[Paper Review] Improved Surrogates in Inertial Confinement Fusion with Manifold and Cycle Consistencies

Rushil Anirudh, Jayaraman J. Thiagarajan+2 more|arXiv (Cornell University)|Dec 17, 2019

Laser-Plasma Interactions and Diagnostics29 references41 citations

TL;DR

This paper proposes Manifold and Cyclically Consistent (MaCC) surrogates for inertial confinement fusion (ICF) that improve predictive performance and robustness by enforcing physical manifold consistency through a latent-space autoencoder and cyclical consistency between forward and inverse models via a jointly trained pseudo-inverse network. The method achieves superior accuracy, data efficiency, and resilience to sampling artifacts, especially in low-data regimes.

ABSTRACT

Neural networks have become very popular in surrogate modeling because of their ability to characterize arbitrary, high dimensional functions in a data driven fashion. This paper advocates for the training of surrogates that are consistent with the physical manifold -- i.e., predictions are always physically meaningful, and are cyclically consistent -- i.e., when the predictions of the surrogate, when passed through an independently trained inverse model give back the original input parameters. We find that these two consistencies lead to surrogates that are superior in terms of predictive performance, more resilient to sampling artifacts, and tend to be more data efficient. Using Inertial Confinement Fusion (ICF) as a test bed problem, we model a 1D semi-analytic numerical simulator and demonstrate the effectiveness of our approach. Code and data are available at https://github.com/rushilanirudh/macc/

Motivation & Objective

• To address the limitations of standard neural network surrogates in scientific computing, which often produce unphysical, brittle, or inconsistent predictions due to high dimensionality and lack of physical constraints.
• To improve surrogate modeling in inertial confinement fusion (ICF), where rich, multi-modal outputs (images, scalars) require high-fidelity, data-efficient models.
• To enforce physical plausibility by mapping predictions into a low-dimensional latent manifold that captures correlations across multi-modal outputs.
• To ensure self-consistency between forward and inverse models by penalizing deviations from the cycle F(x) → G(F(x)) ≈ x, enhancing robustness and interpretability.
• To reduce reliance on large datasets by improving generalization and resilience to sampling artifacts through cyclical regularization.

Proposed method

• Train a variational autoencoder (VAE) to embed multi-modal ICF outputs (images and scalars) into a low-dimensional latent space Z, enabling manifold consistency.
• Define the surrogate as F: X → Z, where X is the input parameter space, instead of directly predicting in the high-dimensional output space Y.
• Train a pseudo-inverse network G: Y → X in tandem with F, using a cyclical consistency loss Lcyc = ∑ᵢ R²(x_scan, G(F(x_scan))) to enforce G(F(x)) ≈ x.
• Optimize the combined model using stochastic gradient descent with a total loss L_total = L_mse + λ_cyc × L_cyc, where L_mse measures prediction error and λ_cyc controls cyclical regularization strength.
• Use bootstrapped training sets to evaluate robustness of cyclical consistency across multiple inverse model solutions, ensuring statistical validity.
• Evaluate model performance using standard metrics (MSE, R²) and sensitivity to input perturbations to assess smoothness and robustness.

Experimental results

Research questions

• RQ1 Can enforcing manifold consistency via a latent-space autoencoder improve the fidelity and generalization of surrogate models in high-dimensional scientific simulations?
• RQ2 Does enforcing cyclical consistency between forward and inverse models lead to more robust and stable predictions, especially under input perturbations?
• RQ3 To what extent does cyclical regularization enhance data efficiency and reduce sensitivity to sampling artifacts in low-data regimes?
• RQ4 Can MaCC surrogates maintain self-consistency across diverse inverse model solutions, even when not explicitly trained on them?
• RQ5 How do MaCC surrogates compare to standard baselines in terms of predictive accuracy, smoothness, and interpretability on real ICF simulation data?

Key findings

• MaCC surrogates achieve significantly lower mean squared error (MSE) on image outputs across all four energy bands, with reductions from 0.0476 to 0.0351 (band 0) and 0.2035 to 0.1742 (band 3) compared to the baseline.
• The R² score for scalar predictions improved from 0.9990 to 0.9974, indicating slightly better but still highly accurate scalar modeling.
• With λ_cyc = 0.05, the MaCC model maintained high predictive performance while achieving strong cyclical consistency, and performance degraded only when λ_cyc exceeded 0.10.
• The model demonstrated superior robustness to input perturbations: cyclical regularization led to significantly smoother predictions under noise, with minimal increase in MSE on perturbed inputs.
• Even when using independently trained pseudo-inverse models from bootstrapped subsets, MaCC surrogates maintained high self-consistency, as measured by R², across all five input parameters.
• In low-data regimes, MaCC models generalized better than baselines, as shown by improved test MSE with fewer training samples, confirming enhanced data efficiency.