LazyDINO: Fast, Scalable, and Efficiently Amortized Bayesian Inversion via Structure-Exploiting and Surrogate-Driven Measure Transport

2025-12-31 · Source: JMLR · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, quick

Summary

LazyDINO is a novel transport map variational inference method designed for solving high-dimensional nonlinear Bayesian inverse problems, particularly those involving expensive parameter-to-observable (PtO) maps. The method operates in two phases: an offline phase constructs a derivative-informed neural surrogate of the PtO map using joint samples of the map and its Jacobian for training. The online phase then rapidly approximates the posterior distribution using this surrogate to train a "lazy map," which is a structure-exploiting transport map with low-dimensional nonlinearity. LazyDINO's surrogate construction is optimized for amortized Bayesian inversion, demonstrating a one to two orders of magnitude reduction in offline cost for accurate online posterior approximation compared to other amortized simulation-based inference methods. It consistently outperforms Laplace approximation with fewer than 1000 offline PtO map evaluations, whereas competing methods often struggle or fail at 16,000 evaluations.

Key takeaway

For AI Scientists and Research Scientists working on high-dimensional Bayesian inverse problems with computationally expensive parameter-to-observable maps, LazyDINO offers a significant advancement. You should consider integrating LazyDINO into your workflow to achieve substantial reductions in offline computational cost, potentially enabling more rapid and accurate posterior approximations than traditional methods or other amortized inference techniques.

Key insights

LazyDINO offers fast, scalable, and efficiently amortized Bayesian inversion using derivative-informed neural surrogates and lazy maps.

Principles

• Derivative-based reduced basis minimizes surrogate posterior error.
• Derivative-informed training minimizes variational inference error.

Method

Construct an offline derivative-informed neural surrogate of the PtO map, then use it online to rapidly train a structure-exploiting "lazy map" for posterior approximation.

In practice

• Achieves 1-2 orders of magnitude cost reduction.
• Outperforms Laplace approximation with <1000 PtO evaluations.

Topics

• LazyDINO
• Bayesian Inverse Problems
• Transport Map Variational Inference
• Neural Surrogates
• Amortized Bayesian Inversion

Code references

• dinoSciML/dinox

Best for: AI Scientist, Research Scientist

Related on AIssential

• Amortized mean-shift interacting particles — A learned map generates weighted nodes for superior Bayesian integral estimation, surpassing Monte-Carlo.
• Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximization — Inverse entropic optimal transport provides a unified likelihood maximization framework for semi-supervised conditional distribution learning using mixed data.
• A Stabilized Path-Space Approach to Diffusion-Based Posterior Sampling — A stabilized path-space framework improves diffusion posterior sampling by connecting it to stochastic optimal control and removing bias.
• Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model — Equilibrium Propagation and Hamiltonian Echo Backpropagation can be extended to skew-gradient systems and deep Energy-Based Models for efficient credit assignment and inference.
• Leveraging tails for adaptation — Heavier p-exponential prior tails (p→0) significantly improve Bayesian posterior contraction rates, enabling full adaptation to unknown function smoothness.
• Amortized Optimal Transport from Sliced Potentials — Amortized optimal transport methods efficiently predict OT plans by reusing learned Kantorovich potentials from sliced OT.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by JMLR.