Latent Diffusion Posterior Sampling with Surrogate Likelihood Guidance for PDE Inverse Problems
arXiv:2606.26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs). The method addresses three challenges in PDE-constrained inversion: implicit sample-based priors without tractable densities, high-dimensional spatially distributed parameters, and the high cost of repeated forward-model evaluations during posterior sampling. L-DPS combines a variational autoencoder, an unconditional latent diffusion model, diffusion posterior sa
The proliferation of advanced AI models, particularly diffusion models, is enabling new approaches for complex scientific and engineering problems.
This work suggests a significant advancement in using AI for solving inverse problems in science and engineering, potentially accelerating discovery and design cycles.
Traditional computationally intensive methods for PDE inverse problems could be augmented or replaced by more efficient, AI-driven probabilistic frameworks.
- · AI/ML researchers
- · Engineering R&D departments
- · Scientific computing sector
- · Traditional numerical simulation firms
- · Manual parameter tuning processes
More efficient and accurate solutions to complex inverse problems in fields like materials science, climate modeling, and medical imaging.
Reduced development costs and faster iteration in industries reliant on PDE-constrained optimization and design.
Accelerated discovery of new materials, drugs, or energy solutions through rapid hypothetical testing and optimization facilitated by advanced inverse problem solvers.
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Read at arXiv cs.LG