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

arXiv: https://arxiv.org/abs/2603.04606 · HTML: https://mlsanity.com/paper/2603.04606/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 44 references that are in the map.
- First posted on arXiv 4 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [Towards Foundation Models for Scientific Machine Learning: Characterizing Scaling and Transfer Behavior](https://mlsanity.com/paper/2306.00258/) (2023)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [Learning two-phase microstructure evolution using neural operators and autoencoder architectures](https://mlsanity.com/paper/2204.07230/) (2022)
- [Improved Surrogates in Inertial Confinement Fusion with Manifold and Cycle Consistencies](https://mlsanity.com/paper/1912.08113/) (2019)
- [MORPH: PDE Foundation Models with Arbitrary Data Modality](https://mlsanity.com/paper/2509.21670/) (2025)
- [A conditional latent autoregressive recurrent model for generation and forecasting of beam dynamics in particle accelerators](https://mlsanity.com/paper/2403.13858/) (2024)
- [Time-inversion of spatiotemporal beam dynamics using uncertainty-aware latent evolution reversal](https://mlsanity.com/paper/2408.07847/) (2024)
- [URSA: The Universal Research and Scientific Agent](https://mlsanity.com/paper/2506.22653/) (2025)
- [Foundation Models for Discovery and Exploration in Chemical Space](https://mlsanity.com/paper/2510.18900/) (2025)
- [Transfer learning driven design optimization for inertial confinement fusion](https://mlsanity.com/paper/2205.13519/) (2022)
- [Physics consistent machine learning framework for inverse modeling with applications to ICF capsule implosions](https://mlsanity.com/paper/2412.20192/) (2024)
- [Towards Reasoning for PDE Foundation Models: A Reward-Model-Driven Inference-Time-Scaling Algorithm](https://mlsanity.com/paper/2509.02846/) (2025)
- [Parallelizing Training of Deep Generative Models on Massive Scientific Datasets](https://mlsanity.com/paper/1910.02270/) (2019)
- [Inverse characterization of composites using guided waves and convolutional neural networks with dual-branch feature fusion](https://mlsanity.com/paper/2204.10486/) (2022)
- [A Foundation Model for Material Fracture Prediction](https://mlsanity.com/paper/2507.23077/) (2025)
- [Exploring Generative Physics Models with Scientific Priors in Inertial Confinement Fusion](https://mlsanity.com/paper/1910.01666/) (2019)

## Built on by (most cited first, 2 of 2)

- [Sim+Real: Joint Simulation-Experiment Training Improves Balanced Prediction in Physical Systems](https://mlsanity.com/paper/2610.01974/) (2026)
- [Physics Foundation Models for Efficient Control of Fluid Flows](https://mlsanity.com/paper/2610.15173/) (2026)

## Abstract (arXiv)

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.