BlastOFormer: Attention and Neural Operator Deep Learning Methods for Explosive Blast Prediction

TL;DR

BlastOFormer introduces a Transformer-based surrogate for full-field blast pressure prediction that encodes obstacle configurations via signed distance functions and processes a grid-to-grid representation with patch-wise tokens. By combining a spatial encoder with a cross-attention-based decoder and an auxiliary UnscalerCNN, it delivers real-time predictions with high magnitude fidelity and spatial coherence, outperforming CNN and FNO baselines on blastFoam-generated data. The approach achieves an unscaled R^2 of 0.9516, MAE around 484 kPa and MAPE near 21%, with inference time of 6.4 ms, representing orders-of-magnitude speedups over CFD. These results demonstrate BlastOFormer’s potential as a practical real-time surrogate for blast-pressure estimation in cluttered environments, with strong generalization across obstacle configurations and plan for future extensions to time-dependent and uncertainty-quantified predictions.

Abstract

Accurate prediction of blast pressure fields is essential for applications in structural safety, defense planning, and hazard mitigation. Traditional methods such as empirical models and computational fluid dynamics (CFD) simulations offer limited trade offs between speed and accuracy; empirical models fail to capture complex interactions in cluttered environments, while CFD simulations are computationally expensive and time consuming. In this work, we introduce BlastOFormer, a novel Transformer based surrogate model for full field maximum pressure prediction from arbitrary obstacle and charge configurations. BlastOFormer leverages a signed distance function (SDF) encoding and a grid to grid attention based architecture inspired by OFormer and Vision Transformer (ViT) frameworks. Trained on a dataset generated using the open source blastFoam CFD solver, our model outperforms convolutional neural networks (CNNs) and Fourier Neural Operators (FNOs) across both log transformed and unscaled domains. Quantitatively, BlastOFormer achieves the highest R2 score (0.9516) and lowest error metrics, while requiring only 6.4 milliseconds for inference, more than 600,000 times faster than CFD simulations. Qualitative visualizations and error analyses further confirm BlastOFormer's superior spatial coherence and generalization capabilities. These results highlight its potential as a real time alternative to conventional CFD approaches for blast pressure estimation in complex environments.

Figures (9)

• Figure 1: High level overview of the BlastOFormer architecture. (A) The input data, consisting of charge mass, charge locations, and obstacle positions, is transformed into a grid based, multi channel format. Charge mass is encoded into a channel by multiplying it with the inverse signed distance function, while each obstacle is encoded into a separate channel representing its signed distance. (B) Inspired by Vision Transformer (ViT), a linear patching layer projects this multi channel grid input into sequences of value and positional tokens. Spatial coordinates for both input and query points undergo a similar patch wise linear transformation. (C) The spatial encoder generates high dimensional embeddings capturing spatial features and input relationships. These embeddings ($z_0, z_1, \dots, z_n$), combined with the encoded coordinate tokens, feed into a point wise decoder. The decoder generates prediction tokens, which are subsequently reassembled into the predicted maximum pressure field through a learned linear depatchification layer.
• Figure 2: The top row displays ground truth pressure maps generated using BlastFoam. The first, second, and third rows show pressure predictions from BlastOFormer, FNO, and a CNN model, respectively. Each column represents a different pressure domain: the left column shows log-scaled pressures, while the right column shows unscaled values. For each model, the corresponding error maps—shown beneath the predictions with greyscale coloring highlight the differences from the ground truth. All three models successfully capture the key features of the BlastFoam simulations. The visualizations use the Jet colormap, which transitions from blue (low values) to red (high values). In particular, the log transformed pressure distributions demonstrate smooth gradients radiating outward from the charge center, consistent with expected behavior for log transformed data.
• Figure 3: The encoder and decoder components from figure \ref{['blastOFormer_model']}. (A) The encoder processes signed distance values ($x_0,x_1,\dots, x_n$) and positional information ($p_0, p_1, \dots, p_n$) pass through a projection layer, expanding the environmental features before being combined into latent initial condition tokens ($z_0, z_1, \dots, z_n$). The decoder is detailed in (B), pictorially visualizing the operations involved to combine initial conditional tokens and output pressure mapping coordinates ($p_0, p_1, \dots, p_n$) to formulate the query, key and value vectors for the attention operation, followed by a linear layer to transform the predicted pressure values back to physical dimensions, outputing the predicted pressure values $(u_0, u_1, \dots, u_n)$.
• Figure 4: (A) From left to right, the log transformed maximum pressure maps generated by blastFoam (ground truth), BlastOFormer, FNO, and CNN. (B) Corresponding unscaled maximum pressure maps from blastFoam, BlastOFormer, FNO, and CNN. All three models effectively capture the essential features present in the ground truth provided by blastFoam. The visualizations utilize the Jet color map, transitioning from blue (lower values) to red (higher values). The log transformed pressure distributions exhibit a smoother gradient from red to blue as the distance from the charge center increases, aligning well with expected physical behavior.
• Figure 5: (A) From left to right, absolute error maps comparing predictions from BlastOFormer, FNO, and CNN to the ground truth in the log domain. (B) Corresponding absolute error maps based on unscaled predictions from BlastOFormer, FNO, and CNN. The visualizations utilize a binary colormap, transitioning from white (lower error) to black (higher error). In both visualizations, BlastOFormer demonstrates lower error compared to the FNO and CNN models, indicating superior predictive accuracy.