Enforcing Reciprocity in Operator Learning for Seismic Wave Propagation

2026-02-12

AI Summary

This work proposes a Transformer-based neural operator architecture for data-driven seismic wavefield modeling that explicitly enforces physical consistency, particularly the reciprocity principle—a constraint often violated in existing approaches. By integrating cross-attention mechanisms with swap-invariant operations, the model hard-codes reciprocity directly into its architecture, ensuring strict adherence to fundamental physical laws. The resulting framework enables interference-free parallel inference across multiple sources and generalizes seamlessly to diverse physical fields, including velocity, pressure, and traveltime. Remarkably, it achieves nearly an order-of-magnitude acceleration in inference speed compared to unconstrained counterparts, while maintaining comparable memory consumption.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Low Level & Physics-based Vision
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Accurate and efficient wavefield modeling underpins seismic structure and source studies. Traditional methods comply with physical laws but are computationally intensive. Data-driven methods, while opening new avenues for advancement, have yet to incorporate strict physical consistency. The principle of reciprocity is one of the most fundamental physical laws in wave propagation. We introduce the Reciprocity-Enforced Neural Operator (RENO), a transformer-based architecture for modeling seismic wave propagation that hard-codes the reciprocity principle. The model leverages the cross-attention mechanism and commutative operations to guarantee invariance under swapping source and receiver positions. Beyond improved physical consistency, the proposed architecture supports simultaneous realizations for multiple sources without crosstalk issues. This yields an order-of-magnitude inference speedup at a similar memory footprint over an reciprocity-unenforced neural operator on a realistic configuration. We demonstrate the functionality using the reciprocity relation for particle velocity fields under single forces. This architecture is also applicable to pressure fields under dilatational sources and travel-time fields governed by the eikonal equation, paving the way for encoding more complex reciprocity relations.

Problem

• reciprocity
• seismic wave propagation
• physical consistency
• operator learning
• neural operator

Innovation

• reciprocity
• neural operator
• transformer
• wavefield modeling
• physical consistency