# Physics consistent machine learning framework for inverse modeling with applications to ICF capsule implosions

arXiv: https://arxiv.org/abs/2412.20192 · HTML: https://mlsanity.com/paper/2412.20192/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 87 references that are in the map.
- First posted on arXiv 28 Dec 2024.

## Builds on (most cited first, 9 of 9)

- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [Least-Squares ReLU Neural Network (LSNN) Method For Scalar Nonlinear Hyperbolic Conservation Law](https://mlsanity.com/paper/2105.11627/) (2021)
- [High-Precision Inversion of Dynamic Radiography Using Hydrodynamic Features](https://mlsanity.com/paper/2112.01627/) (2021)
- [Reconstructing Richtmyer-Meshkov instabilities from noisy radiographs using low dimensional features and attention-based neural networks](https://mlsanity.com/paper/2408.00985/) (2024)
- [Learning Robust Features for Scatter Removal and Reconstruction in Dynamic ICF X-Ray Tomography](https://mlsanity.com/paper/2408.12766/) (2024)
- [On Properties of Adjoint Systems for Evolutionary PDEs](https://mlsanity.com/paper/2404.02320/) (2024)

## Built on by (most cited first, 4 of 4)

- [Learning robust parameter inference and density reconstruction in flyer plate impact experiments](https://mlsanity.com/paper/2506.23914/) (2025)
- [PDE foundation model-accelerated inverse estimation of system parameters in inertial confinement fusion](https://mlsanity.com/paper/2603.04606/) (2026)
- [Causal Multi-fidelity Surrogate Forward and Inverse Models for ICF Implosions](https://mlsanity.com/paper/2509.05510/) (2025)
- [Revealing Low-Dimensional Structure in 2D Richtmyer-Meshkov Instabilities via Parametric Reduced-Order Modeling](https://mlsanity.com/paper/2510.16197/) (2025)

## Abstract (arXiv)

In high energy density physics (HEDP) and inertial confinement fusion (ICF), predictive modeling is complicated by uncertainty in parameters that characterize various aspects of the modeled system, such as those characterizing material properties, equation of state (EOS), opacities, and initial conditions. Typically, however, these parameters are not directly observable. What is observed instead is a time sequence of radiographic projections using X-rays. In this work, we define a set of sparse hydrodynamic features derived from the outgoing shock profile and outer material edge, which can be obtained from radiographic measurements, to directly infer such parameters. Our machine learning (ML)-based methodology involves a pipeline of two architectures, a radiograph-to-features network (R2FNet) and a features-to-parameters network (F2PNet), that are trained independently and later combined to approximate a posterior distribution for the parameters from radiographs. We show that the estimated parameters can be used in a hydrodynamics code to obtain density fields and hydrodynamic shock and outer edge features that are consistent with the data. Finally, we demonstrate that features resulting from an unknown EOS model can be successfully mapped onto parameters of a chosen analytical EOS model, implying that network predictions are learning physics, with a degree of invariance to the underlying choice of EOS model.