symmetry control; second, maximize compression by refining 1D implosion dynamics. To support this approach, a data-driven evolutionary optimization algorithm was introduced to improve target performance, as predicted by the neural network model.

This optimization approach was tested during OMEGA’s experimental campaign where the temperature of cryogenic fuel was lowered to take advantage of the lower density in the central region of the target. One of the highest-performing shots to date, shot 112469, resulted from this process. The shot produced a strong fusion reaction and demonstrated fuel compression and performance levels that provide valuable insights for future experiments.

Three-Dimensional Simulations

The 3D hydrodynamic simulations play a critical role in developing AI tools. They validate the basic principles of neural network modeling by comparing the results of such models with the code predictions. These codes, hydra in this case, play a surrogate role for a real-life experiment [12]. The physics of hydrodynamics, radiation transport, tabular equations of state, nonlocal electron transport, and laser deposition via a fully 3D ray-trace model with cross-beam energy transfer were included in the simulation. The perturbation sources modeled included the 60-beam OMEGA beam geometry, target offset from the center of beam convergence, individual beam mispointing, and individual beam-power histories (including both mistiming and power imbalance) using measured data for all these inputs.

A 3D plot of various isodensity contours at stagnation is shown in (a), with half of the target plot clipped so that the internal structure of the shell and hot spot are visible. Density contours from this machine-learning fine-tuned dec3d simulation data are also shown in (b) with the same scale and isodensity contours for comparison with the hydra data. The plots show good qualitative and quantitative agreement in overall shape and certain smaller-scale features. Some differences in the small-scale features can be attributed to the fact that more features in the OMEGA laser nonuniformity were modeled in the hydra simulation.

Two three-dimensional computer simulation images. The one on the left shows 3D HYDRA and is roughtly a sphere but is very wavy. The one on the right is a 3D ML reconstruction and the image is much more spherical. The height is 70 microns. — Comparison of experimental measurements: hydra simulations and (b) dec3d machine learning reconstruction for OMEGA shot 94017.

Conclusion

AI is beginning to reshape how scientists approach some of the most complex challenges in inertial confinement fusion. By combining machine learning tools with detailed x-ray diagnostics and high-fidelity simulations, researchers are building systems that not only diagnose asymmetries in laser-driven implosions but also actively correct them in real time. These advances have already led to improved experimental performance at the Omega Laser Facility, including some of the highest-yield shots recorded in recent campaigns.

Each element of this framework, 3D reconstruction, data analysis, and optimization, relies on a foundation of robust physical modeling and carefully trained neural networks. When tested against both experiment and simulation, these models show strong agreement and demonstrate practical value in guiding real-world adjustments to laser conditions and target design.

While challenges remain, particularly in extending these techniques to the more-demanding conditions of cryogenic implosions, the results so far suggest that AI-driven strategies may become essential tools for improving implosion performance. By narrowing the gap between prediction and outcome, these systems offer a promising path forward in advancing high-energy-density physics research.

Focus Points

Artificial intelligence and machine learning techniques are helping to reconstruct and analyze the hot spots (areas of high energy) in fusion experiments at the Laboratory for Laser Energetics.
Researchers at LLE have developed a method to create 3D images of hot spots using data from x-ray detectors. The images help scientists understand how well the fusion process is working and help identify any problems.
Maintaining symmetry optimizes the energy production in the fusion process, and LLE uses artificial intelligence and machine learning to help correct asymmetries during fusion experiments.

A version of this article appears in Issue 6 of LLE In Focus, the magazine of the University of Rochester’s Laboratory for Laser Energetics.