Proton radiography is an effective technique for diagnosing field distributions in plasmas. However, due to the complexity of electromagnetic field structure, reconstructing electromagnetic field from proton radiographs is extremely challenging and often requires some simplified symmetry assumptions for the field. Here, we present a machine learning method to reconstruct three-dimensional (3D) magnetic field distributions from complex proton radiographs without relying on such assumptions. In order to do this, we construct the target 3D magnetic fields by linearly superposing multiple elementary magnetic structures generated from the Weibel instability. Each element is characterized by eight parameters—structural parameters (a, b, B₀), spatial coordinates (x₀, y₀, z₀), and rotation angles (θ, ϕ), —resulting in 80 degrees of freedom in total. The parameters are uniformly sampled within ±25% of their baseline values, and a dataset consisting of 50000 magnetic field-proton radiograph pairs is generated through forward simulation using GEANT4. All proton radiographs exist in the caustic regime, exhibiting multiple asymmetric caustics and significant flux concentrations.

A lightweight three-layer convolutional neural network (CNN) is designed for the reconstruction task. The network consists of an input layer, three convolutional modules (in which the first two follow a "convolution–batch normalization–max pooling" cascaded structure, and the third is simplified into a single convolutional layer), a flattening layer, a dropout layer, and an output layer. Bayesian optimization is used to determine the optimal hyperparameters. The model is trained on 40000 samples, with 5000 samples used for validation and 5000 for testing.

On the test set, the CNN achieves a mean absolute percentage error (MAPE) of 8.5% in predicting the 80 magnetic parameters, which is below the random-guessing threshold of 12.9%. Prediction errors for most parameters follow a near-zero-mean Gaussian distribution, with a relative standard deviation of less than 6%. The reconstructed fields show a high degree of spatial consistency with the reference fields, and the corresponding proton images match the original images with a cosine similarity of 0.89.

This study demonstrates that our CNN-based proton radiography reconstruction method can effectively reconstruct complex 3D magnetic fields without the need for symmetry assumptions or manual parameter adjustments, providing a novel tool for diagnosing electromagnetic fields in high-intensity laser-plasma interactions. Future work may combine multi-angle proton radiography with transfer learning from experimental data to improve the practicality and robustness of this method.