PDE foundation model-accelerated inverse estimation of system parameters in inertial confinement fusion

TL;DR

This paper demonstrates that PDE foundation models can be effectively fine-tuned to solve inverse problems in inertial confinement fusion, achieving high accuracy in parameter estimation and hyperspectral reconstruction, especially with limited training data.

Contribution

The study introduces a method for adapting PDE foundation models to inverse problems in ICF, showing improved sample efficiency and performance over training from scratch.

Findings

High-accuracy hyperspectral reconstruction (test MSE 1.2e-3)

Strong parameter estimation (up to R^2=0.995)

Pretrained foundation models outperform scratch training in low-data regimes

Abstract

PDE foundation models are typically pretrained on large, diverse corpora of PDE datasets and can be adapted to new settings with limited task-specific data. However, most downstream evaluations focus on forward problems, such as autoregressive rollout prediction. In this work, we study an inverse problem in inertial confinement fusion (ICF): estimating system parameters (inputs) from multi-modal, snapshot-style observations (outputs). Using the open JAG benchmark, which provides hyperspectral X-ray images and scalar observables per simulation, we finetune the PDE foundation model and train a lightweight task-specific head to jointly reconstruct hyperspectral images and regress system parameters. The fine-tuned model achieves accurate hyperspectral reconstruction (test MSE 1.2e-3) and strong parameter-estimation performance (up to R^2=0.995). Data-scaling experiments (5%-100% of the training set) show consistent improvements in both reconstruction and regression losses as the amount of training data increases, with the largest marginal gains in the low-data regime. Finally, finetuning from pretrained MORPH weights outperforms training the same architecture from scratch, demonstrating that foundation-model initialization improves sample efficiency for data-limited inverse problems in ICF.