New Reinforcement Learning Framework Accelerates Bayesian Experimental Design for PDE Inverse Problems

Global: New Reinforcement Learning Framework Accelerates Bayesian Experimental Design for PDE Inverse Problems

Researchers have introduced a reinforcement‑learning‑based framework that dramatically reduces the computational burden of sequential Bayesian optimal experimental design (SBOED) for inverse problems governed by partial differential equations (PDEs). By learning an amortized design policy, the method enables online selection of sensor placements without repeatedly solving high‑fidelity optimization problems, delivering speedups on the order of 100 × in benchmark tests.

Accelerated Design via Reinforcement Learning

The team formulates SBOED as a finite‑horizon Markov decision process and trains a policy‑gradient reinforcement learning (PGRL) agent to map experiment histories to optimal design actions. This amortized approach replaces nested Bayesian inversion loops with a single forward pass through the learned policy during deployment.

Dimensionality Reduction Techniques

To keep training tractable, the authors apply dual dimension‑reduction: an active‑subspace projection compresses the infinite‑dimensional parameter field, while principal component analysis condenses the high‑dimensional state representation. These reductions preserve the most informative directions for both the unknown parameters and the experimental context.

Surrogate Modeling with Neural Operators

A derivative‑informed latent‑attention neural operator (LANO) surrogate predicts both the parameter‑to‑solution map and its Jacobian. By integrating gradient information, the surrogate maintains fidelity to the underlying PDE while offering rapid evaluations needed for policy training and reward calculation.

Reward Formulation and Alternatives

The primary utility employed is a Laplace‑based D‑optimality metric, which quantifies expected information gain about the parameters. The authors note that alternative utilities such as Kullback‑Leibler divergence could be substituted within the same reinforcement‑learning framework.

Efficient Evaluation Strategy

An eigenvalue‑based evaluation scheme uses prior samples as proxies for maximum‑a‑posteriori (MAP) points, avoiding costly MAP solves while still delivering accurate estimates of information gain for each candidate design.

Empirical Validation

Numerical experiments focus on sequential multi‑sensor placement for contaminant source tracking. The learned policy outperforms random sensor configurations, achieves the reported 100 × speedup relative to high‑fidelity finite‑element solvers, and exhibits physically interpretable behavior, such as prioritizing upstream sensor locations to capture contaminant plumes early.

Broader Impact

By substantially lowering the computational cost of SBOED, the approach opens the possibility of real‑time experimental design in fields ranging from environmental monitoring to medical imaging, where rapid decision‑making under uncertainty is critical.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.