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

Inferring high-dimensional physical states from sparse, ad-hoc sensor arrays is a fundamental challenge across AI for Science, yet standard architectures like CNNs and DeepSets struggle to capture the irregular geometries and relational physics inherent to domains like seismology. To address this, we propose SourceNet, a Transformer-based framework that bridges the profound Sim-to-Real gap via Physics-Structured Domain Randomization (PSDR), a protocol that randomizes governing physical dynamics to enforce invariance to unmodeled environmental heterogeneity. By pre-training on 100,000 synthetic events and fine-tuning on ~2,500 real-world events, SourceNet achieves state-of-the-art precision on held-out real data, demonstrating exceptional data efficiency and real-time capability compared to classical solvers. Beyond prediction, 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.

💡 Research Summary

SourceNet is a novel Transformer‑based framework designed to infer high‑dimensional earthquake source parameters (the full moment tensor and magnitude) from sparse, irregularly arranged seismic stations. The authors identify two fundamental challenges that have limited prior deep‑learning approaches: (1) geometric mismatch, because conventional CNNs require data on a regular grid and set‑based models such as DeepSets lose relational information through global pooling; and (2) the simulation‑to‑real (Sim‑to‑Real) gap, as synthetic seismograms generated with idealized 1‑D velocity models and clean noise fail to capture the complex heterogeneity, scattering, and sensor failures present in field data.

To address the geometric issue, SourceNet treats each station as a token and employs a Set‑Transformer architecture with multi‑head self‑attention. This allows pairwise interactions among all stations to be modeled explicitly, preserving phase polarity, amplitude differences, and directional dependencies that are crucial for source inversion. The network contains three parallel “station encoders”: a P‑Wave tower, an S‑Wave tower (both 1‑D ResNet‑style encoders processing a 6‑second low‑frequency window and its spectral representation), and a scalar metadata stream (azimuth, epicentral distance, amplitude ratios, etc.). The three streams are concatenated into a physics‑aware embedding of dimension 128 per station, which is then fed into the attention module.

The Sim‑to‑Real gap is bridged through Physics‑Structured Domain Randomization (PSDR). Instead of merely adding Gaussian noise, PSDR randomizes four physically meaningful aspects during synthetic data generation: (i) Earth structure – sampling from a library of 17 distinct 1‑D velocity models derived from CRUST1.0 for Southern California; (ii) Signal distortion – applying stochastic time shifts, amplitude scaling, and adding exponentially decaying coda to mimic 3‑D scattering and site effects; (iii) Realistic noise – superimposing recordings from a curated ambient‑noise database rather than synthetic white noise; and (iv) Network availability – randomly dropping stations with a Bernoulli mask to emulate sensor outages and variable network geometry. This produces 100 k “realistic” synthetic events that force the model to learn invariances to the underlying physics rather than memorizing a single propagation medium.

Training proceeds in two stages. First, the entire network is pre‑trained on the PSDR‑augmented synthetic set, optimizing an L2 loss on the five independent components of the moment tensor and on magnitude. Second, a fine‑tuning phase uses about 2.5 k real events from the Southern California catalog, employing a weighted random sampler to balance under‑represented faulting mechanisms. The authors validate the effectiveness of PSDR by visualizing latent spaces with t‑SNE: a baseline model trained on clean synthetics and fine‑tuned on real data shows disjoint clusters, whereas SourceNet’s latent representations align closely with real data, indicating successful domain alignment.

Performance evaluation on a held‑out real test set demonstrates that SourceNet achieves state‑of‑the‑art accuracy: average rotation error of the moment tensor is reduced to ~4.2°, magnitude error to 0.12 Mw, outperforming DeepSets‑based baselines by roughly 30 % and 25 % respectively. Moreover, the model requires only the modest 2.5 k real labels to reach near‑saturation, illustrating strong data efficiency. Inference time on an NVIDIA RTX 3090 is under 50 ms per event, enabling real‑time applications that are infeasible with traditional Green’s‑function iterative solvers which can take seconds to minutes.

Interpretability analysis focuses on the learned attention weights. By aggregating attention scores across events, the authors show that the model automatically identifies “information bottleneck” stations—those that contribute most to reducing uncertainty—and assigns them higher importance, effectively reproducing principles of optimal experimental design (OED) without any explicit supervision. This emergent behavior suggests that the model internalizes a policy for sensor placement that maximizes information gain, a valuable insight for network design and future deployment strategies.

The paper also highlights that SourceNet leverages the full waveform, including coda phases that are typically ignored by first‑motion solvers, thereby extracting additional constraints on source orientation and slip direction. Computationally, the O(N²) attention cost remains tractable for typical seismic networks (N ≈ 10–100), and the hierarchical design keeps memory usage modest.

In conclusion, SourceNet unifies three innovations: (1) a set‑Transformer that respects permutation invariance while preserving rich inter‑station physics; (2) physics‑structured domain randomization that closes the Sim‑to‑Real gap without adversarial adaptation; and (3) emergent, interpretable attention that mirrors optimal experimental design. The authors argue that this framework is broadly applicable to other wave‑based inverse problems such as acoustic tomography, electromagnetic imaging, and medical ultrasound, where sensor geometry is irregular and simulations are imperfect. Future work is suggested on extending PSDR to full 3‑D heterogeneous Earth models, incorporating multi‑scale attention, and exploring unsupervised domain adaptation to further reduce reliance on labeled real data.