Hybrid AI Models Combining Physics-Based Simulations and Data-Driven Approaches in Geophysics

Abstract

Hybrid AI models, often referred to as Physics-Informed Machine Learning (PIML) or Scientific Machine Learning (SciML), integrate first-principle physics (governing PDEs, conservation laws, and symmetries) with data-driven deep learning to overcome the limitations of purely mechanistic or purely empirical approaches in geophysics. These models embed physical constraints directly into neural architectures (Physics-Informed Neural Networks — PINNs), loss functions, or operators (Fourier Neural Operators — FNO, Neural ODEs), enabling data-efficient, physically consistent, and generalizable solutions. Key techniques include multi-objective loss balancing (LRA, GradNorm, SA-PINN), neural operators for parametric PDE solving, and symbolic regression methods like SINDy for equation discovery. Applications span seismic imaging and full-waveform inversion (velocity model reconstruction), reservoir engineering (history matching with 61% RMSD improvement), geotechnical stability (tunneling and slope predictions), and atmospheric/climate modeling (ClimODE for value-conserving forecasts, NVIDIA Earth-2 digital twins with FourCastNetv2). These hybrids reduce computational costs, improve robustness in small-data regimes, bridge synthetic-to-real domain gaps, and support uncertainty quantification. Challenges remain in loss balancing, spectral bias, and scaling to multimodal geo-foundation models. Overall, hybrid AI represents a transformative paradigm for subsurface imaging, resource management, hazard prediction, and climate resilience in geophysics.