Research Paper#Inverse Problems, Latent Diffusion Models, Subsurface Modeling, PDE-constrained optimization🔬 ResearchAnalyzed: Jan 3, 2026 20:03
Differentiable Inverse Modeling with Physics-Constrained Latent Diffusion for Subsurface Parameter Fields
Published:Dec 27, 2025 01:01
•1 min read
•ArXiv
Analysis
This paper introduces a novel method, LD-DIM, for solving inverse problems in subsurface modeling. It leverages latent diffusion models and differentiable numerical solvers to reconstruct heterogeneous parameter fields, improving numerical stability and accuracy compared to existing methods like PINNs and VAEs. The focus on a low-dimensional latent space and adjoint-based gradients is key to its performance.
Key Takeaways
- •LD-DIM is a novel method for solving inverse problems in subsurface modeling.
- •It combines latent diffusion models with differentiable numerical solvers.
- •It improves numerical stability and reconstruction accuracy compared to PINNs and VAEs.
- •The method is demonstrated on a flow in porous media problem.
Reference
“LD-DIM achieves consistently improved numerical stability and reconstruction accuracy of both parameter fields and corresponding PDE solutions compared with physics-informed neural networks (PINNs) and physics-embedded variational autoencoder (VAE) baselines, while maintaining sharp discontinuities and reducing sensitivity to initialization.”