Automated simulation-based design via multi-fidelity active learning and optimisation for laser direct drive implosions

Abstract: The design of inertial fusion experiments is a complex task as driver energy must be delivered in a precise manner to a structured target to achieve a fast, but hydrodynamically stable, implosion. Radiation-hydrodynamics simulation codes are an essential tool in this design process. However, multi-dimensional simulations that capture hydrodynamic instabilities are more computationally expensive than optimistic, 1D, spherically symmetric simulations which are often the primary design tool. In this work, we develop a machine learning framework that aims to effectively use information from a large number of 1D simulations to inform design in the presence of hydrodynamic instabilities. We use an ensemble of neural network surrogate models trained on both 1D and 2D data to capture the space of good designs, i.e. those that are robust to hydrodynamic instabilities. We use this surrogate to perform Bayesian optimisation to find optimal designs for a 25 kJ laser driver. We perform hydrodynamic scaling on these designs to confirm the achievement of high gain for a 2 MJ laser driver, using 2D simulations including alpha heating effects.

• The paper introduces a multi-fidelity simulation and ML-driven framework that transfers information from 1D to 2D for optimized LDD ICF designs.
• It employs Gaussian Processes and ensemble neural networks with active learning and Bayesian optimization to significantly reduce costly 2D simulations.
• Results demonstrate robust design improvements, including a 217-fold yield amplification at 2 MJ compared to traditional 1D-optimized designs.

Automated Multi-Fidelity Simulation-Based Design for Laser Direct Drive Implosions

Introduction and Motivation

The design of inertial confinement fusion (ICF) experiments, particularly for laser direct drive (LDD) implosions, is characterized by a high-dimensional, nonlinearly coupled parameter space. Achieving robust ignition and high gain requires precise control over both target and laser pulse parameters, while simultaneously mitigating hydrodynamic instabilities that degrade performance. Radiation-hydrodynamics (rad-hydro) simulations are essential for design, but the computational cost of multi-dimensional (2D/3D) simulations is prohibitive, especially when compared to 1D simulations that neglect instability growth. This paper presents a ML framework that leverages multi-fidelity surrogate modeling, active learning, and Bayesian optimization to efficiently explore and optimize the LDD design space, transferring information from large ensembles of inexpensive 1D simulations to inform and accelerate the search for robust designs in 2D.

Methodological Framework

Design Space and Objective Function

The design space is parameterized by eight variables: five laser pulse parameters (picket power, foot power, picket-foot delay, foot duration, rise time) and three target parameters (outer radius, ablator thickness, ice thickness). The laser pulse is described by a composite function with a picket, foot, and power-law rise to peak power, while the target consists of a CH ablator, DT ice, and DT gas. The objective function is a physics-informed scalar that combines an ignition metric ($\chi_{S, no \alpha}$) and areal density ($\rho R$), enabling sub-scale optimization that targets ignition and burn propagation at higher energy scales. This formulation allows for hydrodynamic scaling from OMEGA-scale (25 kJ) to NIF-scale (2 MJ) drivers.

Simulation Pipeline

The Chimera code, coupled with the SOLAS 3D laser raytracing model, is used for rad-hydro simulations. 1D simulations are used for large-scale parameter sweeps, while 2D simulations incorporate both deterministic (beam mode) and stochastic (ablator surface perturbations) sources of instability. The 2D simulations employ an automatic restart from spherical to cylindrical geometry to optimize computational efficiency. The computational cost is approximately 1 core-hour for 1D and 200 core-hours for 2D simulations, with parallelization across 32 and 128 CPU cores, respectively.

Surrogate Modeling

Two classes of surrogate models are employed:

• Gaussian Processes (GPs): Used for small-to-moderate datasets, with Matern kernels and anisotropic lengthscales. GPs provide calibrated uncertainty estimates but scale poorly with large datasets ($\mathcal{O}(N^3)$ complexity).
• Ensemble Neural Networks (NNs): Multi-layer perceptrons (MLPs) implemented in PyTorch, trained as ensembles to provide uncertainty estimates via prediction variance. Transfer learning is used to adapt 1D-trained models to 2D with limited 2D data, freezing all but the last two layers during retraining. Calibration of ensemble uncertainty is performed to ensure reliable confidence intervals.

Active Learning and Bayesian Optimization

Active learning is implemented via probabilistic threshold sampling, focusing expensive 2D simulations in regions of the design space predicted to be promising by the surrogate. Bayesian optimization is performed using the log Expected Improvement (LEI) acquisition function, maximizing the surrogate's predicted objective while accounting for uncertainty. Due to the extreme cost disparity between 1D and 2D simulations, Bayesian optimization is performed at fixed fidelity, but with surrogates trained on both fidelities.

Orchestration

The mille-feuille orchestration framework automates the workflow, handling input deck generation, simulation execution, post-processing, surrogate retraining, and optimizer queries. This enables efficient use of HPC resources and supports parallelism at multiple levels.

Optimization Studies and Results

1D Optimization

A Sobol sequence is used to generate $\sim$12,500 1D simulations, with only $\sim$3% achieving $Y > 1$ (ignition-relevant). Active learning further populates the high-performing region, and both GP and NN ensemble surrogates are trained. Bayesian optimization with the NN ensemble converges rapidly to the highest-performing design, outperforming the GP due to better scalability.

2D Optimization and Multi-Fidelity Transfer

A subset of high-performing 1D designs is re-simulated in 2D to form a transfer sample. Transfer learning enables the NN ensemble surrogate to capture the degradation in performance due to hydrodynamic instabilities, with uncertainty reflecting the stochastic nature of 2D perturbations. Active learning with the 2D surrogate efficiently explores the robust region, requiring only $\sim$128 2D simulations. Bayesian optimization identifies a 2D-optimal design with an objective value of $\sim$3.0, compared to $\sim$3.5 in 1D.

Performance at 25 kJ and 2 MJ Scales

At 25 kJ, the 2D-optimized design ($O_{2D}$) exhibits higher hydrodynamic stability (lower IFAR, higher minimum adiabat) and only modest performance degradation relative to the 1D-optimized design ($O_{1D}$). 2D simulations reveal that $O_{2D}$ maintains shell integrity at bang time, while $O_{1D}$ suffers from instability-induced shell breakup.

Hydrodynamic scaling to 2 MJ, with and without alpha heating, demonstrates that $O_{2D}$ achieves a yield amplification of 217 (burn-on/burn-off), compared to only 17 for $O_{1D}$. The $O_{2D}$ design supports robust burn propagation and high burn fraction ($\sim$15%), while $O_{1D}$ fails to confine the hotspot, resulting in poor burn propagation. These results confirm that the multi-fidelity, ML-driven design framework can identify designs that are robust to instabilities and scalable to ignition-relevant conditions.

Implications and Future Directions

The presented framework demonstrates that multi-fidelity surrogate modeling, active learning, and Bayesian optimization can dramatically reduce the number of expensive high-fidelity simulations required for robust ICF design. The use of transfer learning in NN ensembles is shown to be effective for knowledge transfer across fidelities, and the orchestration framework enables scalable, automated design studies.

Key numerical results include:

• Reduction of required 2D simulations by an order of magnitude via transfer learning.
• Yield amplification at 2 MJ scale: 217 for $O_{2D}$ vs. 17 for $O_{1D}$.
• Demonstration that 1D-optimized designs are not robust to hydrodynamic instabilities, while 2D-optimized designs maintain performance under realistic perturbations.

Practical implications:

• The methodology is directly applicable to other high-dimensional, computationally expensive design problems in plasma physics and beyond.
• The open-source orchestration framework (mille-feuille) facilitates integration with other simulation codes and ML models.
• The approach is extensible to higher-dimensional design spaces, additional fidelities (e.g., 3D, experimental data), and alternative ICF schemes (e.g., MagLIF).

Theoretical implications:

• The results highlight the importance of incorporating instability physics and stochastic perturbations in surrogate-based optimization.
• The success of transfer learning in this context suggests broader applicability for multi-fidelity design in other domains with severe cost disparities.

Future work should address scaling to larger design spaces, inclusion of additional physical effects (e.g., cross-beam energy transfer, more realistic perturbations), and exploration of alternative optimization strategies for high-dimensional problems.

Conclusion

This work establishes a robust, automated framework for simulation-based design of LDD ICF implosions, leveraging multi-fidelity surrogate modeling, active learning, and Bayesian optimization. The approach efficiently transfers information from large ensembles of inexpensive 1D simulations to guide the search for robust, high-performing designs in 2D, significantly reducing computational cost. The framework identifies designs that are not only optimal in 1D but also robust to hydrodynamic instabilities in 2D, and scalable to ignition-relevant conditions. The methodology and orchestration tools developed here are broadly applicable to other complex, computationally intensive design problems in plasma physics and related fields.