SourceNet: Interpretable Sim-to-Real Inference on Variable-Geometry Sensor Arrays for Earthquake Source Inversion

TL;DR

The paper tackles inferring high-dimensional earthquake source parameters from sparse, irregular sensor arrays and the Sim-to-Real gap in physics-based inference. It introduces SourceNet, a Transformer-based set architecture that processes variable sensor geometries and uses Physics-Structured Domain Randomization (PSDR) to learn domain-invariant representations, achieving state-of-the-art accuracy on held-out real data after pretraining on 100,000 synthetic events and fine-tuning on ~2,000 real events. The model maps sensor sets X to a 6D source state y that encodes the Moment Tensor and magnitude, while revealing emergent, interpretable strategies such as geometry-aware sensor prioritization akin to optimal experimental design. These results demonstrate real-time, robust, and interpretable inversion and offer insights for developing physical foundation models that learn invariant operators from randomized physics.

Abstract

Inferring high-dimensional physical states from sparse, ad-hoc sensor arrays is a fundamental challenge across AI for Science, as they are complicated by irregular geometries and the profound Sim-to-Real gap in physical modeling. Taking earthquake source characterization as a representative challenge, we address limitations in conventional deep learning: CNNs demand fixed grids, while pooling-based architectures (e.g., DeepSets) struggle to capture the relational wave physics. Here, we propose SourceNet, a Transformer-based framework that treats the sensor array as a flexible set to model arbitrary geometries. To bridge the reality gap, we introduce Physics-Structured Domain Randomization (PSDR). Instead of forcing feature alignment, PSDR randomizes the governing physical dynamics by varying velocity structures, propagation effects, and sensor availability, to force the model to learn robust representations invariant to unmodeled environmental heterogeneity. By pre-training on 100,000 synthetic events and fine-tuning on ~2,000 real world events, SourceNet achieves state-of-the-art precision on held-out real data. This demonstrates exceptional data efficiency, and matches classical solvers while enabling real-time processing. Remarkably, interpretability analysis reveals that the model shows scientific-agent-like features: it autonomously discovers geometric information bottlenecks and learns an attention policy that prioritizes sparse sensor placements, effectively recovering principles of optimal experimental design from data alone.

Figures (5)

• Figure 1: The SourceNet Architecture. A hierarchical Set Transformer designed for irregular sensor arrays. The model operates in three stages: (1) Multi-modal Station Encoders process P/S-waves (time & spectral domains) and scalar metadata into physics-aware embeddings. (2) Self-Attention models global pairwise interactions to resolve local ambiguities. (3) Attention Pooling dynamically weights stations based on information gain to regress the final moment tensor.
• Figure 2: Physics-Structured Training Curriculum. We bridge the reality gap using a two-stage protocol. First, we train on synthetics augmented with aleatoric physical uncertainties (e.g., randomized velocity models, real noise injection, and sensor dropouts) to enforce invariant feature learning. We then fine-tune on a smaller set of real events using a weighted random sampler to correct for the natural imbalance of faulting mechanisms.
• Figure 3: Validation of Physics-Structured Domain Randomization.(a) Comparison of clean synthetic data (top) versus PSDR-augmented data (bottom), which incorporate realistic scattering and noise. (b) t-SNE visualization of the feature space. A naive baseline (Left) shows disjoint clusters for synthetic and real data, indicating a failure to generalize. In contrast, SourceNet (Right) achieves good manifold alignment, which shows that the model has learned invariant physical operators robust to the distribution shift.
• Figure 4: Sim-to-Real Inference Performance. Evaluation on the held-out real-world catalog. (a) Predicted vs. true Magnitude ($M_w$) demonstrates high accuracy ($MAE=0.11$), confirming that the scalar tower successfully disentangles source energy from path attenuation. (b-c) Normalized Moment Tensor components ($M_{xx}, M_{xy}$) maintain robust linearity despite the domain gap. (d) The Kagan angle error distribution (Mean $26.18^\circ$, Median $19.37^\circ$) confirms that SourceNet achieves SOTA precision and effectively hits the label uncertainty floor of the manual catalogs.
• Figure 5: Emergent Scientific Discovery: Learning How to Observe.(a) Learned local strategy. Grad-CAM visualization reveals that the model attends significantly to the P-coda and early scattered phases (red regions), effectively performing an implicit full-waveform inversion using data traditionally discarded as noise. (b) Learned global policy. Aggregated attention weights (bar plot) reveal a learned anisotropy, prioritizing East-West stations. As shown in the station map (c), this directly counters the network's geometric bias (dense N-S coverage along the fault). The model autonomously identified the information bottleneck and recovered principles of Optimal Experimental Design by prioritizing under-sampled orthogonal views.