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# ICF target optimization using generative AI

M Ben Tayeb, Vladimir Tikhonchuk, J-L Feugeas

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M Ben Tayeb, Vladimir Tikhonchuk, J-L Feugeas. ICF target optimization using generative AI. Physics of Plasmas, 2024, 31 (10), pp.103903. 10.1063/5.0228824. hal-04855819

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# ICF target optimization using generative AI 📞 🔧 🔨

M. Ben Tayeb 📧 ; V. Tikhonchuk 📧 ; J.-L. Feugeas 📧

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# ICF target optimization using generative AI EP

Cite as: Phys. Plasmas **31**, 103903 (2024); doi: 10.1063/5.0228824

Submitted: 15 July 2024 · Accepted: 9 September 2024 ·

Published Online: 10 October 2024

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M. Ben Tayeb,<fnref n="1" />,ᵃ⁾ ID V. Tikhonchuk,<fnref n="1" />,<fnref n="2" /> ID and J.-L. Feugeas<fnref n="1" /> ID

## AFFILIATIONS

## ABSTRACT

This paper explores the capabilities of generative artificial intelligence (AI) for target optimization in inertial confinement fusion for energy production. For demonstration purposes, the focus is on optimizing the laser illumination temporal profile assuming a spherical implosion and a given target structure. An optimization protocol is based on the generative AI tool and a dataset for a shock ignition scheme produced with a reference hydrodynamic code. In a first optimization process, the generative AI proposed a family of laser power profiles by introducing a plateau before the shock that doubles the energy gain value of the reference configuration. In a second optimization process, the number of parameters defining the laser power profile is increased according to the results of the first step. The generative AI then suggested more general solutions including multiple plateaus and classical profiles without shock that further double the gain for half the laser energy required. The suggested optimization method can be extended to other configurations of laser-target interaction.

© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0228824

## I. INTRODUCTION

Optimizing complex processes is an essential yet often arduous task, regardless of the application field. Recent advances in generative artificial intelligence (AI) offer new opportunities in this domain, revolutionizing how machines can learn to create content, whether in terms of images, texts, music, or even videos.<fnref n="1" />⁻⁴ Variational autoencoders (VAEs) are one of the key tools in this area, providing dimensionality reduction and data generation capabilities that can facilitate the exploration of vast parameter spaces often inaccessible by classical heuristic approaches.⁵ Based on unsupervised learning, they compress data into a smaller, abstract representation called the latent space, highlighting correlations within the dataset. This tool allows querying the data and generating new instances correlated with the training set. This property is useful in applications such as image synthesis, text modeling, and data generation or optimization processes as presented in this paper.

In the direct drive Inertial Confinement Fusion (ICF) approach,⁶ an array of powerful laser beams converges on a millimeter-scale capsule containing two hydrogen isotopes—deuterium and tritium—that fuse to produce energy. ICF exploration requires expertise in a vast domain of physics and technology, including target hydrodynamics, laser-matter interaction, high-power lasers, and materials at extreme conditions. Because of the inherent complexity of experiments and limited access to high-energy laser facilities, high-performance computational codes are developed and used to design and interpret

experiments. These simulation tools play an important role not only in understanding the complex physical processes underlying this technology but also in optimizing experimental parameters, target geometry and structure, and laser illumination configuration with the goal of maximizing the energy gain—the ratio of thermonuclear fusion energy released to incident laser energy.

Like many other fields of physics, ICF sees the emergence of AI-based publications and counts among the many tools contributing to the rapid progress in this field.⁷⁻¹¹ Recent advances in laser-plasma interaction, target quality, computational power, and AI have coincided to advance this field. The design and construction of a fusion power plant still face challenges that could take decades to be overcome.¹² It is necessary to take advantage of progress in high-repetition-rate lasers, target fabrication, exascale supercomputers, and AI to accelerate this process.

We present here the method to explore the capabilities of generative AI for the ICF target design optimization, taking as an example the direct drive shock ignition scheme.¹³,¹⁴ Among many parameters that define the energy yield of an ICF target, we focus on the laser power temporal profile assuming a spherically symmetric implosion and standard target design.¹⁵,¹⁶

## II. SHOCK IGNITION TARGET DESIGN

In ICF, a spherical shell filled with hydrogen isotopes is irradiated by an intense flux of optical or x-ray radiation. The radiation energy is

<footnote n="1">¹Centre Lasers Intenses et Applications, Université de Bordeaux-CNRS-CEA, 33405 Talence, France</footnote>

<footnote n="2">²Extreme Light Infrastructure ERIC, ELI-Beamlines Facility, 25241 Dolní Březany, Czech Republic</footnote>

<footnote>ᵃ) Author to whom correspondence should be addressed: morad.ben-tayeb@u-bordeaux.fr</footnote>
absorbed at the external surface of the shell, leading to its ablation and conversion of a fraction of laser energy into kinetic energy of the remaining part of the shell. The shell kinetic energy is converted into internal energy of the fuel at the moment of stagnation, thus creating the conditions for the ignition of fusion reactions in the central part of the target. This energy release presents a spark that heats the inner layers of the compressed fuel and propagates fusion reactions. Two laser-driven implosion schemes are considered: in the direct drive, the lasers directly irradiate the spherical shell. It is considered as the approach compatible with fusion energy production that requires an energy gain on the order of 100. The indirect drive includes an additional step of converting laser energy into x rays that irradiate the target. This scheme has already demonstrated a gain larger than 1 in the experiments at the National Ignition Facility,¹⁷ but it is less suited for energy production because of the complexity of target fabrication and laser energy conversion.

The efficiency of target implosion and fusion energy production strongly depends on the temporal profile of laser pulse. In particular, in the shock ignition scheme, the implosion and ignition phases are achieved with two complementary laser pulses. The first one aims to optimize laser energy conversion in the shell kinetic energy and a stable implosion. The second one, called spike, aims to create the hotspot: the central part of fuel where the temperature and areal density satisfy the ignition condition: $T > 5$ keV and $ρR > 0.3$ g/cm². The set of parameters characterizing laser pulses is rather large. Recent studies show that the performance of the shock ignition scheme can be significantly improved.¹⁸ Here, we apply the generative AI approach for the further optimization of the direct drive scheme, aiming at maximizing the energy gain and minimizing laser energy.

The target designed for shock ignition within the HiPER project¹⁵ is shown in Fig. 1(a). It consists of a solid deuterium-tritium (DT) shell with the vapors inside covered by a layer of plastic ablator and a thin protection layer of aluminum. The standard profile of laser pulse power is shown in Fig. 1(b) with a red curve. It consists of five distinct parts. A short prepulse at the very beginning aims to create a plasma cloud by vaporizing the aluminum layer and initiates the first shock. In the second stage, a low-intensity pulse is applied to initiate a shock wave that compresses the fuel and provides it with an initial centripetal

<figure><img src="image_12.png" /><figcaption>FIG. 1. (a) Reference shock ignition target with a spherical layer of DT fuel containing a DT gas inside and covered with a plastic ablator and aluminum protection layer. (b) Temporal profile of the laser power (red) and the shell implosion diagram (black lines): the position of fluid elements as a function of time (Ref. 15). This setup gives an adiabat value around 1.7 for a maximum shell velocity of 300 km/s at time 13.38 ns.</figcaption></figure>

velocity. The third stage starts at approximately 7 or 8 ns. Here, the laser power is gradually increased according to Kidder's law¹⁹ and accelerates the shell isentropically to a velocity of about 300 km/s. The fourth stage corresponds to a constant laser power.

If the shell velocity is sufficiently high, the fuel will ignite at the moment when the shell collapses to the center. This is the case with the standard direct drive scheme. Conversely, shell kinetic energy is not sufficient for the fuel ignition with the shock ignition scheme. Additional energy is supplied with the fifth part of the laser pulse, a spike, that launches a strong converging shock, which collapses to the center and ignites fusion reactions. The trajectories of fluid elements of the shell are shown in Fig. 1(b) with black lines.

Optimization of shell implosion and fuel burn is a very difficult and time-consuming process. Generative AI could provide very useful new efficient tools in this domain. It allows the creation of new and realistic data using probabilistic models. Variational Autoencoders (VAEs) stand out for their ability to generate data in a controlled and coherent manner by constructing a structured and regularized latent space from the dataset.

### III. USING GENERATIVE AI FOR ICF TARGET OPTIMIZATION

#### A. Variational autoencoders

An autoencoder²⁰ consists of two main parts: an encoder and a decoder. The encoder transforms input data into a compressed, or latent, representation, while the decoder reconstructs the original data from this latent representation. The objective is to minimize the difference between the input data and the reconstructed data. VAEs, proposed by Kingma and Welling,⁵ enrich this architecture by adopting a probabilistic approach. A classical autoencoder favors the reconstruction of the dataset at the expense of coherent structuring of the latent space. A VAE introduces the Kullback-Leibler divergence,²¹ which tends to project the dataset representation in the latent space onto a probability distribution, thus regularizing this space and limiting dispersion. This operation slightly penalizes the loss function minimization, influencing the reconstruction phase to improve the quality and diversity of the generated data.

In this correlation space, two nearby points correspond to similar data, thus improving the coherence of data generation. VAEs allow generating intermediate data by merging the characteristics of two latent space points. Their ability to provide compact representations allows data manipulation and generation, and facilitate interpolation between different data instances.

VAEs thus offer considerable potential in searching for optimal solutions to complex problems. Thanks to their ability to generate new data in a regularized latent space, VAEs allow exploring new solutions in an optimization approach.

#### B. Dataset generation

The dataset is built from one-dimensional (1D), spherically symmetric simulations with the radiative hydrodynamics code CHIC.²² This code was developed at CELIA for simulating and interpreting ICF experiments and modeling laser-plasma interaction in high energy density regimes. The code accounts for the laser inverse Bremsstrahlung absorption, multigroup electron and radiation energy transport with a flux limiter $f = 0.07$, and electron-ion temperature
relaxation. It includes also a package describing fusion reactions and
alpha particle transport in the diffusion approximation.

**Figure 1** presents a shock ignition target design, a typical laser illumination profile, and a flow diagram. The shell of a radius of 988 µm contains a cryogenic DT shell of 220 µm thickness with a DT vapor inside, a CH shell of 31 µm, and an aluminum layer of 0.015 µm. The temporal profile of laser power containing the main pulse and the spike is described by 512 points. The flow diagram (b) presents the temporal evolution of the Lagrangian cells of the imploding target. In the reference run, an incident laser energy of 678 kJ produces 36.6 MJ of fusion energy, which corresponds to a gain of 54. 1D simulations neglect multi-dimensional effects that penalize implosion. For this reason, the gain can be largely overestimated. However, our methodology of using generative AI can also be applied to further target optimization with more realistic constraints.

The first dataset is built from variations of four key parameters of
the laser power profile: plateau and spike power and their duration, as
shown in Fig. 2(a). 1200 laser power profiles are simulated with the
CHIC code to obtain the gain for constant laser energy and a given tar-
get structure. They form the dataset to train the VAE. The gain

histogram in Fig. 2(b) shows that 82% of cases have gains below one
but some cases produce slightly higher gains than the reference case.
This dataset is used to train the VAE to find new cases that might fur-
ther increase the target’s performance.

The dataset includes the gain in function of four parameters of
variation. The training is performed in two steps. First, a VAE is
trained on the dataset of 1D laser profiles to have a process that gener-
ates new laser profiles from the latent space. In the second step, a dense
network is trained to predict the gain from the latent space points.
This methodology allows decoding any point in the latent space into a
laser profile and having an estimate of the gain proposed by an artifi-
cial neural network (ANN). Thus, one can visualize in the latent space
the trends in terms of gain and the profiles associated with the areas of
interest. However, the latent space is generally multi-dimensional,
making its exploration challenging. It can be explored in several ways:
choosing two arbitrary dimensions to display the latent space, training
a new neural network on the latent space, using dimensionality reduc-
tion algorithms, etc. To simplify this study, we chose a linear reduction
algorithm, principal component analysis (PCA).²³ This is a commonly
used multivariate statistical technique to reduce the dimensionality of
datasets while retaining as much variation as possible. This method
transforms an initial set of correlated variables into a new set of uncor-
related variables, called principal components, ordered so that the first
principal component explains the largest portion of the total variance,
the second principal component explains the largest portion of the
remaining variance, and so on.

C. Method of optimization

The scheme of the optimization process is shown in Figs. 3 and 4.
First, a VAE is trained to reconstruct laser profiles and create a latent
space for generating new profiles. Second, a network maps a gain to
each point in the latent space to generalize the gain across the entire
latent space.

The VAE consists of two dense networks for the encoder and decoder, each with 10 hidden neuron layers representing about 200 000 parameters to optimize. The training data are 512-sized vectors (the number of points describing the laser power vs time), and the latent space dimension is set to 5 for good reconstruction. The loss is penalized by the Kullback–Leibler divergence, which tends to regularize and structure the data in the latent space. Several iterations were necessary to find a good compromise between good reconstruction and good structuring.

Once the network is trained, all the dataset elements can be
encoded into a latent space of a reduced dimension. Conversely,
decoding these points allows for the reconstruction of the original data
(laser profiles). Additionally, this space enables decoding of points that
are not part of the dataset, showcasing its generative capability.
Decoding each intermediate point in this latent space provides a laser
profile form generated by the VAE: the provided profiles may belong
to the dataset laser profile family but may also deviate significantly. To
facilitate latent space (5D) visualization and new data generation, we
project it into 2D space using PCA.

This process allows for the generation of new laser profiles
that are highly correlated with the dataset but sometimes disrup-
tive. To search for the optimal solution, information about gain
must be added to this space. Therefore, we need to estimate the
gain of the generated profiles and, more generally, the entire latent

<figure><img src="image_13.png" /><figcaption>FIG. 2. Scheme of dataset generation: (a) Four parameters of variation around the reference case. (b) Histogram of performance: a number of cases vs gain.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>FIG. 3. VAE trained on a dataset of temporal laser intensity profiles; the 5D latent space is projected into 2D using PCA.</figcaption></figure>

space. This is achieved by training a second network that receives a laser profile as input and outputs the gain value provided by the hydrodynamic simulation.

After completing the VAE training and constructing the corresponding latent space, each training datum within this space can be assigned a previously calculated gain. To capture gain trends within this latent space, a second neural network is trained. This network, consisting of 10 layers and approximately 30 000 parameters, maps input points from the latent space to predicted gains. This enables the assignment of gains to any point within the latent space. Thus, with the trained network, each point in the latent space can be assigned to a gain, and every profile generated by the VAE receives an estimated gain from this neural network.

The network's performance is evaluated using various metrics, with the primary metric being the loss function, which is minimized during training. Its progression throughout the training iterations (epochs) can be observed in Fig. 5(a). This curve verifies the two criteria: convergence of the loss function and that there is no overfitting—the network can generalize to unseen (validation) data in Fig. 5(a). Additionally, other metrics can be used to have a broader view of network performance, such as a relative error histogram between prediction and true value, as shown in Fig. 5(b).

This histogram shows a relative error of less than 7% and an average value of 2%.

## IV. APPLICATIONS AND RESULTS

### A. First dataset of laser power profiles

The network optimization performance is characterized by mapping gains in the latent space using the second neural network trained on the gain values provided by hydrodynamic simulations. The gains map in the latent space predicted by the neural network is shown in Fig. 6. A high-gain zone in the latent space confirms the possibility of laser profile optimization compared to the reference case shown with the red point. Areas of large gain above 100 in the latent space are zoomed in Fig. 7(a). Two high-gain zones, A and B, are further enlarged in panels (b) and (c). The morphology of these two areas is different: In zone A, the maximum gain area is located at the edge of a ridge and thus close to a zero-gain area, suggesting that the generated solutions would likely be less robust. Conversely, the other maximum gain area B corresponds to more robust high-gain solutions.

By decoding points belonging to these high-gain areas, the VAE proposed new laser power profiles that deviate from the classical shock ignition case shown with the red point in Fig. 7(a). In area A, the laser

<figure><img src="image_15.png" /><figcaption>FIG. 4. Construction of a full latent space gain map: all the hydrodynamic simulations carried out with the CHIC code; for each case in the dataset provides the target gain. These data are used to train an ANN capable of reconstructing the latent space as a whole: (a) latent space from the VAE. (b) Latent space filled in for each case in the dataset with the value of the gain from the CHIC simulations—these data can be used to train the ANN. (c) Latent space reconstructed with the gains estimated by the ANN.</figcaption></figure>
<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /><figcaption>FIG. 5. (a) Evolution of loss as a function of epochs of the iterative learning process. (b) Histogram of relative errors on prediction given by the VAE.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>FIG. 6. Map of dataset gains predicted by the neural network in the 2D latent space projected using PCA. The red point locates the reference case.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>FIG. 7. (a) Map of reconstructed gains decoded in the latent space. Zones A and B are zoomed on panels (b) and (c) along with the corresponding laser power profiles. The red point locates the reference case.</figcaption></figure>

profile contains two plateaus of increasing power followed by a spike. In area B, the power of the second plateau is reduced, followed by a spike of higher intensity. This latter configuration is similar to the “shock-augmented scheme” proposed by Scott et al.¹⁸

The CHIC simulation for the case in zone B yields a maximum gain of 113 for an incident laser energy of 460 kJ. The shell implosion diagram is shown in Fig. 8. Compared to the reference case, the gain is thus doubled, and the required incident laser energy is divided by 1.5. This gain is comparable to the shock-augmented design¹⁸ but with four times smaller laser energy, this may demonstrate the efficiency of the optimization scheme, although due to the different codes employed, we cannot state this conclusively.

## B. Dataset with more general laser profiles

The configuration of two plateaus is further explored by conducting hydrodynamic simulations with laser intensity profiles having six free parameters, as shown in Fig. 9(a). The target remained the same as shown in Fig. 1(a), and the laser energy is maintained within the

<figure><img src="image_20.png" /><figcaption>FIG. 8. Shell implosion diagram for the double plateau hydrodynamic simulation corresponding to the shock-augmented design. The target gain is 113 for the incident laser energy of 460 kJ. This setup gives an adiabat around 2.6 for a maximum shell velocity of 286 km/s at time 14.89 ns.</figcaption></figure>
<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>FIG. 9. (a) Generation of a family of cases including six free parameters around the solution suggested by AI. (b) Histogram of performance: number of cases vs gain.</figcaption></figure>

range of 300–700 kJ. A new VAE is trained on this new dataset, and the histogram of gains is shown in Fig. 9(b). Compared to Fig. 2, this figure confirms the capability of AI in searching for high-gain solutions.

The gain map in the latent space for this new dataset is shown in Fig. 10. The red point indicates the reference case, which is not included in the training dataset. The gain estimated by the network for this point is 59, close to the gain calculated by CHIC, which is 54. The shock-augmented case is shown with the orange point.

Exploring this new latent space reveals other families of laser profiles able to produce even larger gains. Five zones are zoomed in Fig. 11:

* A: double plateau followed by a spike;

* B: double plateau preceded by a dip reminiscent of a generalized shock-augmented profile;

* C: profile close to the reference shock ignition case with another plateau before the shock;

* D: smooth direct drive-like profile;

* E: square direct drive profile.

Interestingly, the highest gains are located at low laser energies, very close to an abrupt cliff near the zero gain zone at the top right of

<figure><img src="image_23.png" /><figcaption>FIG. 10. Map of gains in the latent space computed with the hydrodynamic code for each laser intensity profile in the second dataset. The red and orange points locate the reference case and shock-augmented mode.</figcaption></figure>

the latent space. This particular topology reflects the physics of the shock ignition scheme, which implies a collision of the shock wave launched by the spike and the main shock reflected from the center to occur near the inner surface of the imploding shell, in close vicinity of the hotspot.²⁴⁻²⁶ This requires a fine synchronization of shocks and a precise tuning of the laser pulse profile. Thus, the position of the cliff can be assimilated to the shock collision at the inner edge of the shell.

The interest in double plateau profiles, already observed in the previous case, is confirmed. They can produce gains of around 100 in robust areas of the latent space.

By validating several laser power profiles suggested by the VAE with hydrodynamic simulations, we obtain a gain of 117 in zone D at a laser energy of 348 kJ. This case corresponds to a smooth direct drive. As shown in the flow diagram in Fig. 12, the shock is removed, leading to a twice-larger gain with only half the incident laser energy.

Although this profile is near the zero gain area, it resides in a relatively stable, flat gain region. Moreover, this smooth direct drive temporal laser profile corresponds to a relatively low laser power of less than 100 TW that can be easily realized in high-repetition-rate experiments. The implosion performance can be further improved by optimizing the target design.

V. CONCLUSION AND PERSPECTIVES

Generative AI is a new breakthrough tool that allows efficient exploration of complex parameter spaces and leads to significant advances in ICF target performance. The work presented in this paper demonstrates that VAEs can generate unexpected laser illumination profiles, offering substantially larger thermonuclear gains for lower laser energy and power.

Among the solutions proposed by AI, there are standard direct drive, double plateau profiles, and profiles with a dip. These solutions include already known profiles, such as shock ignition and shock-augmented ignition, and also new configurations with double plateaus or without plateaus. The optimized profiles double the thermonuclear gain while reducing the required incident laser energy by half.

A key aspect of our approach lies in the systematic validation of optimization work by detailed hydrodynamic simulations conducted
<figure><img src="image_24.png" /><figcaption>**FIG. 11.** Gain map in the latent space estimated by the neural network and decoded laser power profiles for five selected zones of high gain. Contour lines indicate laser energy in MJ. (a) Double plateau (laser energy 0.658 MJ, energy gain 54); (b) Double plateau with dip (0.769 MJ, 49); C: shock ignition case (0.586 MJ, 71); (d) smooth direct drive profile (0.348 MJ, 117); and (e) square direct drive profile (0.395 MJ, 109).</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>**FIG. 12.** Target flow diagram (black lines) obtained in the hydrodynamic simulation with a smooth direct drive laser pulse (D, red). The laser energy is 348 kJ and the gain is 117. This setup gives an adiabat value of 2.0 for a maximum shell velocity of 237 km/s at time 13.46 ns.</figcaption></figure>

with a reference hydrodynamic code, confirming the proposed avenues and the potential of this approach. This method can also incorporate robustness criteria, which are particularly important from the perspective of a fusion power plant design that requires a robust operational domain, simple target fabrication, and safe and secure laser operation. Exploring the latent space reveals correlations between the controlling parameters and offers robust solution areas that should be prioritized.

Several challenges and perspectives remain to be explored. The demonstration made in this paper is based on simplified one-dimensional simulations. The gains can be overestimated. However, this can be improved in the future by constructing larger datasets based on more realistic multi-dimensional hydrodynamic simulations, including more physics and experimental inputs. The objective of this paper is to validate a methodology and demonstrate it in a simple example. The target characteristics can also be optimized. Energy gain and incident laser energy are chosen as criteria in the work. A larger number of parameters that are critical for implosion quality will be included in the next steps.

The rapid evolution of high-performance computing and target fabrication technologies, combined with AI advances, presents an extremely favorable framework for advancing ICF research. The synergy
between these fields is not just beneficial but crucial for considering sig-
nificant advances in achieving controlled thermonuclear fusion. This
convergence brings this technology closer to reality than ever before.

ACKNOWLEDGMENTS

We acknowledge the Commissariat à l'Énergie Atomique et
aux Énergies Alternatives for funding this work. We thank Didier
Raffestin for his attention and fruitful discussions in this
groundbreaking field. We thank Aurélia Maïolo for her invaluable
assistance in providing us with results from the CHIC simulation
code. We thank the CELIA IT team for their support.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

**M. Ben Tayeb:** Conceptualization (equal); Writing – original draft (equal); Writing – review & editing (equal). **V. Tikhonchuk:** Conceptualization (supporting); Writing – review & editing (equal). **J.-L. Feugeas:** Conceptualization (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

DATA AVAILABILITY

The data that support the findings of this study are available from
the corresponding author upon reasonable request.

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