Generative prediction of laser-induced rocket ignition with dynamic latent space representations

Tony Zahtila; Ettore Saetta; Murray Cutforth; Davy Brouzet; Diego Rossinelli; Gianluca Iaccarino

cs.LGMar 8, 2026

Generative prediction of laser-induced rocket ignition with dynamic latent space representations

Authors: Tony Zahtila, Ettore Saetta, Murray Cutforth, Davy Brouzet, Diego Rossinelli, Gianluca Iaccarino

Organizations: Center for Turbulence Research, Stanford University, USA · University of Naples Federico II, Italy

Abstract

Accurate and predictive scale-resolving simulations of laser-ignited rocket engines are highly time-consuming because the problem includes turbulent fuel-oxidizer mixing dynamics, laser-induced energy deposition, and high-speed flame growth. This is conflated with the large design space primarily corresponding to the laser operating conditions and target location. To enable rapid exploration and uncertainty quantification, we propose a data-driven surrogate modeling approach that combines convolutional autoencoders (cAEs) with neural ordinary differential equations (neural ODEs). The present target application of an ML-based surrogate model to leading-edge multi-physics turbulence simulation is part of a paradigm shift in the deployment of surrogate models towards increasing real-world complexity. Sequentially, the cAE spatially compresses high-dimensional flow fields into a low-dimensional latent space, wherein the system's temporal dynamics are learned via neural ODEs. Once trained, the model generates fast spatiotemporal predictions from initial conditions and specified operating inputs. By learning a surrogate to replace the entirety of the time-evolving simulation, the cost of predicting an ignition trial is reduced by several orders of magnitude, allowing efficient exploration of the input parameter space. Further, as the current framework yields a spatiotemporal field prediction, appraisal of the model output's physical grounding is more tractable. This approach marks a significant step toward real-time digital twins for laser-ignited rocket combustors and represents surrogate modeling in a complex system context.

Figures & tables

Figure 1: Workflow describing the construction and deployment of the neural ODE and decoder as a generative model.

Figure 2: Ignition probability density functions (PDFs) marginalized over the input parameters $\xi_{0}$ through $\xi_{14}$ , comparing ignition success (red) and ignition failure (blue) through kernel density estimates; green check marks denote the five parameters with the largest KL divergence between igniting and non-igniting cases. Full description of parameters in Table 2 in Appendix A .

Figure 3: Quantity of interest: spatiotemporal fields, (a) rendered simulation output of the successfully ignited combustor, (b) illustration of the integrated quantity acquisition, (1) light beam generation, (2) ray evolution according to the Eikonal equation , (3) Snell’s law and occlusion, and (4) irradiance sampling, (c) successful and unsuccessful time-series for the computational infrared, and (d) computational Schlieren.

Figure 4: Architecture schematic. (a) Encoder: a sequence of convolutional, with residual connections and pooling blocks maps the single–channel input to progressively smaller but deeper feature maps, which are then flattened and passed through fully-connected layers to obtain an 8-dimensional latent state

\mathbf{V}

. (b) NODE: the latent state is augmented with the control inputs (

\xi,t

), with two fully connected layers and the latent vector

\mathbf{V}

is forecast for the duration of the ignition trial. (c) Decoder: the latent state

\mathbf{V}

is lifted back to high dimension by fully-connected layers and a sequence of convolutional and upsampling blocks reconstructing the output field.

Figure 5: (a) Evolution of the validation loss against epoch during the training of the AE, for choices of latent-space dimension hyperparameter $N_{\ell}=1,4,8$ and $16$ . (b) Representative loss during training of the NODE for the 200,000 iterations, for choice of hidden layer width hyperparameter $w=400$ . The horizontal black line indicates the loss criterion for a curriculum learning increment, and markers at spike locations denote curriculum updates.

Figure 6: Representative case of latent-space trajectories ${V}_{i}$ illustrating the curriculum learning process. Panels (a)–(d) display the advancing training window (gray band), highlighting the progressive learning of newly revealed trajectory segments as the time horizon extends. Dashed lines indicate the beginning prediction at the start of the update, while solid lines show the final learned trajectory.

Figure 7: Latent variables, up-sampled in time, for the reacting rocket combustor LES ensemble, post-processed with coloring by a component of the input vector, $\xi_{2}=\beta=R_{1}/R_{2}$ .

Figure 8: Latent-space projections of $V_{5}$ against all other latent variables for the reacting sparks simulation ensemble, colored by the input parameter $\xi_{2}=\beta=R_{1}/R_{2}$ . Each trajectory begins at a green hollow circle and terminates at a red hollow circle, illustrating consistent trajectories in the low-dimensional manifold and separation of igniting from non-igniting cases.

Figure 9: Training (left) and validation (right) trajectories generated by the neural ODE, overlaid on the latent space representation learned by the AE for predictions with RMSE error of

5^{th}

50^{th}

, and

95^{th}

percentiles indicating strong, median and weak prediction. Ensemble distribution for entire latent space trajectories also shaded.

Metric	Train				Validation
	Q1	Q2	Q3	Q4	Q1	Q2	Q3	Q4
Fréchet Distance	0.009	0.013	0.018	0.035	0.075	0.100	0.190	0.289
L2 Norm	0.002	0.003	0.005	0.007	0.021	0.029	0.048	0.080

Table 1: Error metric in NODE-predicted latent space trajectories across four temporal quarters (Q1–Q4) across train-validation data split. Results reflect transition from early-time kernel dynamics to late-time divergence in the chaotic reacting phase

Figure 10: Confusion matrices for the binary classification of ignition outcomes. Left panel shows the training set results, with near-perfect separation between failure and success cases. Right panel shows the validation set performance.

Figure 11: One-to-one comparison of DnAE reconstructions with CFD reference sequences for representative ignition outcomes corresponding to the confusion-matrix categories in Figure 10 . (a) Training ignition success, (b) training non-igniting case, (c) correctly predicted non-ignition, (d) spurious ignition prediction, (e) missed ignition prediction, and (f) correctly predicted ignition.

Figure 12: Examples of generative latent-space trajectory predictions for unseen cases, classified as either igniting or non-igniting. For reference, range of trajectories on the low-dimensional manifold extracted from compressed CFD data are shaded in background, where $\hat{V}_{f}$ denotes latent trajectories with ignition failure and $\hat{V}_{s}$ for success.

Figure 13: Joint ignition probability distributions, estimated via Monte Carlo sampling of the NODE latent space trajectories, as a function of the parameter pairs (

\beta,E

) (top row) and (

\beta,l_{axial}

) (bottom row), obtained using, (a) 300 samples, (b) 200,000 samples, (c) 500,000 samples, and (d) 1,000,000 samples. Additionally marked are decision boundaries for

Pr(ign)=0.5,0.75,0.9

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Uncertainty ID	Description	Experiments	Distribution
$\xi_{0}\!:\Delta x_{l}$	Streamwise focal imprecision	Y	$N\sim(0.29\,\text{mm},0.04\,\text{mm}^{2})$
$\xi_{1}\!:\Delta x_{r}$	Radial focal location	Y	$N\sim(-0.54\,\text{mm},0.20\,\text{mm}^{2})$
$\xi_{2}\!:\beta=R1/R2$	Lobe radii ratio		$U\sim[1.1,2.1]$
$\xi_{3}\!:\alpha=l_{axial}/2R1$	Aspect ratio		$U\sim[2.0,2.5]$
$\xi_{4}\!:l_{axial}$	Laser axial length		$U\sim[1.44\text{mm},2.16\text{mm}]$
$\xi_{5}\!:E$	Energy deposited	Y	$U\sim[20\,\text{mJ},54\,\text{mJ}]$

Appendix

Table 2: Summary of the uncertainty parameters,

\xi_{i}

, of the laser pulse for the ignition trials, including their descriptions and associated probability distributions. Probability distributions are denoted as

U\sim[a,b]

(uniform probability between

a

and

b

) or

N\sim(\mu,\sigma^{2})

(normal distribution with mean

\mu

and variance

\sigma^{2}

Neural Surrogate Modeling

Neural surrogate modeling uses learned models to approximate costly simulations, enabling faster prediction, design, control, and inference.

See all 410 papers

A convolutional autoencoder and neural ODE surrogate modeling framework applied to transient counterflow flames
Mar 16, 2026Mert Yakup Baykan, Weitao Liu, Mohammad Rafi Malik +4Autoencoders PDE Surrogate Modeling
Department of Aerospace Engineering, KAIST, Daejeon, Republic of Korea · Clean Energy Research Platform (CERP), KAUST, Thuwal, Saudi Arabia · Institute for Reactive Flows (IRST), University of Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany
A Deep Learning-based surrogate model for Severe Accidents in nuclear reactors using ASTEC
Jul 5, 2026Alessandro Longhi, Danny Lathouwers, Zoltán PerkóNeural Surrogate Modeling Surrogate Modeling
TU Delft · Department of Radiation Science and Technology · Delft, The Netherlands
Adaptive surrogate modeling for high-dimensional spatio-temporal output
Aug 18, 2026Berkcan Kapusuzoglu, Shunsaku Matsumoto, Yoshitomo Miyagi +2Surrogate Modeling Adaptive Sampling
Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN 37235, USA · Strength Research Department, Research and Innovation Center, Mitsubishi Heavy Industries, Ltd., Nagasaki, 851-0392, Japan · Strength Research Department, Research and Innovation Center, Mitsubishi Heavy Industries, Ltd., Takasago, 676-8686, Japan

Mar 16, 2026J/K move · Enter open · S save

A convolutional autoencoder and neural ODE surrogate modeling framework applied to transient counterflow flames

Mert Yakup Baykan, Weitao Liu, Mohammad Rafi Malik, Thorsten Zirwes+3

Department of Aerospace Engineering, KAIST, Daejeon, Republic of Korea · Clean Energy Research Platform (CERP), KAUST, Thuwal, Saudi Arabia · Institute for Reactive Flows (IRST), University of Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany

Autoencoders PDE Surrogate Modeling Convolutional Autoencoder Reduced-Order Modeling Neural ODEs Computational Fluid Dynamics

Open paper AskPDF arXiv

A novel convolutional autoencoder and neural ODE (CAE-NODE) framework is proposed for a reduced-order model (ROM) applied to transient 2D counterflow flames, as an extension of AE-NODE methods in homogeneous reactive systems to spatially resolved flows. The multidimensional thermochemical fields (256 x 256 grid, 21 variables) obtained from direct numerical simulations (DNS) are used in training the CAE, where convolutional layers learned the underlying spatial correlations, allowing the CAE to construct an unsupervised 3D latent manifold that is physically meaningful, smooth, and continuous in time. This results in a compression ratio of over 400,000 times. The NODE then subsequently learns the continuous-time dynamics on the latent manifold, enabling the prediction of the full temporal evolution of the flames by integrating forward in time from an initial condition. The results demonstrate that the CAE-NODE can accurately capture the entire transient process, including ignition, flame propagation, and the gradual transition to a non-premixed condition, with excellent agreement with the DNS, while adhering to conservation principles at virtually no computational cost compared to the reference DNS. Predictions remain accurate at strain rates outside the training range. Moreover, despite being unsupervised, the learned latent manifold is highly correlated with the flame-state descriptors such as the progress variable, mixture fraction, and the scalar dissipation rate. This study, for the first time, highlights the potential of CAE-NODE for surrogate modeling of unsteady dynamics of multi-dimensional reacting flows.

Abstract

Neural Surrogate Modeling

Explore similar work

A convolutional autoencoder and neural ODE surrogate modeling framework applied to transient counterflow flames

A Deep Learning-based surrogate model for Severe Accidents in nuclear reactors using ASTEC

Adaptive surrogate modeling for high-dimensional spatio-temporal output