Beyond optimization in molecular dynamics: goal-directed Bayesian design with trajectory-based noise modeling
2026 AIChE Annual Meeting, 10D: Advances in Computational Methods and Numerical Analysis, 2026 Presenting author
Abstract
Molecular dynamics (MD) simulations are a powerful tool for probing molecular-scale structure and
dynamics, but systematically exploring simulation inputs such as composition, temperature, or
solvent conditions quickly becomes computationally prohibitive. This challenge is amplified when the
target observables are estimated from finite, autocorrelated trajectories, so the magnitude of the
statistical noise varies across the input space. In addition, in many MD settings, the scientific
objective is not simply to optimize a single scalar quantity, but rather to identify broader
system-level features such as threshold regions, level sets, and transition boundaries. To address
these challenges, we present MD-BAX [1], a goal-directed Bayesian design framework for molecular
simulation campaigns that builds on Bayesian Algorithm Execution (BAX) [2] and its
posterior-sampling variant [3], while explicitly accounting for input-dependent noise through
trajectory statistics. Rather than assuming constant observation noise, MD-BAX estimates the
uncertainty at each simulated input directly from the underlying MD trajectory using
autocorrelation-based analysis and incorporates these estimates into a fixed-noise Gaussian process
surrogate (see, e.g., [4] for more details on input-dependent Gaussian process models). The
resulting surrogate provides more reliable uncertainty quantification for guiding adaptive sampling
toward the scientific objective of interest. We demonstrate the framework on coarse-grained
simulations of amphiphilic block copolymers, using the radius of gyration as the primary observable.
In particular, we consider tasks involving identification of threshold-exceeding regions and mapping
coil-to-globule transition behavior as a function of polymer composition [5] and solvent quality
[6]. In both cases, MD-BAX concentrates simulations in the most informative regions of parameter
space and recovers physically meaningful structures such as level-set boundaries and transition
manifolds with substantially fewer simulations than non-adaptive sampling. These gains are closely
tied to improved uncertainty calibration, consistent with recent work emphasizing the importance of
evaluating predictive uncertainty rather than mean accuracy alone [7]. Overall, MD-BAX provides a
practical route to closed-loop, goal-directed design in molecular simulation. More broadly, this
work shows that observation-noise modeling is not merely a technical detail in adaptive MD
workflows; when the objective is to learn system behavior from noisy trajectories, propagating
trajectory-derived uncertainty through the design loop can materially improve where computational
effort is spent. Because the framework is modular, it can be extended readily to a broad range of
molecular simulation settings in which observables are estimated from noisy trajectories and the
goal is to infer “scientifically meaningful” system behavior rather than identify a single optimal
condition. References [1] Tan, Tianhong, et al. "MD-BAX: A general-purpose Bayesian design framework
for molecular dynamics simulations with input-dependent noise." The Journal of Chemical Physics
164.8 (2026). [2] Neiswanger, Willie, Ke Alexander Wang, and Stefano Ermon. "Bayesian algorithm
execution: Estimating computable properties of black-box functions using mutual information."
International Conference on Machine Learning. PMLR, 2021. [3] Cheng, Chu X., et al. "Practical
bayesian algorithm execution via posterior sampling." Advances in Neural Information Processing
Systems 37 (2024): 135186-135207. [4] Goldberg, Paul, Christopher Williams, and Christopher Bishop.
"Regression with input-dependent noise: A Gaussian process treatment." Advances in neural
information processing systems 10 (1997). [5] Van den Oever, J. M. P., et al. "Coil-globule
transition for regular, random, and specially designed copolymers: Monte Carlo simulation and
self-consistent field theory." Physical Review E 65.4 (2002): 041708. [6] Spaeth, Justin R., Ioannis
G. Kevrekidis, and Athanassios Z. Panagiotopoulos. "A comparison of implicit-and explicit-solvent
simulations of self-assembly in block copolymer and solute systems." The Journal of chemical physics
134.16 (2011). [7] Rasmussen, Maria H., et al. "Uncertain of uncertainties? A comparison of
uncertainty quantification metrics for chemical data sets." Journal of Cheminformatics 15.1 (2023):
121.