Neural Operator Accelerated BOED

Making BOED scalable for expensive PDE-governed systems

Goal: make Bayesian optimal experimental design practical for large-scale scientific models.

BOED often requires thousands of forward and derivative evaluations. For PDE-governed systems, this cost quickly becomes prohibitive. My approach is to replace expensive solvers with neural operator surrogates that preserve the quantities needed for design optimization.

Derivative-Informed Neural Operators for BOED

A key bottleneck in BOED is evaluating the parameter-to-observable (PtO) map and its derivatives repeatedly during design optimization. We apply derivative-informed neural operators (DINO), which use derivative-informed dimension reduction to compress high-dimensional parameter spaces into compact latent representations and are trained with Jacobian information for accurate surrogate modeling. DINO enables efficient computation of MAP estimates, posterior covariance eigenvalues, and standard optimality criteria (A-, D-, E-optimal), achieving over 1000× speedup compared to high-fidelity solvers for a 3D nonlinear convection-diffusion-reaction system with tens of thousands of parameters (Go & Chen, 2025).

DINO-based BOED framework. Derivative-informed dimension reduction compresses high-dimensional parameter and observable spaces into compact latent representations, enabling efficient surrogate-based design optimization.

Sequential BOED with Latent Attention Neural Operators

Extending to sequential settings introduces additional challenges: the surrogate must capture temporal dynamics and support posterior updates across design stages. We propose a latent-variable attention-based neural operator (LANO) that combines derivative-informed dimension reduction with an attention mechanism to model dynamics in latent space. LANO supports efficient computation of MAP points, posterior eigenpairs, and posterior sampling, enabling adaptive sequential BOED for time-dependent PDE systems. We demonstrate 180× amortized speedup on an MRI observation scheduling problem for for monitoring tumor growth (Go & Chen, 2025).

LANO architecture combining derivative-informed latent encoding with an attention mechanism for temporal dynamics in sequential BOED.
MRI-based tumor growth monitoring. (Left to right) Prior uncertainty, optimal static observation design, posterior uncertainty under uniform observation, and adaptive sequential design. The adaptive design concentrates observations on informative regions, achieving greater uncertainty reduction than uniform or static baselines.

Key takeaways

  • Neural operator surrogates make BOED tractable for large-scale PDE-governed systems without sacrificing accuracy
  • Derivative information is critical for both dimension reduction and surrogate training
  • LANO generalizes naturally to sequential and time-dependent settings

References

2025

  1. CMAME
    Accurate, Scalable, and Efficient Bayesian Optimal Experimental Design with Derivative-Informed Neural Operators
    Jinwoo Go and Peng Chen
    Computer Methods in Applied Mechanics and Engineering, 2025
    Abs HTML
  2. JCP
    Sequential Infinite-Dimensional Bayesian Optimal Experimental Design with Derivative-Informed Latent Attention Neural Operator
    Jinwoo Go and Peng Chen
    Journal of Computational Physics, 2025
    Abs HTML