# Causal Multi-fidelity Surrogate Forward and Inverse Models for ICF Implosions

arXiv: https://arxiv.org/abs/2509.05510 · HTML: https://mlsanity.com/paper/2509.05510/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 62 references that are in the map.
- First posted on arXiv 5 Sep 2025.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [A Structured Self-attentive Sentence Embedding](https://mlsanity.com/paper/1703.03130/) (2017)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [A Convolutional Neural Network for Modelling Sentences](https://mlsanity.com/paper/1404.2188/) (2014)
- [Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport](https://mlsanity.com/paper/2204.06684/) (2022)
- [Improved architectures and training algorithms for deep operator networks](https://mlsanity.com/paper/2110.01654/) (2021)
- [Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems](https://mlsanity.com/paper/2204.09157/) (2022)
- [Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network](https://mlsanity.com/paper/2201.02217/) (2022)
- [Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity](https://mlsanity.com/paper/2405.19166/) (2024)
- [Transfer learning to model inertial confinement fusion experiments](https://mlsanity.com/paper/1812.06055/) (2018)
- [Improved Surrogates in Inertial Confinement Fusion with Manifold and Cycle Consistencies](https://mlsanity.com/paper/1912.08113/) (2019)
- [Multi-fidelity wavelet neural operator with application to uncertainty quantification](https://mlsanity.com/paper/2208.05606/) (2022)
- [Operator inference with roll outs for learning reduced models from scarce and low-quality data](https://mlsanity.com/paper/2212.01418/) (2022)
- [Multi-fidelity Fourier Neural Operator for Fast Modeling of Large-Scale Geological Carbon Storage](https://mlsanity.com/paper/2308.09113/) (2023)
- [A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficients](https://mlsanity.com/paper/2311.03639/) (2023)
- [Physics consistent machine learning framework for inverse modeling with applications to ICF capsule implosions](https://mlsanity.com/paper/2412.20192/) (2024)
- [Learning robust parameter inference and density reconstruction in flyer plate impact experiments](https://mlsanity.com/paper/2506.23914/) (2025)
- [Predicting the time-evolution of multi-physics systems with sequence-to-sequence models](https://mlsanity.com/paper/1811.05852/) (2018)

## Built on by (most cited first, 1 of 1)

- [Revealing Low-Dimensional Structure in 2D Richtmyer-Meshkov Instabilities via Parametric Reduced-Order Modeling](https://mlsanity.com/paper/2510.16197/) (2025)

## Abstract (arXiv)

Continued progress in inertial confinement fusion (ICF) requires solving inverse problems relating experimental observations to simulation input parameters, followed by design optimization. However, such high-dimensional dynamic PDE-constrained optimization problems are extremely challenging or even intractable. It has been recently shown that inverse problems can be solved by only considering certain robust features. Here we consider the ICF capsule's deuterium-tritium (DT) interface, and construct a causal, dynamic, multifidelity reduced-order surrogate that maps from a time-dependent radiation temperature drive to the interface's radius and velocity dynamics. The surrogate targets an ODE embedding of DT interface dynamics, and is constructed by learning a controller for a base analytical model using low- and high-fidelity simulation training data with respect to radiation energy group structure. After demonstrating excellent accuracy of the surrogate interface model, we use machine learning (ML) models with surrogate-generated data to solve inverse problems optimizing radiation temperature drive to reproduce observed interface dynamics. For sparse snapshots in time, the ML model further characterizes the most informative times at which to sample dynamics. Altogether we demonstrate how operator learning, causal architectures, and physical inductive bias can be integrated to accelerate discovery, design, and diagnostics in high-energy-density systems.